decimal numbers

Student Researchers/ Authors:

PAMN FAYE HAZEL M. VALINRON ANGELO A. DRONA

ASST. PROF. BEATRIZ P. RAYMUNDOModule Consultant

MR. FOR – IAN V. SANDOVALModule Adviser

Contents

Content Next

A premier university in CALABARZON, offering academic programs and related services designed to respond to the requirements of the Philippines and the global economy, particularly, Asian countries.

NextBack

The University shall primarily provide advanced education, professional, technological and vocational instruction in agriculture, fisheries, forestry, science, engineering, industrial technologies, teacher education, medicine, law, arts and sciences, information technology and other related fields. It shall also undertake research and extension services, and provide a progressive leadership in its areas of specialization.

NextBack

In pursuit of college mission/vision the college of education is committed to develop the full potential of the individuals and equip them with knowledge, skills and attitudes in teacher education allied fields effectively responds to the increasing demands, challenge and opportunities of changing time for global competitiveness.

NextBack

1. Produce graduates who can demonstrate and practice the professional and ethical requirements for the Bachelor of Elementary Education such as: 2. Acquire basic and major trainings in Bachelor of Elementary Education focusing on General Education and Pre - School Education. 3. Produce mentors who are knowledgeable and skilled in teaching pre - school learners and elementary grades and with desirable values and attitudes or efficiency and effectiveness. 4. Conduct research and development in teacher education and other related fields. 5. Extend services and other related activities for the advancement of community life.

ContentBack

Content Next

This Teacher’s Guide Module entitled “Learning to Solve Decimal Numbers (Modular Workbook for Grade VI)” is part of the requirements in Educational Technology 2 under the revised curriculum for Bachelor in Secondary Education based on CHED Memorandum Order (CMO)-30, Series of 2004. Educational Technology 2 is a three (3)-unit course designed to introduce both traditional and innovative technologies to facilitate and foster meaningful and effective learning where students are expected to demonstrate a sound understanding of the nature, application and production of the various types of educational technologies.

NextBack

The students are provided with guidance and assistance of selected faculty members of the university through the selection, production and utilization of appropriate technology tools in developing technology-based teacher support materials. Through the role and functions of computers especially the Internet, the student researchers and the advisers are able to design and develop various types of alternative delivery systems. These kind of activities offer a remarkable learning experience for the education students as future mentors especially in the preparation of instructional materials.

NextBack

The output of the group’s effort may serve as an educational research of the institution in providing effective and quality education. The lessons and evaluations presented in this module may also function as a supplementary reference for secondary teachers and students.

Back Next

FOR-IAN V. SANDOVAL Computer Instructor / Adviser Educational Technology 2

BEATRIZ P. RAYMUNDO Assistant Professor II /

Consultant

LYDIA R. CHAVEZ Dean College of Education

ContentBack

Content Next

This instructional modular workbook entitled “Learning to Solve Decimal Numbers (Modular Workbook for Grade VI)”, which geared toward the objective of making quality education available to all and offers you a very interesting and helpful friend in your journey to the world of decimal numbers.

Back Next

This modular workbook offers you many experiences in learning decimal numbers. This time, you will study how to read, write, and name decimal numbers and how to compare order and round off decimal numbers. Of course you will also express the equivalent fractions and decimals.

Back Next

You will also experience the four (4) fundamental operations (Addition, Subtraction, Multiplication and Division) dealing with decimal numbers. Lastly, you will also solve more difficult problems involving the four (4) fundamental operations using decimal numbers. Learning decimal content is much more skillful in drilling with the application of FUN WITH MATH which designed to achieve with outmost skill and convenience.

Back Next

The authors feel that you can benefit much from this modular workbook if you follow the direction carefully. Be mindful as you lead yourselves to challenge the situation and circumstances and as you faces in every living as well as for the near future. If you do these, you will realize that indeed this modular workbook can be a very interesting and helpful companion.

Back Content

NextContent

We would like to express our sincerest gratitude for the following whom in are ways or another help us making this modular workbook become possible:

To Prof. Corazon N. San Agustin, for her kindness and understanding to this modular workbook.

NextBack

To Mr. For – Ian V. Sandoval, our instructor and adviser in Educational Technology 2, for giving sufficient technical trainings, suggestions, constructive criticism and unending support in our every needs.

To Assistant Professor Beatriz P. Raymundo, our Module Consultant, for making her available most of the time for comments, suggestions and revision of the modular workbook.

NextBack

To Professor Lydia R. Chavez, our Dean, College of Education, for inspiring advises and encouragement.

To our classmates and friends for their never ending support.

NextBack

To our beloved families, for unconditional love, emotional, spiritual and financial support all the way to used and for the filling up our duties in our home.

And most importantly to Almighty God, for rendering abilities, wisdom, good health, strength, courage, source of enlightenment and inspiration to pursue doing this piece of material.

ContentBack

VMGO’s

FOREWORD

PREFACE

ACKNOWLEDGEMENT

TABLE OF CONTENTS

UNIT I Decimal NumbersLesson 1 What is Decimal?Lesson 2 Reading and Writing Decimal NumbersLesson 3 Reading and Writing Mixed Decimal NumbersLesson 4 Reading and Writing Decimal Numbers Used in Technical and Science WorkLesson 5 Place ValueLesson 6 Comparing Decimal NumbersLesson 7 Ordering Decimal NumbersLesson 8 How to Round Decimal Numbers?Lesson 9 The Self-Replicating Gene

UNIT II Equivalent Fractions and DecimalsLesson 10 Expressing Fractions to DecimalsLesson 11 Expressing Mixed Fractional Numbers to Mixed DecimalsLesson 12 Expressing Decimals to FractionsLesson 13 Expressing Mixed Decimals Numbers to Mixed Numbers (Fractions)

UNIT III Addition and Subtraction of Decimal Numbers

Lesson 14 Meaning of Addition and Subtraction of Decimal Numbers

Lesson 15 Addition and Subtraction of Decimal Numbers without RegroupingLesson 16 Addition and Subtraction of Decimal Numbers with RegroupingLesson 17 Adding and Subtracting Mixed DecimalsLesson 18 Estimating Sum and Difference of Whole Numbers and DecimalsLesson 19 Minuend with Two ZerosLesson 20 Problem Solving Involving Addition and Subtraction of Decimal Numbers

UNIT IV Multiplication of Decimals

Lesson 21 Meaning of Multiplication of Decimals

Lesson 22 Multiplying Decimals

Lesson 23 Multiplying Mixed Decimals by Whole Numbers

Lesson 24 Multiplication of Mixed Decimals by Whole Numbers

Lesson 25 Multiplying Decimals by 10, 100 and 1000

Lesson 26 Estimating Products of Decimal Numbers

Lesson 27 Problem Solving Involving Multiplication of Decimal Numbers

UNIT V Division of Decimal Numbers

Lesson 28 Meaning of Division of Decimals

Lesson 29 Dividing Decimals by Whole Numbers

Lesson 30 Dividing Mixed Decimals by Whole Numbers

Lesson 31 Dividing Whole Numbers by Decimals

Lesson 32 Dividing Whole Numbers by Mixed Decimals

Lesson 33 Dividing Decimals by Decimals

Lesson 34 Dividing Mixed Decimals by Mixed Decimals

CURRICULUM VITAE

REFERENCES

Content Next

OVERVIEW OF THE MODULAR WORKBOOK

In this modular workbook, you will understand the concept of the language of decimal numbers. This modular workbook, will help you to read, write, and name decimal numbers for a given models, standard, mixed and technical and science work form. It provides the knowledge about place value, with the aid of a place - value chart. It also provides information on how to compare and order decimal numbers and also how to round off decimal numbers. This module will provide you a more difficult work in mathematics. Exercises will help the learners evaluate themselves to understand decimal numbers.

Back Next

OBJECTIVES OF THE MODULAR WORKBOOK

After completing this modular workbook, you expected to:

1. Know the language of decimal numbers.2. Read, write, and name decimal numbers in different forms.3. Read and write decimal numbers with the aids of place - value chart.4. Compare and order decimal numbers.5. Rounding off decimal numbers by following its rule.

Back Next

Lesson 1 WHAT IS DECIMAL?

Lesson ObjectivesAfter accomplishing the lesson, the students are expected to:

1. Define decimals.2. Identify the terms in decimal numbers.3. Familiarize the language of decimal numbers.

Content Next

One important feature of our number system is the decimal. It involved many computational operations. It is very useful in the measurement of very thin sheets and in the computation involving in exact amount.

But what is decimal? Look at the following examples:

Back Next

• .3 = 3 .03 = 3 10 100

.003 = 3 .0003 = 3 1000 10000b. .5 = 5 .05 = 5

10 100.005 = 5 .0005 = 5 1000 10000

Back Next

From the example given above, a “decimal” may be defined as a fraction whose denominator is in the power of 10.

Back Next

Numbers in the power of 10 are 10, 100, 1000, 1000, etc. The dot before a digit in a decimal is called “decimal point” which is an indicator that the number is a decimal. The place on the position occupied by a digit at the right of the decimal point is called a “decimal place”.

Back Exercises

I. Give the meaning and explain the use of the following.

1. What are

decimals?

2. What is

decimal point?

3. What is

decimal place?

4. Give some

examples of

decimal numbers.

Back Next

1.Decimals ____________________________________________________________________________________

2. Decimal Point ____________________________________________________________________________________

3. Decimal Place ____________________________________________________________________________________

4. Examples

____________________________________________________________________________________

Back Next

II. Change the decimal numbers to fractional form.Example: 0.8 = 8

101. 0.9 =_______________2. 0.1 =_______________3. 0.04 =_______________4. 0.06 =_______________5. 0.09 =_______________6. 0.001 =_______________7. 0.009 =_______________8. 0.0071 =_______________9. 0.0009 =_______________10. 0.0003 =_______________

Back Next

11. 0.0004 =________________12. 0.0005 =________________13. 0.00008 =________________14. 0.00009 =________________15. 0.148 =________________16. 0.79 =________________17. 0.1459 =________________18. 0.6 =________________19. 0.01 =________________20. 0.051 =________________

Back Home

Lesson 2READING AND WRITING DECIMAL

NUMBERS

Lesson ObjectivesAfter accomplishing the lesson, you are expected to:

1. Read and write decimal numbers.2. Follow the rules in reading and writing decimal numbers.3. Use the place value chart in order to read and write decimal numbers.

Content Next

How to read and write decimals or decimal numbers? A decimal is read and write according to the number of decimal place it has.

Here are the rules in reading and writing decimal numbers.

Back Next

RULE I. A decimal of one decimal place is to be read and to be written as tenth.

.4 is read as “4 tenths” and is to be written as “four tenths”; 4/10.2 is read as “2 tenths” and is to be written as “two tenths”. 2/10

Back Next

RULE II. A decimal of two decimal places is to be read and to be written

as hundredth.

.35 is read as “35 hundredths” and is to be written as “thirty – five hundredths”; 35/100.43 is read as “43 hundredths” and is to be written as “forty – three hundredths”.43/100

Back Next

RULE III. A decimal of three decimal places is to be read and written as

thousandth.

.261 is read as “261 thousandths” and is to be written as “two hundred sixty – one thousandths”; 261/1000.578 is read as “578 thousandths” and is to be written as “five hundred seventy – eight thousandths”.578/1000

Back Next

RULE IV. A decimal of four decimal places is to be read and to be written as ten

thousandth.

.4917 is read as “4917 ten thousandths” and is to be written as “four thousand, nine hundred seventeen ten thousandths”; 4917/10,000.5087 is read as “5087 ten thousandths” and is to be written as “five thousand eighty - seven ten thousandths”.5078/10,000

Back Next

A decimal is read and written like an integer with the name of the order of the right most digits added.

tenths

hundredths

thousandths

ten thousandths

hundred thousandths

Millionths

ten millionths

hundred millionths

billionths

ten billionths

hundred billionths

trillionths

0 . 4 3 5 7 8 9 6 1 2 5 3 4 Back Next

Note: the names of the order of the

different decimal places.

QuadrillionthsPentillionthsHexillionthsHeptillionthsOctillionthsNonillionthsDecillionths

UndecillionthsDodecillionthsTridecillionths

…

Back Next

Examples: 0.4 Read as four tenths.

0.43 Read as forty-three hundredths.

0.435 Read as four hundred thirty-five thousandths.

0.4357 Read as four thousand, three hundred fifty-seven ten thousandths.

Back Next

0.43578 Read as forty-three thousand, five hundred seventy-eight hundred

thousandths.

0.435789 Read as four hundred thirty-five thousand, seven hundred eighty

nine millionths.

0.4357896 Read as four million, three hundred fifty-seven thousand, eight

hundred ninety-six ten millionths.

Back Next

0.43578961 Read as forty three million, five hundred seventy-eight thousand, nine hundred sixty-one hundred millionths.

0.435789612Read as four hundred thirty-five million, seven hundred eighty nine

thousand, six hundred twelve billionths.

0.4357896125 Read as four billion, three hundred fifty seven million, eight hundred ninety six

thousand, one hundred twenty five ten billionths. Back Next

0.43578961253 Read as forty-three billion, five hundred seventy eight million, nine

hundred sixty-one thousand, two hundred fifty three hundred billionths.

0.435789612534 Read as four hundred thirty-five billion, seven hundred eighty-nine

million, six hundred twelve thousand, five hundred thirty-four trillionths.

Back Exercises

I. Write each decimal numbers in words on the space provided.

1. 0.167213143__________________________________________________________________

2. 0.52541876_____________________________ ______________________________________3. 0.263411859____________________________

______________________________________4. 0.984562910____________________________ ______________________________________5. 0.439621512____________________________ _______________________________________

Back Next

II. Write the decimal number in standard form.

1. Nine tenths______________________________________________2. Four hundredths______________________________________________

3. Two thousand, two hundred and two hundred thousandths____________________________________________4. Four hundred seventy – six millionths________________________________________________

5. Forty thousand, one hundred forty – one millionths________________________________________________

Back Home

Lesson 3READING AND WRITING MIXED DECIMAL

NUMBERS

Lesson ObjectivesAt the end of the lesson, the students were expected to:

1. Read mixed decimal numbers.2. Follow the rules in reading and writing mixed decimal numbers.3. Write mixed decimal numbers.

Content Next

Look at the following examples:

a. 5.8 is read as “5 and 8 tenths” and is to be written as “five and eight tenths”

b. 26.38 is read as “26 and 38 hundredths” and is to be written as “twenty – six and thirty – eight hundredths”

c. 49.246 is read as “49 and 246 thousandths” and is to be written as “forty – nine and two hundred forty – six thousandths”

d. 348.578 is read as “348 and 578 thousandths” and is to be written as “three hundred forty – eight and five hundred seventy – eight thousandths”Back Next

It is seen that the following rule has been followed in the above examples.

RULE:

In reading a mixed decimal numbers, read the integral part as usual “and” in place of the decimal point, the decimal point is read as usual also.

Back Exercises

1.246.819_____________________________________________________________________________________

2.65.42387____________________________________________________________________________________

3.9023.145867_________________________________________________________________________________

4.87.5843_____________________________________________________________________________________

5.48.0089_____________________________________________________________________________________

I. Write the words of decimal number for each of the following:

Back Next

II. Write decimal numbers for each of the following sentences:

1. Sixteen and sixteen hundredths _____________________________________________

2.Two and one ten – thousandths _____________________________________________

3.Ten thousand four and fourteen ten – thousandths _____________________________________________

4. Ninety – nine billion and eight tenths _____________________________________________

5. Twelve hundred two and seven millionths _____________________________________________

Back Next

6. Ninety – nine and nine hundred nine thousand, nine millionths_________________________________7. Five billion and sixty – five hundredths ______________________________________________8. Three billion, six thousand and three thousand six millionths _____________________________________9. Seventy – one million, one hundred and fifty – five hundred thousandths ______________________________________________10. Two hundred two million, two thousand, two and two hundred two thousand two millionths ______________________________________________

Content Home

Lesson 4READING AND WRITING DECIMALS USED

INTECHNICAL AND SCIENCE WORK

Lesson ObjectivesAt the end of the lesson, the pupil should be able to:

1. Read and write decimals used in technical and science work.

2. Follow the rules in reading and writing decimals used in technical and science work.3. Know the simple way of reading and writing decimals that can be used in technical and science work.

Content Next

This method of reading decimals and mixed decimals is often used by people engaged in technical and science work.

But this can be used by lay people especially if the part of the number has many digits.Observe the following examples: Back Next

a. 5.8 is read as “5 point 8” and is to be written as “five point eight”

b. .9 is read as “point 9” and is to be written as “point nine”

c. 6.893 is read as “6 point 893” and is to be written as “six point eight nine three”

d. 348.09536 is read as “348 point 09536” and is to be written as “three four eight point zero nine five three six“

e. 8945.874205 is read as “8945 point 874205” and is to be written as “eight nine four five point eight seven four two zero five”

Back Next

The rule followed in the above examples is as follows:

To read decimals or mixed decimal numbers used in technical and science work or when the numbers of digits in the decimal is too many, just mention the values of the digits and separate the integral part by saying “point” instead of “and”.

RULE:

Back Exercises

1.0.009Read:_________________________________________

__Write:_________________________________________

__2. 45.78Read:_________________________________________

_Write:_________________________________________

_3. 3148Read:

___________________________________________Write:_________________________________________

__4. 3.456Read:_________________________________________

__Write:_________________________________________

_

I. Read and write the following in technical or science way.

Back Next

4. 3.456Read:______________________________________Write:______________________________________5. 47.629Read:

___________________________________________

Write:___________________________________________

6. 5.78456Read:

___________________________________________

Write:___________________________________________

7. 0.491Read:______________________________________

_____Write:______________________________________

____

Back Next

8. 28.652Read:__________________________________________Write:_________________________________________9. 4928.95Read:__________________________________________Write:_________________________________________9. 4928.95Read:__________________________________________Write:_________________________________________10. 376.732Read:__________________________________________Write:_________________________________________

Back Next

11. 841.50Read:__________________________________________Write:_________________________________________12. 3.62Read:__________________________________________Write:_________________________________________13. 0.03Read:__________________________________________Write:_________________________________________14. 97.5Read:__________________________________________Write:________________________________________15. 2.3148Read:_________________________________________Write:________________________________________

Back Next

II. Write the following using decimal numbers.

1. one seven point three ___________________________________________

2. point five four two nine ___________________________________________

3. one two point zero nine ___________________________________________

4. four three point one eight nine ___________________________________________

5. two four point seven three two __________________________________________

Back Next

6. three point seven six nine ______________________________________________7. two one seven point one five ____________________________________________8. point zero eight zero zero zero ___________________________________________9. nine point zero four zero ______________________________________________10. two point six seven two five ____________________________________________11. zero point nine eight nine ______________________________________________

Back Next

12. zero point five two six eight two nine ____________________________________________13. five six zero point four zero one eight ____________________________________________14. one point one nine one eight ____________________________________________15. eight point five four three ____________________________________________

Back Home

Lesson 5 PLACE VALUE

Lesson ObjectivesIn this lesson, the pupils are expected to:

1. Distinguish the relationship of place value in its place.2. Write common fractions in decimal forms.3. Give the place value for every digit.

Content Next

PLACE VALUE CHART

PlaceValueNames

MILLIONS

H TU H N OD UR S E AD N D S

T TE HN O U S A ND

S

THOUS ANDS

HUNDREDS

TENS

ONES

TENTHS

HUNDREDTHS

THOUS ANTHS

T T E H N O

U S A N T H S

H TU H N OD UR S E AD N T H S

MILLIONTHS

Numerals

1 9 4 6 3 4 1 . 1 3 4 5 8 7

× × × × × × × . × × × × × ×

106 105 104 103 102

101 1/10 1/101 1/102 1/103 1/104 1/105 1/106

Back Next

What relationship exists in the diagram? What does the 1 in the tenths place mean? What does the 3 in the hundreds place represent? How about the 3 in the hundredths place?

Back Next

Notice that:0.1 = 1 × 1/10 = 1/10 (one tenth)0.13 = 13 × 1/102 = 13/100 (thirteen

hundredths)0.134 = 134 × 1/103 = 134/1000 (one hundred

thirty – four thousandths) 0.1345 = 1345 × 1/104 = 1345/10000 (one

thousand three hundred forty – five ten thousandths)

0.13458 = 13458 × 1/105 = 13458/100000 (thirteen thousand four hundred fifty – eight

hundred thousandths)0.134587 = 134587 × 1/106 = 134587/1000000 (one

hundred thirty – four thousand five hundred eighty – seven millionths)Back Exercises

I. Complete the equivalent decimals to fractions.

Decimal Fraction

1. 0.23

2. 4.165

3. 0.937

4. 1.52

5. 0.041

6. 2.003

7. 0.1527

8. 16.775

9. 0.000658

10. 685.95 Back Next

II. Answer the following.

1. In 246.819, what number is in each of the following place value?Example: __6__a. ones _246_c. hundreds _46__b. tens__.8__d. tenths _.81__e. hundredths

__.819_f. thousandths2. In 65.42387, tell what number is in each of the following places._____a. tenths _____d. ten–thousandths _____b. hundredths _____e. hundred – thousandths_____c. thousandths _____f. ones

_____g. tensBack Next

3. In 9023.45867, tell what number is in each of the following places._____a. ones _____e. hundredths_____b. tens _____f. thousandths_____c. tenths _____g. thousands_____d. hundreds _____h. ten – thousandths

_____i. hundred–thousandths_____j. millionths

Back Home

Lesson 6COMPARING DECIMAL NUMBERS

Lesson ObjectivesAt the end of the lesson, the pupils are expected to:

1. Compare decimal numbers.2. Use fractional number to compare decimals.3. Know the sign in comparing decimal numbers.

Content Next

If there are two decimal numbers we can compare them. One number is either greater than (>), less than (<) or equal to (=) the other number.

Back Next

A decimal number is just a fractional number. Comparing 0.7 and 0.07 is clearer if we compared 7/10 to 7/100. The fraction 7/10 is equivalent to 70/100 which is clearly larger than 7/1000.

Back Next

Therefore, when decimals are compared start with tenths place and then hundredths place, etc. If one decimal has a higher number in the tenths place then it is larger than a decimal with fewer tenths. If the tenths are equal, compare the hundredths, then the thousandths, etc. Until one decimal is larger or there are no more places to compare. If each decimal place value is the same then the decimals are equal.

Back Exercises

I. Fill the frame with the correct sign (>) “less than”, (=) “equal to”, or (>) “greater than” between two given numbers.

Example:0.9 = 9/10 0.90 = 10/100

=

Back Next

b. 9.004 0.040 f. 51.6 51.59

c. 20.80533 20.06 g. 50.470 50.469

d. 0.070 0.07 h. 0.90 0.9

e. 0.540 0.054 i. 0.003 0.03

j. 0.8000 0.080

Back Home

Lesson 7ORDERING DECIMAL NUMBERS

Lesson ObjectivesAfter accomplishing the lesson, the pupils are

expected to:1.Order decimal numbers.2.Know the terms in arranging decimal

numbers.3.Understand how to arrange decimal

numbers.

Content Next

Numbers have an order or arrangement. The number two is between one and three. Three or more numbers can be placed in order. A number may come before the other numbers or it may come between them or after them.

Back Next

Examples: If we start with numbers 4.3 and 8.78, the number 5.2764 would come between them, the number 9.1 would come after them and the number 2 would come before them.(Descending- 9.1; 8.87; 5.2764; 4.3) 9.1> 8.87>5.2764>4.3

If we start with the numbers 4.3 and 4.78, the number 4.2764 would come before both of them; the number 4.5232 would come between them.(Ascending- 4.2764; 4.3; 4.5232; 4.78) 4.2764< 4.3<4.5232<4.78

Back Next

REMEMBER:The order may be

ascending (getting larger in value) or descending(becoming smaller in value).

Back Exercises

I. Write in order from ascending order and descending order by completing the table.

Ascending Order

Descending Order

1. 2.0342; 2.3042; 2.3104

Example:2.03422.30422.3104

2.31042.30422.0342

2. 5; 5.012; 5.1; .502

3. 0.6; 0.6065; 0.6059;0.6061

Back Next

5. 6.3942; 6.3924; 6.9342; 6.4269

6. 0.0990; 0.0099; 0.999; 0.90

7. 3.01; 3.001; 3.1; 3.001

8. 0.123; 0.112; 0.12; 0.121

9. 7.635; 7.628; 7.63; 7.625

4. 12.9; 12.09; 12.9100; 12.9150; 12

10. 4.349; 4.34; 4. 3600; 4.3560

Back Next

Arrange the given decimal numbers from the least to greatest and you will find a famous quotation by Shakespeare.

Back Next

Shakespeare(least)7.301All

8.043climb

7.8except

7.310ambitious

8.88or

7.84those

9.100of

7.911which

10.5mankind

7.33are

8.43up

8.513upward

7.352lawful

8.901the

9.003miseries

Back Next

All___ _______ ________ ________ ________ ________ 7.301 _______ ________ ________ ________ ________

_______ ________ ________ ________ ________ _______________ ________ ________ ________ ________ ________ _______ ________ ________

_______ ________ ________ . - Shakespeare II. Answer the following.

a. The list below is the memory recall time of 5 personal computers. Which model has the fastest memory recall?

Back Next

Model Recall Time

Sterling PC 0.0195 sec.

XQR 2000 0.01936 sec.

Redi-mate 0.02045 sec.

Vision 0.1897 sec.

Sal 970 0.019 sec.

Answer: ______________________________________________________________________________________

Back Next

b.Arrange the memory recall time of computers in number 1 in ascending order.

Answer: __________________________________________________________________________________

c. A carpenter uses different sizes of drill bits in boring holes. The sizes are in fractional form and their equivalent decimals. Arrange the decimal equivalent in descending order.

1/16 = 0.0625 ¼ = 0.251/8 = 0.125 5/6 = 0.3125

Back Next

Answer: ______________________________________________________________________________________

d.Which has the smallest decimal equivalent among the drill bits in item C?

Answer: ________________________________________

________________________________________

Back Next

e. Which has the greatest decimal equivalent the drill bits in item C?

Answer: ________________________________________________________________________________

Back Home

Lesson 8ROUNDING OFF DECIMALS

Lesson Objectives After accomplishing the lesson, the pupils are expected to:

1. Round decimals. 2. Tabulate data in the chart. 3. Show rules in rounding decimal numbers.

Content Next

To round decimal numbers means to drop off the digits to the right of the place-value indicated and replace them by zeros.

The accuracy of the place-value needed must be stated and it depends on the purpose for which rounding is done. We give rounded decimal numbers when we do not need the exact value or number. Instead, we are after an estimated value or measure that will serve our purpose. These are many instances in daily life when rounded numbers are what we need to use.

Back Next

How well do you remember in rounding whole numbers? Study the example below.

Round to the nearest4935 ten 4940

hundred 4900thousand 5000

Back Next

See how the following decimals are rounded.

Rounded to the nearest0.31659 tenths 0.3

hundredths 0.32thousandths 0.317ten thousandths 0.3166

Back Next

To round decimals, follow these rules:

1. Look at the digit immediately to the right of the digit in the rounding place.

2. All digits to the right of the place to which the number is rounded are dropped.

3. If the first of the digits to be dropped is 0,1,2,3 or 4, the last kept digit is not changed.

4. Increase the last kept digit by 1, when the first digit dropped is:

a. 6,7,8 or 9;orb. 5 followed by non-zero digit(s); orc. 5 (alone or followed by zero or zeros) and the

last kept digit is odd. Back Next

Example:

Round off 78.4651 to the nearest hundredths.

7 8 . 4 6 5 1 = 78.47

Dropping digit Decimal number to be rounded off

Examples: Round the following.

a. 5.767 to the nearest tenths = 5.8Since the digit to the right of 7 is 6.

Back Next

b. 65.499 to the nearest hundredths = 65.50Since the digit to the right of 9 is 9.

c. 896.4321 to the nearest thousandths= 896.432Since the digit to the right of 2 is 1.

d. 32.28 to the nearest tenths = 32.3Since the digit to the right of 2 is 8

e. 1000.756 to the nearest hundredths = 1000.80Since the digit to the right of 5 is 6

f. 56.58691 to the nearest thousandths = 56.5870Since the digit to the right of 6 is 9

Back Exercises

1. 29.8492 to the nearest:a. tenths ___________________b. ones ___________________c. hundredths ___________________d. thousandths ___________________e. tens ___________________

I. Round off the following decimal numbers.

Back Next

2. 3.097591 to the nearest: a. ones _______________________ b. tenths _______________________ c. hundredths _______________________ d. thousandths _______________________ e. ten-thousandths _______________________

3. 6.152292 to the nearest: a. ones ______________________ b. tenths ______________________ c. hundredths ______________________ d. thousandths ______________________ e. ten-thousandths ______________________

Back Next

4. 10.01856 to the nearest: a. ones ____________________ b. tenths ____________________ c. hundredths ____________________ d. thousandths ____________________ e. ten-thousandths ____________________

5. 123.831408 to the nearest: a. ones ____________________ b. tenths ____________________ c. hundredths ____________________ d. thousandths ____________________ e. ten-thousandths ____________________

Back Next

III. Select the best answer.

A. 0.4278 rounded to the nearest thousandthsa. 0.462b. 0.46c. 0.430d. 0.464

B. 0.0042 rounded to the nearest thousandthsa. 0.003b. 0.0031c. 0.004d. 0.04

Back Next

C. 0.6354 rounded to the nearest thousandths

a. 0.635b. 0.6c. 0.630d. 0.64D. 0.635`4 rounded to the nearest hundredthsa. 0.635b. 0.6c. 0.630d. 0.64

E. 0.6354 rounded to the nearest tenthsa. 0.635b. 0.6c. 0.630d. 0.64 Back Next

IV. Answer the following with TRUE or FALSE.

________________ 1. 0.32 rounded to the nearest tenths is 0.3.

________________ 2. 0.084 rounded to the nearest hundredths is 0.09.

________________3. 0.483 rounded to the nearest thousandths is 0.048.

________________4. 0.075 rounded to the nearest hundredths is 0.06.

________________5. 0.375 rounded to the nearest tenths is 0.4.

Back Next

V. Round each of the following by completing the tables. Number 1 serves as an example.

DecimalsRound to the nearest

Tenths Hundredths ThousandthsTen

Thousandths

Example:1. 0.89432

0.9 0.89 0.8940.8943

2. 5.09998

3. 2.96425

4. 5.2358

5. 5.39485

6. 0.86302

7. 28154

8. 42356

Back Next

9. 2.38425

10. 0.56893

11. 2.9625

12. 62.84213

13. 29.04347

14. 85.42998

15. 1539485

Back Next

I. Find the answer by rounding off to the nearest place value indicated. Draw a line to the correct rounded number. Each line will pass through a letter. Write the letter next to the rounded number.

ONES1.6 ● ● 1.63 __________5.38 ● ● 3.4 __________52.52 ● ● 2 __________TENTHS0.45 ● ● 3.433 __________3.421 ● ● 53 __________12.76 ● ● 0.35 __________88.55 ● ● 5 __________HUNDREDTHS0.345 ● ● 12.8 __________1.634 ● ● 0.044 __________13.479 ● ● 0.5 __________201.045 ● ● 11.68 __________11.677 ● ● 16.778 __________THOUSANDTHS0.0437 ● ● 88.6 __________3.4325 ● ● 105.312 __________16.7777 ● ● 13.48 __________23.40092 ● ● 23.401 __________105.31238 ● ● 201.05 __________

T

V

E

H

W

G

E

N

T

O

OL

H

M S

ET

What happened to the man who stole

the calendar?

Back Home

Lesson 9FACTS AND FIGURES

(The self-replicating Gene)

or centuries, generations of scientists in Numerica had been working relentlessly on what had been dubbed as The Genetic Enterprise. It was founded for the purpose of controlling a runaway gene that had beleaguered the Decimal citizens of Numerica for millennia: the repeating decimal gene.

Content Next

Their history revealed that it all began when a woman named Four (4) united with a man named Forty-Four (44) positioned as 4/44. Their first offspring, a fraction, came out all right, and they named her Three-Thirty-thirds (3/33). Such a beautiful fraction she was. But their second child came out with the first problematic replicating gene--- the boy looked different and came with a long tail: 0.0909090909…

Arbitrarily multiplying both sides of the equation by any power of ten does not change the value of the decimal nor does it destroy the balance of the equation. This is because of the Multiplication Property of Equality of the Real Numbers.

Back Next

That wasn’t the end of it. Every week, the boy’s tail added a new segment of 09, and it just never ended! It wasn’t so much the unusual appearance of the boy that worried every one, as the difficulty of naming him. Point-Zero-Nine-Zero-Nine-Zero-Nine- Zero -Nine-Zero-Nine, going on forever, was just too long a name!

There were many others in the community whose tails also continuously and regularly increased. Despite their peculiar form, though, those trouble with the repeating gene were never shunned, were treated equally with love, respect, and total acceptance. Still, the continually growing tail proved cumbersome for the Decimals, and they prayed to be changed to regular forms. Back Next

Arbitrarily multiplying both sides of the equation by any power of ten does not change the value of the decimal nor does it destroy the balance of the equation. This is because of the Multiplication Property of Equality of the Real Numbers.

Back Next

One fateful day, the newspaper headlines screamed: “The Genetic Enterprise: Finally Success!” All of Numerica was thrilled!

At the state conference the next day, every citizen was present, especially those with continuously growing tails.

“And now, I must ask for a volunteer,” said Doctor One Half (½), head scientist of the project, over the microphone.

Immediately, 0.33333…, friend of Point-Zero-Nine-Zero-Nine…, was up the stage.

“O-Point-Three-Three-Three…” One Half began, “do not be afraid. Go into that glass capsule to your left, for we must first clone you.”

Back Next

The crowd was aghast. One Half reassured every one immediately. “Do not worry, it is only temporary.”

When 0.33333… came out, his clone came out from the other capsule.

The doctor spoke again. “I will run you all through the process as we proceed. First, we shall designate the clone as Ex = 0.33333… “Now, 0.33333…, go back into the capsule---we will introduce a new gene into you. This gene is called Tenn (10), and this will change your appearance, so that we will temporarily call you Tennexx (10x). Do not be alarmed!” One Half added quickly at every one’s reaction.

Back Next

When 0.33333… stepped out of the capsule, he had become 3.33333…

10x = 10 x 0.3333… = 3.3333…10x = 3.3333…

The crowd was mesmerized. “Tennexx, go back into the capsule. Exx, go into the other capsule. This time, we shall remove the repeating gene from Tennexx---by taking out Exx!”10x – x = 3.3333… - 0.333… 9x = 3

Now, Tennex come out! Let us all see what you have become…” One Half said dramatically.

Back Next

The purpose of assigning a variable and multiplying both sides of the equation by 10 is to come up with whole numbers on both sides of the equation (on one side, with the variable, and on the other side of the equation, with just an integer). From this form we obtain a fraction equal to the original decimal. Note when finally making a subtraction, the digits in the decimal parts MUST be the same in order for the difference to be an integer.

Back Next

When Tennex came out, he had become 1/3.9x = 3x = 3/9 or 1/3

The applause was thunderous! 1/3 spoke on the microphone, tears of joy poring down his cheeks. “Once! Was Zero-point-Three- -Three-Three-Three-Three… now I am One-Third. Thank you, Doctor One Half!” he said.

Back Next

LESSON LEARNEDIn the article, we see that there is still

hope for repeating Decimal genes like Point O Nine O Nine O Nine and O Point Three-Three-Three. It is all about representing them using any variable, say, x, and taking away their never-ending tail.

Any repeating decimal represents a geometric series 0.3333… is 0.3 + 0.03+ 0.03+… The common ratio is 0.1, that is, the next term is obtained by multiplyingthe previous term by 0.1. The formula S= a1/1-rmay be used if (r) < 1.

S = a1/1-rS = 0.3/1-0.1 = 0.3/0.9 or 1/3

Back Next

PROBLEM BUSTER

A DIFFERENT GENE

May I have another Volunteer? Ah, yes.

Do you think we can change 0.833333...in exactly the same way as what we did to 0.33333…? Notice that in this case, the numeral 8 does not repeat. If we introduced 10 like we did to0.33333…, by multiplying 0.833333…by 10, 0.833333…will become 8.33333… Following the process, we have, 10x –x = 8.33333… - 0.833333… which is the same as 9x =7.5 where the

right side of the equation is not an integer! What are we to do?

Back Next

What we need to do is keep multiplying by 10, until we get two numbers whose digits or numerals in the decimal parts are exactly the same. Thus,

x = 0.833333 – 10x = 10 x 0.833333… -- 10x = 8.33333… -- 10x (10) = 8.33333… x 10 -- 100x = 83.3333…

With 0.33333…, it was enough to subtract x from 10x because the digits or numerals in their decimal parts are already exactly the same. Recall that when we subtracted them, we arrived at an integer on either side of the equation. This time, we subtract 10x from 100x, because the decimal parts of these two numbers have exactly the same digits or numerals. So that,100x – 10x =83.3333… - 8.3333…

-- 90x =75 -- x = 75/90 -- x = 5/6 -- 0.833333… 5/6 Therefore, 0.833333… is 5/6!

Back Exercises

1. 0.88888…as a fraction is:

b. 5/11 b. 7/8 c. 8/9 d. 10/11

2. 0.22222… in fraction form is:

a. 3/7 b. 2/11 c. 3/10 d. 2/9

I. Choose the correct answer:

Back Next

II. Change the following to fraction in simplest form.

3. 0.77777…

4. 0.9166666…

5. 0.9545454…

6. 0.891891891…

7. 0.153846153846153846…

8. 0.9692307692307692307… Back Home

Content Next

This modular workbook provides knowledge about different form or ways of computing fractions to decimals and decimals to fraction. This will help you to understand better what equivalent fraction and decimal is and you can use it in your everyday life.


Back Next

After completing this Unit, you are expected to:1. Transform fraction/mixed fractional numbers to decimals/mixed decimal.2. Change decimal/mixed decimal to fraction /mixed numbers (fractions).3. Follow the rules in expressing equivalent fractions and decimals.


Back Next

Lesson 10EXPRESSING FRACTIONS TO DECIMALS

Lesson ObjectivesAfter accomplishing the lesson, you are expected to:

1. Change fractions to decimals.2. Know the rules in changing fractions to decimals.3. Understand the equivalent fractions and decimals.

Content Next

Decimals are a type of fractional number.

Let us now study how to write fractions to decimal form.

Back Next

We will apply the principle of equality of fractions that is,if a/b =c/d then ad = bc.

Back Next

Example 1:

Write the fraction 2/5 as a tenth decimal. In this case we are interested to find the value of x such that 2/5=x/10.

Since the two fractions name the same rational number, we can proceed:

5x = 2(10) – applying equality principle5x = 20 x = 20/5 or 4

Hence, 2/5 = 4/10 = 0.4

Back Next

Example 2:

Write the fraction 3 as a hundredth decimal. We are 4interested to find the value of x such 3 that = x . 4 100 Applying the principle of equality we have

4x = 3(100)4x = 300 x = 75

Hence, ¾ = 75/100 = 0.75

Back Next

On the other hand, fractions can also be expressed as a decimal without using the equality principle. Instead we have to think of a fraction as a quotient of two integers that is a/b=a = a b.

Example 3:

Express 2/5 as a decimal.

Expressing 2/5 as quotient of 2 and 5 we have 2/5 = 0.4

Back Next

RULE

To change a fraction to decimal, divide the numerator by the denominator up to the desired number of decimal places.

Back Exercises

I. Give the meaning and explain the use of the following

1. How to change

fractions to

decimal?

2. What are the rules in changing fractions to decimals?

3. What is decimal?

4. Give some

examples of

fractions to decimals.

Back Next

1. Change fractions to decimal __________________________________________

2. Rules in changing fractions to decimals __________________________________________

3. Decimal __________________________________________

4. Examples of fractions to decimals __________________________________________

Back Next

II. Change the following fractions to decimals. Limit the number to tree decimal places.

1. 2/3 =_____________2. 2. ¾ =___________3. 6/7 =_____________4. 8/9 =_____________5. 2/15 =_____________-6. 1/9 =_____________7. 5/6 =_____________9. 4/5 =_____________

10. 3/16 =_____________

Back Next

11. 13/14 =__________12. ½ =__________ 13. 3/8 =__________ 14. 1/8 =__________ 15. 3/7 =__________ 16. 6/10 =__________ 17. 25/100 =__________18. 3/5 =__________19. 5/8 =__________ 20. 2/3 =__________

Back Next

It was very fortunate that Sophie Germain, a woman mathematician was born at a time when people looked down on women. In 1776, women then were not allowed to study formal, higher level mathematics. Thus, this persistent woman reads books of famous mathematicians and studied on her own. Aware of her situation, she shared her theorems and mathematical formulae to other mathematicians and teachers through correspondence using a pseudonym.

Back Next

Can you guess the pseudonym that she used?Yes, you can. Simply follow the instruction.

Back Next

Select the right answer to the equation below. Write the letter of the correct answer on the respective number decode pseudonym that she used. You may use the letter twice.

______ ______ ______ ______ (1) (2) (3) (4)

______ ______ ______ ______ (5) (6) (7) (8)

______ ______ ______ (9) (10) (11)

______ ______ ______ ______ (12) (13) (14) (15)

Back Next

Answers:A = 0.25 F = 0.65 K = 0.512 P = 0.27B = 0.15 G = 0.28 L = 0.125 Q = 0.006C = 0.6 H = 0.77 M = 0.333… R = 0.72D = 0.54 I = 0.24 N = 0.40 S = 0.6E = 0.76 J = 0.532O = 0.75 T = 0.4113

U = 0.325

Back Home

Lesson 11EXPRESSING MIZED FRACTIONAL NUMBERS TO MIXED DECIMALS

Lesson ObjectivesAfter accomplishing this lesson, you are expected to:

1. Express mixed fractional numbers to mixed decimals.2. Know the rules in expressing mixed fractional

numbers to mixed decimals.3. Interpret the mixed fractional numbers to mixed

decimals.

NextContent

How can we change mixed fractional numbers to mixed decimals?See the following examples.

4 1/2 = 4.5 c. 21 1/8 = 21.12514 3/8 = 14.375 d. 32 3/7 = 32.4285

Back Next

From the examples given above, it can be seen that the rule in changing a mixed fractional number to mixed decimal is:

Back Next

RULE

To change a mixed fractional number to a mixed decimal, change the fraction to decimal up to the number of decimal places desired and then annex it to the integral part.

Back Exercises

I. Change the following mixed fractional numbers to mixed decimals. Limit the number to three decimal places.

1. 4 2/5 = _____________________

2. 2. 3 4/5 = ______________________

3. 7 3/16 = ______________________

4. 10 13/14 = ______________________

5. 12 9/17 = ______________________

6. 21 14/19 = ______________________

7. 32 21/41 = ______________________

Back Next

8. 2 ¼ = _______________9. 3 5/7 = _______________ 10. 4 ½ = _______________11. 8 ¼ = _______________ 12. 2 1/3 = _______________13. 5 4/6 = _______________14. 10 4/5 = _______________15. 3 ¼ = _______________16. 10 3/7 = _______________ 17.10 11/20 = _______________18. 8 3/10 = _______________19. 6 15/16 = _______________20. 8 1/10 =_______________

Back Next

II. Copy the correct mixed decimal to mixed fractional numbers.

1. 1 3/10 3. 31 503/100a. 1.03 a. 31.0503b. 1.30 b. 31.035c. 1.013 c. 31.00503d 1.13 d. 31.5030

2. 8 420/1000 4. 8 143/1000a. 8.0420 a. 8.1430b. 8.240 b. 8.0143c. 8.420 c. 8.1043d. 8.0042 d. 8.00143

Back Next

5. 9 6/100a. 9.16b. 9.600c. 9.006d. 9.06

Back Home

Lesson 12EXPRESSING DECIMALS TO FRACTIONS

Lesson ObjectivesAt the end of the lesson, the students are expected to:

1. Change the decimals to fractions.2. Follow the rule in expressing decimals to fractions.3. Understand the equivalent decimals and fractions.

NextContent

As what we have learned earlier, decimals are common fractions written in different way.

Back Next

There are certain instances when it becomes necessary to change decimal into fraction. Hence, it is necessary to acquire skill in changing a decimal to faction.

Now we will study how to write decimals in fractions.

Back Next

Example 1: Write 0.5 in a faction form.5 or 1 10 2

0.5 = 5(1/10) Example 2: Write 0.72 in a fraction form.

0.72 = 7(1/10) + 2(1/100)1825

= 72/100 or 1825

Back Next

On the other hand, a simple way of expressing decimal to factions is possible without writing the numeral in expanded form. What we need is only to determine the place value of the last digit as we read if from left to right.

Back Next

Example 1: Write 0.5 in a faction form.

Notice that the digit 5 is in the tenth place, we can write immediately:

0.5 = or 12

__5__1000

Back Next

The digit 2 is in the thousandths place so we write:

0.072 = 72/1000 = 9/125

Back Next

Some Common Equivalent Decimals and

Factions0and 1/10

0and 2/10 or 1/51.5 and 1 ½ or 1 5/10 or 1

½0.25 and 25/100 or ¼0.50 and 50/100 or ½0.75 and 75/100 or ¾

Back Next

Identifying Equivalent Decimals and Fractions

Decimals are a type of fractional number. The decimal 0.5 represents the fraction 5/10. The decimal 0.25 represents the

fraction 25/100. Decimal fractions always have a denominator based on a power of

10.We know that 5/10 is equivalent to 1/2 since 1/2 times 5/5 is 5/10. Therefore, the decimal 0.5 is equivalent to 1/2 or 2/4, etc.

Back Next

It can be seen from the examples above the rule in changing a decimal to fraction is as follows:

Back Next

RULE

To change a decimal number to a fraction, discard the decimal point and the zeros at the left of the left-most non-zero digit and write the remaining digits over the indicated denominator and reduce the resulting fraction to its lowest terms. (The number of zeros in the denominator is equal to the number of decimal places in the decimal number.

Back Exercises

Change the following decimals to factional form and simplify them.

1. 0.4 = ________________2. 0.007 = ________________3. 0.603 = ________________4. 0896 = ________________5. 056 = ________________6. 0.06 = ________________7. 0.125 = ________________8. 0.5 = ________________9. 0.42857 = ________________10. 0.375 = ________________

Back Next

11. 0.54 = ________________12. 0.14 = ________________13. 0.8187 = ________________14. 0.956 = ________________15. 0.3567 = ________________16. 0.578 =_________________17. 0.34878 =_________________18. 0.47891 =_________________19. 0.12489 =_________________10. 0.14789 =_________________

Back Next

How can you make a tall man short?

To find the answer, change the following decimal number to lowest factional form. Each time an answer is given in the code, write the letter for that exercise.

Back Next

1. 0.6 = A 6. 0.24 = _______ O 2. 0.5 = _______B 7. 0.125 = _______ H 3. 0.7 = _______N 8. 0.55 = _______ L 4. 0.4 = _______I 9. 0.3 = _______W 5. 0.75 = _______ O 10. 0.048 = _______R

11. 0.25 = ______O12. 0.75 = _____ L13. 0.2 = _____ E 14. 0.225 =______O 15. 0.24 = _____Y16. 0.8 = _____S17. 0.5688=______R

Back Next

_____ _____ _____ ______ ______ _____ ½ 6/25 6/125 711/1250 225/ 1000 3/10

__A___ ______ ______ 3/5 ¾ 11/20

_____ ______ ______ 1/8 4/10 12/15

_____ _____ _____ _____ _______ 8/32 12/16 14/20 18/90 36/150

Back Home

Lesson 13EXPRESSING MIXED DECIMAL NUMBERS TO

MIXED FRACTIONAL NUMBERS

Lesson Objectives At the end of the lesson, the pupils should be able to

1. Express mixed decimal numbers to mixed fractional numbers.2. Follow the rules in expressing mixed decimal

numbers to mixed fractions. 3. Identify mixed decimals to mixed fractions.

NextContent

How can we change mixed decimals to mixed fractions? Study the following examples:

Back Next

a. 5.03 = 5 3/100b. b. 6.2 = 6 2/10 = 6 1/5a. 24.75 = 24 75/100 = 24 ¾d. 37.248 = 37 248/1000 = 37

31/125The rule applied to the above example is:

RULE

To change a mixed decimal number to a mixed fractional number, do not change the integral part, change the decimal part to a fraction according to the rule, and write the result as a mixed fractional number.

Back Exercises

Change the following mixed decimals to mixed fractional numbers. (First is an example.)

1. 3.06 = 3 6/10 6. 67.7362 = ___________2. 5.72 = ________ 7. 62.72 = ___________3. 11.302 = ________ 8. 71.4684 = ___________4. 10.642 = ________ 9. 92.5896 = __________5. 51.136 = ________ 10. 4.789 = __________

Back Next

II. Identify the following by writing D if it is mixed decimals and F if it is mixed fractional numbers.

_____1. 1 217/100 _____ 11. 14.3245_____ 2. 1.0124 _____ 12. 18 18/24_____ 3. 1.4568 _____ 13. 9.28_____ 4. 32 8/18 _____ 14. 1.0406_____ 5. 2.510 _____ 15. 4 235/1000_____ 6. 10.01 _____ 16. 450 11 /111_____ 7. 39 45/100 _____ 17. 1.5345_____ 8. 45 105/265 _____ 18. 143.445254_____ 9. 101 81/411 _____ 19. 12 34/91_____ 10. 1.01123 _____ 20. 653 185/1124

Back Home

Content Next

OVERVIEW OF THE MODULAR WORKBOOKThis modular workbook provides you greater understanding in all aspects of addition and subtraction of decimal numbers. It enables you to perform the operation correctly and critically. It includes all the needed information about the addition and subtraction of decimal numbers, its terminologists to remember, how to add and how to subtract decimals with or without regrouping, how to estimate sum and differences, and subtracting decimal numbers involving zeros in minuends. This modular work will help you to enhance your minds and ability in answering problems deeper understanding and analysis regarding all aspects of adding and subtracting decimal numbers.

Back Next


After completing this Unit, you are expected to:1. Familiarize the language in addition and subtraction.2. Learn how to add and subtract decimal numbers with

or without regrouping.3. Know how to check the answers.4. Estimate the sum and differences and how it is done.5. Know how to subtract decimal numbers with zeros in

the minuend.6. Develop speed in adding and subtracting decimal numbers.7. Analyze problems critically.

Back Next

Lesson 14MEANING OF ADDITION AND SUBTRACTION OF

DECIMAL NUMBERS

Lesson Objectives:After accomplishing this lesson, you are expected

to:1. Define addition and Subtraction.

2. Identify the parts of addition and subtraction. 3. Familiarize the language in addition and subtraction.

NextContent

Addition is the process of combining together two or more decimal numbers. It is putting together two groups or sets of thing or people.

Back Next

Example: 0.5 + 0.3 = 0.8

Addends Sum or Total

Addends are the decimal numbers that are added. Sum is the answer in addition. The symbol used for addition is the plus sign (+).

Back Next

The process of taking one number or quantity from another is called Subtraction. It is undoing process or inverse operation of addition. It is an operation of taking away a part of a set or group of things or people.

Note: Decimal points is arrange in one column like in addition of decimals.

Back Next

Example: 14. 345 Minuend

- 3.120 Subtrahend11.232 Difference

Minuend is in the top place and the bigger number in subtraction. The number subtracted from the minuend is called subtrahend. It is the smaller number in subtraction. The subtrahend is subtracted or taken from the minuend to find the difference. Difference is the answer in subtraction. The symbol used for subtraction is the minus sign (-).

Back Exercises


1. What is addition?

2. What is subtraction?

3. What are the parts of addition?

4. What are the parts of subtraction?

Back Next

1. Addition ______________________________________________2 Subtraction ______________________________________________3. Parts of addition ______________________________________________4. Parts of subtraction______________________________________________

Back Next

II. Identify the following decimal numbers whether it is addends, sum, minuend, subtrahend or difference. Put an if addends, if sum, if minuend, if subtrahend and if difference.

1. 0.9 _______ + 0.8 _______

1.7 _______

2. 2.24 _______ + 2.38 _______ 4.62 _______

3. 12.85 _______ - 0. 87 _______ 11.98 _______

4. 7.602 _______ - 2.664 _______ 4.938 _______

Back Next

5. 0.312 _______ + 0.050 _______ 0.362 _______

6. 6.781 _______ - 1.89 _______

8.676 _______

7. 0.215 _______ + 0.001 _______ 0.216 _______

8. 0.156 _______ + 1.811 _______ 1.967 _______

9. 0.113 _______ + 0.009 _______ 0.122 _______

10. 0.689 _______ - 1.510 _______ 2.199 _______

Back Next

III. Answer the following by completing the letter in each box which indicate the parts of addition and subtraction of decimals.

1. It is the numbers that are added.

2. The answer in addition.

3. It is the process of combining together two or more numbers.

Back Next

4. Sign used for addition.

5. It is undoing process or inverse operation of addition.

6. Sign used for subtraction.

7. It is the answer in subtraction.

Back Next

8. It is in the top place and the bigger number in subtraction.

9. It is the smaller number in subtraction.

10. Subtraction is an operation of _________ a part of a set or group of things or people.

Back Home

Lesson 15ADDITION AND SUBTRACTION OF DECIMAL

NUMBERS WITHOUT REGROUPING

Lesson Objectives: After finishing the lesson, the students are expected to:

1. Know how to add and subtract decimal numbers without regrouping.2. Develop speed in adding and subtracting

decimal number.3. Follow the steps in adding and subtracting decimal numbers.

NextContent

Add the following decimals: 28. 143 and 11.721.

If you added them this way, you are

right.

28. 143 + 11. 721

39. 864

Let us add the decimals by following these steps.

Back Next

STEP 1 STEP 2

Add the thousandths place

3+ 1 = 4 28. 143 + 11. 721 4

Add the hundredths place

4 + 2 = 6 28. 143 + 11. 721

64

Back Next

STEP 3

Add the tenths place

7 + 1 = 8 28. 143 + 11. 721 864

STEP 4

Add the following up to the ones.

8 + 1 = 9 28. 143 + 11. 721 9. 864

Back Next

STEP 5

Add the following up to the tens.

2 + 1 = 3 28. 143 + 11. 721 39. 864

Back Next

Now subtract 39. 864 to 11. 721.

39. 864 minuend - 11. 721 subtrahend 28. 143 difference

Back Next

2 Ways of Checking the Answer

1. minuend – difference = subtrahend39. 864 minuend

- 28. 143 difference11. 721 subtrahend

2. difference + subtrahend = minuend28. 143 difference

+11. 721 subtrahend39. 864 minuend

Back Next

If you subtract the difference from minuend and the answer is subtrahend the answer is correct. Also, adding the difference and subtrahend will the result to the minuend: it is also correct.

Back Next

As a procedure for adding or subtracting decimal numbers, we have the following:

2. Write the decimal numbers with the decimal points falling in one column.2. Add or subtract as if they were whole numbers.3. Place the decimal point of the result in the same column as the other numbers.

Back Exercises

Add and subtract as fast as you can.

Back Next

Back Next

Add and subtract the following to find the mystery words and write the letter of each answer in the code below.

This appears twice in the Bible (In Matthew VI and Luke II).

Back Next

1. 85. 367 2. 645. 987

+ 16. 252 - 314.625 R P

1. 74. 617

+ 21. 721 O

1. 2,936. 475

- 1,421.061 S

1. 51. 437 6. 658.325

+ 18. 042 - 137.210 Y L

1. 895. 399 8. 945. 374

- 471. 287 + 33. 161 A R

9. 32. 511

+ 11. 621 R

Back Next

1. 7,649.251 11. 66.341

- 36.030 + 12.412 E D

_______

521. 115

_______

96. 338

_______

44. 132

_______

78. 753

_______

1515. 414

_______

331.362

_______

101.619

_______

424.112

_______

69.478

_______

7613.221

_______

978.535 Back Home

Lesson 16ADDITION AND SUBTRACTION OF DECIMAL

NUMBERS WITH REGROUPING

Lesson Objectives: After accomplishing the lesson, the students are expected to be able to:

1. Define regrouping.2. Learn how to add and subtract decimal

numbers with regrouping.3. Answer and perform the operation critically and correctly.

NextContent

In the past lesson, you’ve learned how to add and subtract decimal numbers without regrouping. The only difference in this lesson is that it involves regrouping and borrowing. It is easy to add and subtract decimal numbers without regrouping.

Back Next

Regrouping is a process of putting numbers in their proper place values in our number system to make it easier to add and subtract.

Here’s how to add decimal numbers with regrouping.

Back Next

Example 1: 0. 7

+ 0. 5

Ones . Tenths

1 0+ 0

.

.75

1 . 2

0.7 + 0.5 = 1210 tenths is regroup as

(1) one.

Back Next

Example 2: 0.09

+ 0.06

O . T H

00

.

.00

96

0 . 1 5

0.9 + 0.6 = 15 hundredths10 hundredths is 1 regrouped as 1 tenth.

Back Next

Example 3: 0.065

+ 0.008

O T H Th

0.+ 0.

00

60

58

0. 0 7 3

5 + 8 = 13 thousandths 10 thousandths is regrouped as 1

hundredth.

Back Next

Subtract decimals like you were subtracting whole numbers.

Back Next

Example 4: 0. 93- 0. 28

ones tenths hundredths

0. 9 3

0. 8 - 1 10

0. 8 3

0. 8 13

9 is renamed as 8 + 1 tenths. 1

tenth is regrouped as

10 hundredths.

0. 9 3 - 0. 2 8 0. 6 5

Check: 0. 28+ 0. 65

0. 93

Back Next

Example 5: 0.730

- 0.518

2 10

0.730 - 0.518 0.212

ones tenths hundredths thousandths

0. 7 3 0

0. 7 2+1 10

0. 7 - 5

2 - 1

0 - 80.

0. 2 1 2

Check: 0.518

+ 0.212 0.730

Back Exercises

I. Answer the following.A. Add the following and check your answer

on the Check Box below.

• 0.6 2. 0.07 + 0.8 + 0.49

• 0.36 4. 0.746 + 0.56 + 0.235

Back Next

B. Subtract the following and check your answer on the Check Box below.

1. 0.62 2. 0.762 - 0.58 - 0.325

3. 0.850 4. 0.452 - 0.328 - 0.235

Back Next

II. Write on the blank (+) or (-) sign to make the statement TRUE.

1. 4.793 ___ 3.549 = 8.3422. 72.685 ___ 45.726 ___ 13.493 = 104.9183. 1.45 ___ 0.50 ___ 3.95 ___ 5.66 = 11.564. 36.58 ___ 35.789 ___ 354.587 = 426.9565. 6.57 ___ 0.456 ___ 236.5 ___ 5 ___ 213.66 = 34.8666. 28. 625 ___ 25.361 = 3.2647. 57.54 ___ 0.25 = 57.298. 86.3 ___ 0.456 ___ 32.58 = 118.4249. 39 ___ 5.65 = 33.3510. 53.654 ___ 5.236 = 48.418

Back Home

Lesson 17 ADDING AND SUBTRACTING MIXED

DECIMALS

Lesson Objectives: After finishing the lesson, the students are expected to:1. Understand and know how to add and subtract

mixed decimal numbers. 2. Follow the rules in adding and subtracting mixed decimal numbers. 3. Perform the operation correctly.

NextContent

Ramon traveled from his house to school, a distance of 1.39845 kilometers. After class, he traveled to his friend’s house 1.85672 kilometer away in another direction. From his friends to his own house, he rode another 1.23714 km over. How many kilometers did Ramon traveled?

3 . T H Th T Th H Th

1 1 1+1

.

.

.

1382

2953

1867

1471

524

4 . 4 9 2 3 1

Back Next

He traveled a total of 4.49231 km. The following day, he traveled to the school and the seashore for a total of 6.35021 km. How many more kilometers did Ramon traveled than previous day?

O T H Th T Th H Th5

6-4

.

.

12

34

14

59

9

02

12

23

11

1 . 8 5 7 9 0

Back Next

Ramon traveled 1.85790 kilometers more.

In adding and subtracting mixed decimals, remember to align the decimal points and regroup when necessary.

Back Exercises

I. Add or subtract these mixed decimals.

1. 4.59804 2. 3.14879 3. 5.11788

7.81657 5.37896 1.93523

+ 1.30493 + 2.95321 + 3.40175

4. 2.42814 5. 7.20453 6. 9.57128 - 1.19905 - 4.35712 - 2.89340

Back Next

II. Rewrite with the correct alignment of decimal points on the space provided. Find the sum and difference.

1. 4.930000 4. 18.17932 57.5244 + 2.41256

+ 637.3672

5. 73.59203 5. 12.48004 + 154.38762 - 9.86327

3. 142.567021 6. 42.20239

- 85.791503 - 2.34876

Back Next

4. 18.16532 9. 5.306321 - 4.01985 002.7509

+ 4.952005

5. 951.235 7.18902 10. 103.93284 + 00.3 + 43.76895

Back Home

Lesson 18ESTIMATING SUM AND DIFFERENCE OF

WHOLE NUMBERS AND DECIMALSLesson Objectives:

After understanding the lesson, you must be able to:

1. Define estimation. 2. Know the two methods in making estimates.

3. Learn how to estimate sum and difference and how it is done.

NextContent

Estimation is a way of answering a problem which does not require an exact answer. An estimate is all that is needed when an exact value is not possible. Estimation is easy to use and or to compute. Rounding is one way of making estimation. Each decimal number is rounding to some place value, usually to the greatest value and the necessary operation is performance on the rounded decimal numbers.

Back Next

Two methods are used in making estimation, the rounding off the desired

digit one and finding the sum of the first digit only. We have learned how to round decimal numbers in this section, first only the front digits are used. If an improved or refined estimate is desired,

the next digits are used.

Back Next

When large decimal numbers are involved, it is wise to estimate before computing the exact and user is expected to be about or close to the estimate.

Method 1: Sum of the First Digit only

Estimate in Addition3.455 + 2.672 + 5.135

Back Next

Rounded off to the nearest ones

3.455 3.0002.672 3.000

+ 5.134 + 5.000 11.000

Rounded off to the nearest tenths

3.455 0.500 2.672 0.700 + 5.134 + 0.100

1.300

to be added the first estimate if desired or required.

Back Next

Thus the sum 3.455 + 2.672 + 5.134 can be roughly estimated by 11.000. If a better estimate is required or desired, then add 1.300 to get 11.300.

Back Next

Estimate 5.472147 – 2.976543

Rounded to the nearest onesActual Subtraction

5.472147 5.000000 5.472147 - 2.976543 - 3.000000 - 2.976543

2.000000 2.495604

Back Next

Method 2: Rounding Method

a. Estimate the sum by rounding method in place of whole numbers.Example:6.567 7.000

5.482 5.000 + 4.619 +5.000

17.000

Back Next

b. Estimate the difference by rounding method.

Example: 14.525 15.000 - 11.018 - 11.000 4.000

By the rounding method, the first example is estimated by 17.000 and the second one by 4.000. The actual value of the sum of example no.1 is 16.668 and the difference of example no. 2 is 3.507 respectively. Both methods give a reasonable estimate.

Back Next

Remember:In estimating the sums, first round each addend

to its greatest place value position. Then add. If the estimate is close to the exact sum, it is a good estimate. Estimating helps you expect the exact answer to be about a little less or a little more than the estimate.

However, in estimating difference, first round the decimal number to the nearest place value asked for. Then subtract the rounded decimal numbers. Check the result by actual subtraction.

Back Exercises

I. Estimates the sum and difference to the greatest place value. Check how close the estimated sum (E.S.) / estimated difference (E.D.) by getting the actual sum (A.S.) and actual difference (A.D.).

A. Actual Sum/ Estimated Sum1. 3.417 3.000 2. 36.243 36.000

2.719 3.000 29.641 30.000 + 1.829 + 2.00 + 110.278 + 110.000 A.S. E.S. A.S. E.S.

Back Next

3. 648.937 649.000 4. 871.055 871.000214.562 215.000 276.386 276.000

+ 450.211 + 450.000 + 107.891 + 108.000 A.S. E.S. A.S. E.S.

5. 374.738 375.000 6. 342.165 342.000469.345 469.000 178.627 179.000

+ 213.543 + 213.500 + 748.715 + 749.000 A.S. E.S. A.S. E.S.

Back Next

B. Actual Difference/ Estimated Difference7. 14.255 14.000 8. 28.267 28.000 - 11.812 - 12.000 - 16.380 - 16.000 A.D. E.D A.D. E.D.

9. 345.678 346.000 10. 92.365 92.000 - 212.792 - 213.000 - 75.647 - 76.000 A.D. E.D. A.D. E.D.

11. 62.495 62.000 12. 9.2875 9.0000 - 17.928 - 18.000 - 6.8340 - 7.0000A.D. E.D. A.D. E.D.

Back Next

Match a given decimals with the correct estimated sum / difference to the greatest place – value.

The shortest verse in the Bible consists of two words.

Back Next

To find out, connect each decimals with he correct estimated sum / difference to the greatest place – value. Write the letter that corresponds to the correct answer below it.

1. 36.5+18.91+55.41 U. 939.002. 639.27-422.30 S. 216.003. 48.21+168.2 P. 2.00004. 285.15+27.35+627.30 E. 146.0005. 8.941-8.149 W. 28.106. 18.95+9.25 J. 111.007. 129.235+16.41 T. 537.008. 9.2875-6.834 S. 1.0009. 989.15-451.85 E. 217.00

Back Next

_____ ______ ______ ______ ______ 1 2 3 4 5

_____ ______ ______ ______ 6 7 8 9

Back Home

Lesson 19MINUEND WITH TWO ZEROS


1. Know how to subtract decimal numbers with two zeros in minuend.

2. Follow the steps in subtraction of numbers involving zeros.

3. Check the answer and perform the operation correctly.

NextContent

You always have to regroup in subtracting decimal numbers with zeros. You will have to

regroup from one place to the next until all successive zeros

are renamed and ready for subtraction.

Back Next

STEPS IN SUBTRACTION OF DECIMAL NUMBER INVOLVING ZEROS

1. Arrange the digits in column.2. Regroup from one place to the next until all successive zeros are renamed.3. Subtract to find the answer.4. Check the answer.

Back Next

Example:

0.8005

- 0.6372

O T H Th T Th

0. 8 0 0 5

0. 7+1 10

9+1 10

0. 7 9 10 5

0. 6 3 7 2

0. 1 6 3 3

Back Next

Rewriting: 0.8005- 0.6372

Difference 0.1633

Checking:0.6372

+ 0.16330.8005

Back Exercises

I. Subtract the following and check.1. 16.004 - 2.875

2. 28.009 - 11.226

3. 18.003 - 5.739

4. 11.001 - 9.291

5. 4.0075 - 2.9876

1. 0.10013 - 0.00011

7. 2.00143 - 0.88043

7. 0.7008 - 0.5383

9. 0.8008 - 0.0880

10. 0.14003 - 0.03333 Back Next

Answer the following to find the mystery words.

In what type of ball can you carry?

To find the answer, draw a line connecting each decimal number with its equal difference. The lines pass through a box with a letter on it. Write what is in the box on the blank next to the answer.

Back Next

Back Home

Lesson 20PROBLEM SOLVING INVOLVING ADDITION AND

SUBTRACTION OF DECIMALS


1. Follow the step of solving problem.2. Analyze the problem critically.3. Develop interest in solving word problem.

NextContent

Kristina saves her extra money to buy a pair of shoes for Christmas. Last week she saved Php. 82.60; two weeks ago, she saved Php. 100.05. This week she saved Php. 92.60. How much did she save in three weeks?

Steps in Solving a Problem

1. Analyze the problem

2. What is asked? Total amount did Kristina save in three weeks.3. What are the given facts? Php. 82.60, Php. 100.05, and Php. 96.10

Know

Back Next

3. What is the word clue? Save.

What operation will you use? We use addition.4. What is the number sentence? Php. 82.60 + Php. 100.05 + Php. 96.10 = N5. What is the solution? Php. 82.60

Php. 100.05 + Php. 96.10

Php. 278.75

Solve

Decide

Show

Back Next

Check

6. How do you check your answer?We add downward.Php. 82.60Php. 100.05

+ Php. 96.10 Php. 278.75

“Kristina saves Php. 278.75 in three weeks.”

It is easy to solve word

problems by simply

following the steps in

solving word problem. Back Exercises

I. Read the problem below and analyze it.

A. Baranggay Maligaya is 28.5 km from the town proper. In going there Angelo traveled 12.75 km by jeep, 8.5 km by tricycle and the rest by hiking. How many km did Angelo hike?

1. What is asked?_____________________________________________

_____________________________________________

2. What are the given facts?_____________________________________________

_____________________________________________

Back Next

3. What is the process to be used?_______________________________________________

_______________________________________________

4. What is the mathematical sentence?_______________________________________________

_______________________________________________

5. How the solution is done?

6. What is the answer?_______________________________________________

_______________________________________________

Back Next

7. How do you check the answer?

B. Faye filled the basin with 2.95 liters of water. Her brother used 0.21 liter when he washed his hands and her sister used 0.8 liter when she washed her face. How much water was left in the basin?

Back Next

1. What is asked?_____________________________________________

_____________________________________________


_____________________________________________

3. What is the process to be used?_____________________________________________

_____________________________________________

4. What is the mathematical sentence?_____________________________________________

_____________________________________________


Back Next

6. What is the answer?__________________________________________________________________________________________


Back Next

C. Ron cut four pieces of bamboo. The first piece was 0.75 meter; the second was 2.278 meters; the third was 6.11 meters and the fourth was 6.72 meters. How much longer were the third and fourth pieces put together than the first and second pieces put together?

1. What is asked?_____________________________________________

_____________________________________________


_____________________________________________

Back Next

3. What is the process to be used?_______________________________________________

_______________________________________________


_______________________________________________



_______________________________________________

Back Next


D. Pamn and Hazel went to a book fair. Pamn found 2 good books which cost Php. 45.00 and Php. 67.50. She only had Php.85.00 in her purse but she wanted to buy the books. Hazel offered to give her money. How much did Hazel share to Pamn?

Back Next

1. What is asked?_____________________________________________

_____________________________________________


_____________________________________________


_____________________________________________

4. What is the mathematical sentence?_____________________________________________

_____________________________________________


Back Next

6. What is the answer?__________________________________________________________________________________________


Back Next

E. Marlene wants to buy a bag that cost Php. 375.95. If she has saved Php. 148.50 for it, how much more does she need?

1. What is asked?_____________________________________________

_____________________________________________


_____________________________________________


_____________________________________________

Back Next


_______________________________________________



_______________________________________________


Back Home

Content Next


This modular workbook provides you with the understanding of the meaning of multiplication of decimals, multiply decimals in different form and how to estimate products. It will develop the ability of the students in multiplying decimal numbers. This modular workbook will help you to solve problems accurately and systematically.

Back Next


After completing this Unit, you are expected to:1. Define multiplication, multiplicand, multiplier, products and factors.2. Know the ways of multiplying decimal numbers.3. Learn the ways of multiplying decimal numbers involving zeros.4. Learn how to make an estimate and know the ways of making estimates.

Back Next

Lesson 21MEANING OF MULTIPLICATION OF DECIMAL

NUMBERS

Lesson Objectives: After learning this lesson, you are expected

to:3.Define multiplication.2.Locate where the multiplicand, multiplier and

product are.3.Familiarize the terms in multiplication.

NextContent

.4 + .4 + .4 + .4 + .4 + .4 = 2.4In multiplication, it is written as:

.4 → multiplicand x 6 → multiplier 2.4 → product (answer in multiplication)

factors

Multiplication is a short cut for repeated addition. It is a

short way of adding the same decimal number. It is the

inverse if division.

Back Next

The decimal numbers we multiply are called multiplicand and multiplier is the decimal number that multiplies. The answer in the multiplication is the product. The decimal numbers multiplied together are factors.

Another examples:

9 0.08 1.24 0.007x 0.5 x 3 x 2 x 4

4.5 0.24 2.48 0.028

Back Exercises

1. What is multiplication

?

2. What are

factors?

3. What are

products?4. Give some examples of multiplication

decimals.


Back Next

1.multiplication ________________________________________________________________________________

2. factors ________________________________________________________________________________

3. products ________________________________________________________________________________

4. Examples of multiplication decimals ________________________________________________________________________________

Back Next

• Identify the words by looping vertically ,horizontally and diagonally directions. (Word – Puzzle)

Back Next

____________ 1. The number we if multiply.

____________ 2. The numbers multiplied together.

____________ 3. The number that multiplies.

____________ 4. It is a short way of adding the same number of number times.

____________ 5. Multiplication is the inverse of _____________

Back Next

I. Complete the following that corresponds to themissing answer.

1. 0.42 - ______ 6. 0.183 - ______ x 0.34 - ______ x 0.141 - ______ _____ - product _____ - product

2. 0.12 - ______ 7. 12.55 - ______ x ____ - multiplier x 21.45 - ______0.0132 - ______ _____ - product

3. ____ - multiplicand 8. ____ - multiplicand x 4.62 - _______ x 0.96 - _______ 0.1848 - _______ 0.1848 - _______

Back Next

4. 56.08 - ______ 9. 1.45 - ______ x 31.901 - ______ x 6.56 - _____________ - product ______ - product

5. 8.08 - multiplicand 10. 8.145 - multiplicandx 8.14 - multiplier x 6.001 - multiplier _____ -________ _____ -________

Back Home

Lesson 22MULTIPLYING DECIMALS

Lesson Objectives: After finishing the lesson, the students are expected to:1. Learn how to multiply decimal numbers.2. Follow the steps in multiplying decimal numbers.3. Know how to place the decimal point in the product.

NextContent

Study these examples. Where do you place the decimal point in the product?

0.432 0.614 × 0.15 × 0.37

2160 4298 + 432 + 1842_ 0.06480 0.22718

Back Next

Remember:In multiplying decimals, the

placement of the decimal point in the product is determined by the total number of decimal places in the factors. Count the number of decimal places from the right. To check, divide the product by either factors.

Back Next

6480 four digits 22718 five digitsAdd a zero to make Additional zeros isfive decimal places in theproduct. not needed.0.06480 0.2271

AdditionalZero

Add the decimal places in the factors. Then see how many decimal places the product has.

0.432 × 0.15

Five decimal places

0.614 × 0.37

Five decimal places

Back Next

PRACTICE:

Find the product by fill in the boxes for the correct answer.

0.3 0.2 0.4

0.1 0.5 0.6

0.4 0.7 0.3

0.5 0.4 0.3

0.7 0.6 0.8

0.4 0.2 0.10.5 0.4 0.3

0.7 0.6 0.8

0.4 0.2 0.1

Back Next

1.9 1.5 1.8

2.5 3.5 2.0

3.5 3.8 3.1

0.1 0.44 0.87

0.54 0.53 0.09

0.9 0.76 0.36

1.90 1.2 2.9

1.8 2.2 2.99

1.66 0.8 1.52.2 1.4 1.9

1.4 1.7 1.9

1.7 2.0 2.7 1.6 1.8 1.7

1.89 1.89 1.7

2.7 2.6 2.9

Back Exercises

• Put the decimal point on the product for the correct places.

1. 0.192 x 0.428 1536

384 + 768__

82176

2. 0.342 x 0.153

1026 1710 + 342

52326

3. 0.208 x 0.274

832 1456 + 416 56992

Back Next

4. 0.263 x 0.29

2367 + 526 7627

5. 0.1594 x 0.37

11158 + 47852 58978

I. Multiply the following decimal numbers and putthe decimal point.

1. 0.987 x 0. 270

2. 0.158x 0.258

3. 0.4789 x 0.1247

Back Next

4. 0.2547 x 0.2479

5. 0.3647 x 0.1248

Back Next

What did the big flower say about the little flower?

To find the answer, write each of the following productsin multiplying decimals.

Back Next

__________ ___________ ___________ __________

0. 7537344 0.0132 0.0003 0.08537832

___________ ___________

0.001445 0.290523

_________ __________ _________ ________ ________

0.0000195 0.0044902 0.000492 0.05626725 0.0006

Back Home

Lesson 23MULTIPLYING MIXED DECIMALS BY

WHOLE NUMBERS

Lesson Objectives: After finishing the lesson, the students are expected to:1. Multiply mixed decimals by whole numbers.

2. Find the partial products. 3.Understand the rules in multiplying mixed decimals by whole numbers.

NextContent

Christopher can save Php. 18.65 in one month. How much money can he save in four months?

18.6 → two decimal placesx 474.60

Decimals are multiplied the same way as whole number.

Back Next

Remember:In multiplying mixed decimals by whole

numbers, count the decimal places in the mixed decimal to determine the placement of the decimal point in the product. Start counting the number of decimal places from the right.

Back Next

Study other examples.

23.729 → three decimal placesx 47

166103 + 94916 1115.263

↑

Partialproduct

Back Next

6.3572 → four decimal placesx 158

508576 317860 + 63572 1004.4376

↑

Partialproduct

Back Exercises

I. In the following problems, the final product is given. Find the partial products. Place the decimal points in the correct position.

1. 81.83 2. 62.872 3. 7.0194 × 57 × 34 × 271

+ + 466431 2137648 +

19022574

Back Next

4. 17.59 5. 48.723 6. 8.0035 × 83 × 52 × 179

+ + 145997 2533596 +

14326265

Back Next

II. Find the product.

7. 934.04 8. 282.5601 9. 37.5852 × 251 x 49 × 784

10. 51.207 11. 4672.397 12. 693.3521 × 490 × 268 × 922

Back Next

13. 75.373 14. 149.1811 15. 10.1496 x 44 x 1012 x 189

Back Home

Lesson 24MULTIPLICATION OF MIXED DECIMALS BY

MIXED DECIMALS

Lesson Objectives: After accomplishing this lesson, you are expected to:1. Multiplying mixed decimals by mixed decimals.

2. Perform the operation correctly. 3. Understand the rules in multiplying mixed

decimals by mixed decimals.

NextContent

What is the area of Ariel’s backyard if it is 12.932 m long and 8.45 m wide? NOTE:

Area = length x width = 12.93m x 8.45m = 109.27540 sq.m² = m x m = m²

12.932 → three decimal places × 8.45 → two decimal places

64660 51728+ 103456 109.27540 → five decimal places

The backyard is 109.27540 square meters.

Back Next

NOTE:Area = length x width = 12.93m x 8.45m = 109.27540 sq.m² = m x m = m²

When multiplying mixed decimals

by mixed decimals, the

decimal point of the product is determined in this manner.

Back Next

Decimal Decimal DecimalPlaces of first Places of second Places of Factor Factor the product

Back Exercises

I. Rewrite and arrange the partial products properly. Find the product and place the decimal points in the correct position.

1. 4.9526 2. 9.18234 × 3.215 × 75.68 247630 7345872

49526 5509404 99052 451170

+ 148578 + 6427638

Back Next

3. 57.6012 4. 2.01938 × 4.765 × 36.24

2880060 8077523456072 4038764032084 1211628

+ 2304048 + 605814

Back Next

Find the product.

5. 15.6027 6. 92.46355 7. 8.932682 × 8.306 × 1.728 × 9.1865

8. 743.9516 9. 268.924 10. 5.1367× 4.321 × 4.321 × 9.824

Back Home

Lesson 25MULTIPLYING DECIMALS BY 10, 100 and 1000

Lesson Objectives: At the end of the lesson, you are expected to:1. Multiply decimals by 10, 100 and 1000.

2. Write the product correctly. 3. Observe the rules in multiplying decimals

by 10, 100 and 1000.

NextContent

Take a decimal, 0.7568. Multiply it by 10, by 100 and by 1,000. What are the products?

Look at the following:

0.7568 0.7568 0.7568 × 10 × 100 × 1000

7.5680 75.6800 756.8000

Back Next

You see that the number of zeros contained in the factors 10, 100 and 1,000 tells how many places the decimal point in the other factor must be moved to the right to get the product.

Examples:

10 × 0.75 = _______100 × 0.75 = _______1,000 × 0.75 = _______

Back Next

Observe:

750.75.7.5

0. 7500. 750.75

0.7500.750.750.75

× 1,000× 100× 10Decimal

Move 1 place to the right.

Move 2 place to

the right.

Move 3 place to the

right.

Back Exercises

Complete the following equations.

1.3.67 × 10 = ______2.100 × _____ = 45213.1000 × _____ = 0.00494._____ × 100 = 854.85.2.918 × _____ = 29186.35.66 × _____ = 356607.0.0074 × _____ = 7.48._____ × 10 = 0.1639.0.089 × 10 = _____10. _____ × 100 = 100.78

Back Next

II. Complete the table by multiplying each factor by 10, 100 and 1,000.

Back Next

III. Multiply the following. Write your answers in the blanks provided:

1. 0.386 × 10 = ________2. 0.86 × 100 = ________3. 0.36 × 1000 = ________4. 0.473 × 1000 = ________5. 0.496 × 10 = ________6. 0.85 × 1000 = ________7. 0.7 × 1000 = ________8. 0.512 × 100 = ________9. 0.93 × 100 = ________10. 0.603 × 10 = ________

Back Home

Lesson 26ESTIMATING PRODUCTS OF DECIMAL

NUMBERS

Lesson Objectives: After understanding the lesson, you must able to:1. Learn how to estimate the products correctly.

2. Learn how to make an estimates product infastest way.

3. Follow the steps in estimating products.

NextContent

The fastest way of solving problem is to estimate. In estimating the products:

Round the given decimal numbers to the highest place value.

Estimate and multiply. Compute the exact answer.

Products can be estimated in the same way as sum and difference.

Back Next

1. Rounding Method

4.52 × 6 27.12

Actual Value Rounded Value

5.00× 6 30.00

2. Front End Method

4.56 4.00 4.52 .50 450 × 6 × 6 × 6 × 6 × 6 24.00 + 3.00 = 27.00

Back Next

The front – end method with adjustment is usually closer to the actual value.

Back Exercises

I.Estimate the product using rounding and front-end with adjustment.

1. 3.754 2. 48.263 3. 28.169 × 8 × 5 × 7

Back Next

4. 38.721 5. 28.765 6. 75.814 × 3 × 9 × 13

7. 96.250 8. 18.263 9. 927.231 × 42 × 41 × 507

Back Next

10. 36.287 11. 76.298 12. 28.183 × 206 × 304 × 543

Back Home

Lesson 27PROBLEM SOLVING INVOLVING

MULTIPLICATION OF DECIMAL NUMBERS

Lesson Objectives: After understanding the lesson, you must

able to:2.Solve word problem involving multiplication of

decimals.3.Write the numbers sentence.4.Solve word problems correctly and accurately.

NextContent

Example 1:

A cone of ice cream costs Php. 16.25, how much in all did the 6 children spend for ice cream?

Back Next

Example 2:

What is the area of a rectangle with a length of 9.72 cm and width of 6.34 cm?

Back Exercises

Read, analyze and translate these problems to number sentence then solve.

1. Mrs. Hernandez baked 1,000 pineapple pies for a party of her daughter Kiana. If each pie costs Php. 17.85, how much did the 1,000 pies cost?

Back Next

2. If a car travels 55.6 km an hour, how far will it travel in 8 hours?

Back Next

3. Mang Freddie sold 46 cotton candies at Php. 2.15 each. How much altogether is the cost of the cotton candies?

Back Next

4. A rope measures 4.63 m. How long is it in centimeters?

Back Next

5. If 1 meter of cloth costs Php. 72.95, how would 6.5 meters cost?

Back Next

6. Mang John, a balot vendor bought 120 new duck eggs at Php. 3.85 each. How much did he pay all the eggs?

Back Next

7. A can of powdered milk has a mass of 0.345 kilogram. What is the mass of 12 cans of milk?

Back Next

8. Mr. Gelo Drona bought a residential lot with an area of 180.75 m at Php. 650.00 per square meter. How much did he pay for the lot?

Back Next

9. Niña works 40 hours a week. If his hourly rate is Php. 640.25, how much is she paid a week?

Back Next

10. The rental for a Tamaraw FX is Php. 3,500 a day. What will it cost you to rent it in 3.5 days?

Back Home

Content Next


This modular workbook provides you’re the language of division of decimal numbers and how to divide decimals in different ways.

OBJECTIVES OF THE MODULAR WORKBOOKAfter finishing this unit, you are expected to:

1. Understand the language of division of decimals.

2. Know how to divide decimal numbers.3. Follow the steps in division of decimal numbers.4. Participate actively in division of decimal numbers.5. Learn the different form of dividing decimal numbers. Back Next

Lesson 28MEANING OF DIVISION OF DECIMAL

NUMBERS

Lesson Objectives:After accomplishing this lesson, you are

expected to:1. Define division.2. Understand the language in division of decimals.3. Know the parts in dividing decimal numbers.

NextContent

Division is the process of finding out how many times one number is contained in another number.

0.09 → quotient9 0.81 → dividend - 0 81 - 81 0

Divisor

Back Next

The number that contains another number a number of times is called the dividend. The number that is contained in another number a number of times is called the divisor. The number that indicated how many times a number contained in another number is called the quotient.

Division may also be defined as the process of separating a number into as many equal parts as indicated by another number. The symbol for division ( ÷ ), which is read as “divided by”. Thus, 0.81 ÷ 9 = 0.09 is read as “eight-one hundredths divided by nine equals nine thousandths.”

Back Next

Another symbol is a line written over and above the dividend and a slanting line connecting it at the left of the dividend and at the right of the divisor.

Another symbol is a line over which the dividend is written and the divisor below.

0.81 9

Back Exercises

I. Give the meaning and explain the use of the following: 5points each.

What is division?

What is divisor?

What is dividend? What is

quotient?

Back Next

1. Division ____________________________________________________________________________________

2. Divisor____________________________________________________________________________________

3. Dividend ____________________________________________________________________________________

4. Quotient ____________________________________________________________________________________

Back Next

II. Enumeration…

A. What are the parts of division?B. What symbols that can be used in dividing numbers?

A._____________________________________________________________________________________________________________________________

B._____________________________________________________________________________________________________________________________ Back Home

Lesson 29DIVIDING DECIMAL BY WHOLE NUMBERS

Lesson Objectives:After accomplishing this lesson, you are

expected to:1. Divide decimals by whole numbers.2. Follow the rules in dividing decimals by whole numbers.3. Find the quotient correctly.4. Using two methods in dividing decimals.

NextContent

Dividing decimals by a whole number is the same as dividing a whole number by another whole number.

Observe the following examples.

0.15 0.054 0.60 9 0.45 - 4 - 0 20 45 - 20 - 45 0 0

Back Next

To check the answer, multiply the quotient by the divisor:

0.15 x 4

0.60

0.05 x 9

0.45

In dividing decimals by whole numbers, the number of decimal places in the quotient equals the number of decimal in the dividend.

Back Next

Look at the other examples: Example 1: 0.6 ÷ 3 = _____

We used 2 methods in dividing decimals by whole numbers.

Back Next

1. Using a region

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

0.2 0.2 0.2 0.2 0.2

0.6

A whole is divided into 10 equal parts. Each part is called 1/10 or 0.1. 6/10 or 0.6 are shaded.0.6 is divided into 3 groups.

How many tenths are in each group?

Back Next

2. Using computations

6 ÷ 3 = 6 ÷ 3 = 210 1 10 ÷ 1 = 10

0.2 3 0.6 6 0

Let us check by using reciprocals.

Fractional Division:

6 ÷ 2 = 6 x 3 = 6 x 3 = 18 10 3 10 2 10 x 2 20

Back Next

6 ÷ 3 = 6 × 1 = 6 = 1 = 0.2 and 110 10 3 30 5 5

is equivalent

to 0.2

Why? Explain. 6 ÷ 6 = 1 30 6 5

0.2 5 1.0 1.0 0

Back Next

Let us divide hundredths by a whole number.

Example 2: 6 0.18

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 910

1. Using a region A whole is divided into 100 equal pairs. Each part is called 1/100. Eighteen parts are called 18/100 or 0.18. We divide 0.18 in 6 groups.

Back Next

How many hundredths are in each group?

Using computation 18 ÷ 6 = 18 ÷ 6 = 3100 1 100 ÷ 1 100

to get the tenths place. 0.03 → Quotient

6 0.18 - 18

0

Check: 6× 0.03 0.18

Back Exercises

I. Find the quotient by using region and computations.

1.3 0.12 2. 5 0.35 3. 7 0.14

4. 3 0.42 5. 8 0.64 6. 4 0.56

Back Next

7. 2 0.6 8. 9 0.81 9. 4 0.424

I.Find the quotients. Answer the question that follows.

1. 6 0.732 2. 4 0.524 3. 2 0.236

4. 5 0.655 5. 4 0.435 6. 7 0.851

Back Next

How many decimal places are in the dividends of 1 to 6?________________________________________________________________________________How many decimal places should there be in the quotient?________________________________________________________________________________How many we use zero in the quotient?________________________________________________________________________________

Back Home

Lesson 30DIVIDING MIXED DECIMAL BY WHOLE

NUMBERS

Lesson Objectives:After accomplishing this lesson, you are expected to:1.Divide mixed decimals by whole numbers.2.Understand the rule in dividing mixed

decimals by whole numbers.3.Answer the operation correctly.

NextContent

Divide mixed decimals in the same way as in dividing whole numbers. To check, multiply the quotient by the divisor.Long method of division:

1.5734 5 7.8670 - 5

28 - 25 36 - 35

17 - 15 20 - 20 0

To check, multiply the quotient by the divisor.

1.5734x 57.8670

Back Next

Remember that zeros added to a number to the right of the decimal point does not affect the value of the number.

7.8670 = 7.867

When dividing mixed decimals by whole numbers. The number of decimal places in the quotient is equal to the number of decimal places in the dividend. Align the decimal points of the quotient with that of the dividend.

Back Next

Do another division.

To check, multiply…

Answer (quotient by

division)

5.1268x 14 205072 51268 71.7752

5.1268 14 71.1152

- 70 17 - 14

37 - 28

95 - 85

112 - 112 0

Back Exercises

I. Find the quotient. Check bymultiplication.

CHECKING:

1.48.102 ÷ 21 =

6.56.381 ÷ 87 =

Back Next

3. 140.722 ÷ 9 =

4. 28.6134 ÷ 5 =

5. 189.526 ÷ 32=

Back Next

II. Solve for the quotient and check by longmultiplication method.

CHECKING:

• 83.7169 ÷ 21 =

2. 92.0314 ÷ 37 =

Back Next

3. 152.51 ÷ 28 =

4. 293.763 ÷ 48 =

5. 451.306 ÷ 89 =

Back Home

Lesson 31DIVIDING WHOLE NUMBERS BY DECIMALS

Lesson Objectives:After accomplishing the lesson, the students are expected to:1. Divide whole numbers by decimals.2. State the rule for dividing a whole number by a decimal.3. Find the quotient correctly.

NextContent

Let us divide whole numbers by decimals in

tenths.

Example 1: 0.8 72

Here are the steps in dividing whole numbers by

decimals...

STEP 1 Before we divide, we must change the divisor to a whole number. We multiply 0.8 by 10. We have 8.

Back Next

STEP 2 We multiply the dividends by 10 also. 10 x 72 = 720, we

have 720 as dividend.

STEP 3 Then we begin to divide. 90 → quotient8 720 - 72 0

We check: 90 × 0.8

72.0

Back Next

STEP 4

How we divide a whole number by a decimal in the

hundredths?

Follow this step to find the quotient.

Back Next

Example 2: 0.14 588

STEP 1 Make the divisor a whole number.Multiply it by 100.

0.14 x 100 = 14 0.14 588

STEP 2 Multiply the dividend by 100.

14 588.00

Back Next

STEP 3 Then divide as if dividing whole numbers. 4200

14 58800 -56 28 - 28 0

STEP 4 We check: 4200x 0.14 16800 4200 58000

Back Exercises

I. Find the quotient and check.

1. 0.3 ÷ 936 =

2. 0.8 ÷ 856 =

CHECKING:

Back Next

1. 0.9 ÷ 756 =

6. 0.5 ÷ 485 =

• 0.4 ÷ 348 =

Back Next

6. 0.6 ÷ 911 =

7. 0.2 ÷ 613 =

8. 0.7 ÷ 518 =

Back Next

9. 0.2 ÷ 434 =

10. 0.5 ÷ 775 =

11. 0.7 ÷ 434 =

Back Next

12. 0.7 ÷ 714 =

13. 0.8 ÷ 872 =

14. 0.6 ÷ 846 =

15. 0.5 ÷ 305 =Back Home

Lesson 32DIVIDING WHOLE NUMBERS BY MIXED

DECIMALS

Lesson Objectives:At the end of the lesson, the students are expected to: 1. Divide whole numbers by mixed decimals 2. Follow the rule in dividing whole numbers by mixed decimals. 3. Study division where the quotient is found to the ten thousandths place.

NextContent

Let us observe the rule in dividing whole numbers by mixed decimals.

Example 1:Move the decimal point in the divisor to make it a whole number. The number of places the decimal has been moved to the right in the divisor is the same as the number of places the decimal point is to be moved in the dividend. Add the appropriate zeros to the dividend. Align the decimal point of the dividend.

Back Next

In dividing decimals always try to divide to the last digit. When there are too many digits to divide, you can stop at the division by multiplying the quotient by the divisor. Divide 84 by 1.25.

67.21.25 84.00.0 - 750 900 - 875 250 - 250 0

67.2 x 1.25 33.60 13.44+ 67.2 84.000

Back Next

Check the divisor by multiplying the quotient by the divisor.

Study another division where the quotient is found to the ten thousandths place.

Back Next

Example 2: 16.0516

5.42 87.00.0000

- 542 3280 - 3252 280 - 000 2800 - 2710 900 - 542 3580 - 3252 328

To check:

16.0516 × 5.42 0.321032 6.42064 80.2580 86.999672 + 0.000328 87.000000

Back Exercises

I. Find the quotient to the ten thousandths place then check.

CHECKING:

1.15 ÷ 4.7 =

2. 9 ÷ 5.28 =

3. 86 ÷ 7.245 =

Back Next

4. 16. ÷ 7.32 =

5. 23 ÷ 8.16 =

6. 43 ÷ 15.8 =

Back Next

7. 8 ÷ 1.43 =

8. 15 ÷ 3.786 =

9. 74 ÷ 16.37 =

10. 22 ÷ 5.61 =

Back Home

Lesson 33DIVIDING DECIMAL BY DECIMALS

Lesson Objectives:At the end of the lesson, the students are expected to:1. Divide decimals by decimals.2. Follow the step in dividing decimals by decimals3. Use fraction in checking the division of decimals.

NextContent

How is division done with decimals? What do we do with the decimal points? Let’s observe the following example.

STEP 1 STEP 2 STEP 30.5 0.75 5 0.7.5 1.5

5 7.5 - 5 25 - 25 0

Multiply 0.5 by 10 to make it a whole number.

Multiply 0.75 by 10 also. What we do with the divisor, we do to the dividend.

Divide just like whole numbers. The quotient has the same number of decimal places as the dividend.

Example: 0.5 0.75

Back Next

Let us check by using fractions.

75 ÷ 5 = 75 ÷ 5 = 15 or 1 5 or 1.5100 10 100 ÷ 10 10 10

Back Exercises

I. Divide the following and check it by using fractions.

1.0.72 ÷ 0.3 =

2. 0.96 ÷ 0.4 =

3. 0.387 ÷ 0.09 =

CHECKING:

Back Next

4. 0.516 ÷ 0.6 =

5. 0.81 ÷ 0.9 =

6. 0.96 ÷ 0.8 =

Back Next

7. 0.441 ÷ 0.7 =

8. 0.558 ÷ 0.06 =

9. 0.36 ÷ 0.3 =

10. 0.72 ÷ 0.8 = Back Next

II. Try to analyze. Check your answer.

6. 0.56 ÷ 0.008 =

2. 0.90 ÷ 0.090 =

CHECKING:

Back Next

3. 0.72 ÷ 0.4 =

4. 0.26 ÷ 0.2 =

5. 0.9015 ÷ 0.5 =

Back Home

Lesson 34Dividing Mixed Decimals by Mixed Decimals

Lesson Objectives:At the end of the lesson, the students are

expected to:1.Divide mixed decimals by mixed decimals.

2. Observe the rule in dividing mixed decimals by mixed decimals.3. Perform the operation correctly.

NextContent

A full-grown Philippine eagle can grow to length of 102.6 cm including its tail. The tail can reach 49. 8 cm. When one of its wings is spread out, it can reach 63.2 cm. The length of its tail is what part of its whole length?Divide 102.6 cm (total length) by 49.8 cm (tail) to the hundredthsplace.

Back Next

Move the decimal point one place to the right. The number of decimal places point has been moved in the divisor determines the number of decimal places it is moved in the dividend.

2. 0649.8. 102. 6. 00

- 996 300 - 000 3000 - 2988 12

To check, multiply it.

49.8 x 2.06 2.9 88 0.00 99.6__102.5 88+ 0.0 12102.6 00

In the case like this, when the remainder is added, the sum is equal to the dividend.

Back Next

Mixed Decimals are divided in the same way as whole numbers. In dividing mixed decimals by mixed decimals, remember that the decimal point in the divisor is moved to the right to make it a whole number.

Back Exercises

I. Find the quotient to the tenths place. Check it through multiplication.

1.8.376 ÷ 1.942 =

2. 7.801 ÷ 2.334 =

3. 9.482 ÷ 4.7636 =

CHECKING:

Back Next

4. 10.857 ÷ 6.135 =

5. 23.154 ÷ 5.719 =

6. 41.028 ÷ 12.149 =

Back Next

7. 183.945 ÷ 20.132 =

8. 151.932 ÷ 46.741 =

9. 273.921 ÷ 87.553 =

10. 491.72 ÷ 78.521 =Back Home

Content Next

PAMN FAYE HAZEL M. VALIN

Brgy Bagong Pook Sta. Maria, LagunaJanuary 8, 1991E-mail Address :

[email protected]

Back Next

EDUCATIONAL ATTAINMENTElementary

Santa Maria Elementary SchoolSecondary

Santa Maria National High SchoolTertiary

Laguna State Polytechnic University (Formerly LSPC) Siniloan Host Campus

CourseBachelor of Elementary Education

MajorGeneral Education

Back Next

RON ANGELO A. DRONA

Patricio Street, Brgy. San Jose Pangil, LagunaJune 04, 1991

E-mail Address : [email protected]

Back Next

EDUCATIONAL ATTAINMENTElementary

Pangil Elementary SchoolSecondary

Laguna State Polytechnic University (Formerly LSPC) Siniloan Host Campus

TertiaryLaguna State Polytechnic University (Formerly LSPC) Siniloan Host Campus

CourseBachelor of Elementary Education

MajorGeneral Education

Back Next

BEATRIZ P. RAYMUNDO

Brgy Bagong Pook Sta. Maria, LagunaApril 21, 1951


Back Next

EDUCATIONAL ATTAINMENT

ElementarySanta Maria Elementary School

SecondarySanta Maria Academy

TertiaryImmaculate Conception College

CourseBachelor of Secondary Education

Back Next

MajorMathematics

MinorEnglish

Master’s DegreeMA Teaching (National Teacher’s College,

Manila)Teacher in Values Education and Filipino

Back Next

FOR-IAN V. SANDOVAL

Siniloan, LagunaApril 5, 1979


Back Next

EDUCATIONAL ATTAINMENT

ElementaryPalasan Elementary School

SecondaryUnion College of Laguna

TertiaryFar Eastern University

CourseBachelor of Science in MathematicsBachelor of Secondary Education

(Unit Earner)

Back Next

MajorComputer Science

Master’s DegreeMaster of Arts in Education Major in

Educational Management (with units)

Back Home

Benigno, Gloria D. Basic Mathematics for College Students. Manila: REX Bookstore. 1993.

Calderon, Jose F. Basic Mathematics I. Quezon City: Great Books Trading. 1994.

Del Fiero, Jong. Power in Numbers 6. Manila: Saint Mary’s Publishing Corporation. 1999.

Department of Education Culture and Sports. Mathematics in Everyday Life (textbook for Grade V) Revised edition. Manila: Cacho Hermanos Inc., 1993.

Department of Education. Lesson Guides in Elementary (Mathematics for Grade VI). Bureau of Elementary Education in coordination with Ateneo de Manila University., 2003

Ibe, Milagros D. et. al. Highschool Mathematics-Concept and Operation, 3rd edition, First Year. Manila: DIWA Learning Systems Inc., 1999.

Jovero, Natividad V. Power in Numbers IV (Teachers Manual, Mathematics 4). Manila: Saint Mary’s Publishing Corporation. 1999.

Llanes, Estrelita M. and Li, Bernardino Q. Living with Math VI. Revised Edition. Quezon City: FNB Educational Inc. 1988.

Lopez, Kelli L., The Self-replicating Gene. Tatsulok. Vol. 14 No. 2 1st year. Pp 4-6,15.

Mendoza, Marilyn O. Workbook in Mathematics. Manila: Gintong Aral Publication. 1997.

Roxas, Mia P. and Zara, Evelyn F. Elementary Algebra. High School Mathematics. (Worktext I). EFEREZA Pulbication House. 2003.

http://www.321know.com

http://whyslopes.com

http://www.321know.com/

http://www.ask.com/pictures

http://images.google.com.ph

http://images.search.yahoo.com

http://photobucket.com/images

http://www.ask.com/pictures

http://images.google.com.ph/

http://images.search.yahoo.com/

decimal numbers

Education

teacher education

college of education

secondary education

general education

advanced education

pre school education

educational technology

related fields