lesson ready to go on? skills intervention...
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Copyright © by Holt, Rinehart and Winston. 62 Holt MathematicsAll rights reserved.
Name Date Class
Ready to Go On? Skills InterventionDivisibility4-1
LESSON
A number is divisible by another number if the quotient is a wholenumber with no remainder. There are many rules you can use tocheck whether a number is divisible by another number.
Checking DivisibilityTell whether 850 is divisible by 2, 3, 4, 5, 6, 9, and 10.
Numbers that are divisible by more than two numbers are calledcomposite numbers. A prime number is divisible by only thenumber 1 and itself.
Identifying Prime and Composite NumbersTell whether each number is a prime or composite number.A. 56
56 is divisible by , , , , , , , .
So, 56 is a number.
B. 29
29 is divisible by , .
So, 29 is a number.
567
Vocabulary
divisiblecomposite numberprime number
Rule Divisible or Not
2 Is the last digit odd or even? Divisible
3 The sum of the digits of 850:
� � � .
Is divisible by 3?
4 The last two digits form the number .
Is divisible by 4?
5 The last digit is . Is it divisible by 5?
6 Is 850 divisible by 2? by 3?
9 The sum of the digits of 850:
� � � .
Is divisible by 9?
10 What is the last digit of 850?
Is it divisible by 10?
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Copyright © by Holt, Rinehart and Winston. 63 Holt MathematicsAll rights reserved.
Name Date Class
Ready to Go On? Problem Solving InterventionDivisibility4-1
LESSON
You can use divisibility rules to solve some problems withoutdividing, even if you haven’t learned a rule for the specific numberin the problem.
A chicken farm has 1,764 eggs to pack. Each carton will hold adozen eggs. Will there be any leftover eggs?
Understand the Problem
1. How many eggs are there? How many go into each carton?
Make a Plan
2. What number could you divide 1,764 by to solve the problem?
3. Will there be leftovers if the number of eggs is divisible by 12? If it isn’t divisible by 12?
4. If a number is divisible by 12, why must it also be divisible by 3 and by 4?
5. Test the divisibility rule for 12. Choose some numbers divisibleby 12 and see if they are divisible by 3 and by 4.
Solve
6. Is 1,764 divisible by 3? Explain.
7. Is 1,764 divisible by 4? Explain.
Check
8. Make sure you answer the question being asked in the problem.
Tell whether the first number is divisible by the second number.
9. 1,346 by 12? 10. 2,004 by 12? 11. 13,412 by 12?
MSM07C1_RTGO_ch04_062-088_B 6/17/06 5:28 PM Page 63 (Black plate)
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Copyright © by Holt, Rinehart and Winston. 64 Holt MathematicsAll rights reserved.
Name Date Class
Ready to Go On? Skills InterventionFactors and Prime Factorization4-2
LESSON
Whole numbers that are multiplied to find a product are calledfactors of that product. A number is divisible by its factors.
Finding FactorsList all of the factors of each number.A. 31
31 � • 31 Begin listing factors in pairs.
Is 31 divisible by any other whole numbers?
The factors of 31 are and .
Is 31 a prime or composite number?
B. 28
Begin by listing factors in pairs.
28 � • 28 1 is a factor.
28 � • 14 is a factor.
3 is not a factor.
28 � • 7 is a factor.
is not a factor.
is not a factor.
28 � • 4 and 4 have already been listed, so stop here.
The factors of 28 are , , , , , and .
The prime factorization of a number is the number written as theproduct of its prime factors.
Writing Prime FactorizationWrite the prime factorization of 64. Use a ladder diagram.
Choose a prime factor of 64 to begin.
Keep dividing by prime factors until the quotient is .
The prime factorization for 64 is 2 • 2 • 2 • • • , or 2 .
1
2
2
8
2
32
642
Vocabulary
factorprime factorization
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Copyright © by Holt, Rinehart and Winston. 65 Holt MathematicsAll rights reserved.
Name Date Class
Ready to Go On? Problem Solving InterventionFactors and Prime Factorization4-2
LESSON
You can use prime factorization to divide large numbers.
A sign is placed every 176 feet along a 1-mile path. How manysigns are needed? 1 mile � 5,280 feet.
Understand the Problem
1. How many signs would you need for one 176-foot-long section? Two sections? Three sections?
2. How can you tell how many 176-foot-long sections there are?
Make a Plan
3. Dividing by 2 and then by 3 is the same as dividing by what number?
4. Dividing by 10 and then by 2 is the same as dividing by what number?
5. If you knew the prime factorization of 5,280 and of 176, howcould you use that to divide 5,280 by 176?
Solve
6. What are the prime factorizations of 5,280 and 176?
7. Use the prime factorizations to divide 5,280 by 176.
8. How many signs are needed for the 1-mile path?
Check
9. If you multiply your answer to Exercise 7 by 176, what should the product be? Check to see.
Complete the prime factorization and then divide.
10. �1,
65375� � �
3 • 3 • 5 • 5 • 7� � 11. �
42,81300
� � �2 • 3 • 5 • 7 • 23
� �
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Copyright © by Holt, Rinehart and Winston. 66 Holt MathematicsAll rights reserved.
Name Date Class
Ready to Go On? Skills InterventionGreatest Common Factor4-3
LESSON
Factors shared by two or more whole numbers are called commonfactors. The largest of the common factors is called the greatestcommon factor, or GCF.
Finding the GCFFind the GCF of each set of numbers.
A. 26 and 38Method 1 List the factors.
factors of 26: , , , List all of the factors.
factors of 38: , , ,
What is the largest factor that is shared by 26 and 38?
The GCF of 26 and 38 is .
B. 18, 27, and 72Method 2 Use prime factorization.
18 � 2 • • Write the prime factorization of each
27 � 3 • • number.
72 � 2 • • • • What are the common prime
factors?
• � Find the product of the commonprime factors.
The GCF of 18, 27, and 72 is .
Problem SolvingNoah has 18 books and 30 magazines. He wants to place themonto the greatest number of bookshelves so that each bookshelfhas the same number of books and the same number ofmagazines. How many bookshelves will he use?
Method 3: Use a ladder diagram.
Begin with a factor that divides into each number.
Keep dividing until the two numbers have no common factors.
The GCF of 18 and 30 is 2 • or .
Noah will use bookshelves.
9
30182
Vocabulary
greatest commonfactor (GCF)
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You can use what you know about GCFs to solve some puzzles.
The GCF of x and y is 9. The GCF of y and z is 15. The GCF of xand z is 12. If x � y � z � 100, what are the values of x, y, and z?
Understand the Problem
1. If the GCF of two numbers is 9, why must both numbers be amultiple of 9?
2. Why must y be a multiple of 9 and of 15?
Make a Plan
3. What are the two possible values for y? Remember y � 100.
4. Of what two numbers must x be a multiple?
5. What are the two possible values for x? Remember x � 100.
6. How can you use logical reasoning to solve the problem?
Solve
7. What two numbers must z be a multiple of? What are thepossible values for z ?
8. Of the possible values for x, y, and z, which values meet thecondition that x � y � z?
Check
9. What is the GCF of 36 and 45? Of 45 and 60? Of 36 and 60?
Name Date Class
Ready to Go On? Problem Solving InterventionGreatest Common Factor4-3
LESSON
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4-1 DivisibilityTell whether each number is divisible by 2, 3, 4, 5, 6, 9, and 10.
1. 240 2. 135
3. 516 4. 342
5. The distance around a farmer’s field is 882 feet. If he places afence post every 9 feet, will the posts be evenly spaced aroundthe field? Explain.
Tell whether each number is prime or composite.
6. 52 7. 91
8. 67 9. 49
4-2 Factors and Prime FactorizationList all of the factors of each number.
10. 6 11. 37
12. 24 13. 36
14. The Ogden School marching band has 91 student musicians. If there are 7 student musicians in each row, how many rows are there?
Write the prime factorization of each number.
15. 48 16. 100 17. 24 18. 189
Complete the diagrams. Write the prime factorization.
19. 20. 3 | 81
3 | 273 | 9
3 | 334
125
525
53
5 5
Copyright © by Holt, Rinehart and Winston. 68 Holt MathematicsAll rights reserved.
Name Date Class
Ready to Go On? Quiz4A
SECTION
MSM07C1_RTGO_ch04_062-088_B 6/17/06 5:28 PM Page 68 (Black plate)
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Name Date Class
Ready to Go On? Quiz continued
4ASECTION
4-3 Greatest Common FactorList all the factors of both numbers. Circle the GCF.
21. 108
54
22. 72
64
Find the GCF of each set of numbers.
23. 16 and 24 24. 18 and 2 25. 48 and 72 26. 35 and 75
27. There are 42 pens and 63 pencils. All of the pens and pencils are given to the students in Mr. Antico’s class. Each student receives the same number of pens and pencils. What is the maximum number of students in the class?
28. There are 16 boys and 12 girls in Mrs. Hart’s math class. She divides the class into study groups so that each group has the same number of boys and the same number of girls. What is the greatest number of study groups she can make if every student is assigned to a group?
29. Mr. Hernandez, a farmer, has 160 apples, 80 plums, and 120 pears. He wants to divide the fruit into packages with the same number of apples, the same number of plums, and the same number of pears in each package. What is the greatest number of packages he can have if every piece of fruit is placed in a package?
30. Michael has 27 baseball cards, 9 football cards and 6 basketball cards. What is the greatest number of friends he can give the cards to so that each friend receives the same number of baseball, football, and basketball cards and he gives all the cards away?
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Copyright © by Holt, Rinehart and Winston. 70 Holt MathematicsAll rights reserved.
Name Date Class
Ready to Go On? EnrichmentHow Many Different Factors?4A
SECTION
You can determine how many factors a number has and evaluatethe factors from the prime factorization of the number.
The number 12 has 6 factors. They are 1, 2, 3, 4, 6, and 12.
The prime factorization of 12 is 2 • 2 • 3 � 22 • 31. The factors of 12as a product of a power of 2 and a power of 3 are shown in the table.
Compare the greatest power of each prime factor with the numberof times the factor is displayed with an exponent in the table.
The number of times 2 is displayed with an exponent is than ,the exponent of 2 in the prime factorization of 12.
The number of times 3 is displayed with an exponent is than ,the understood exponent of 3 in the prime factorization of 12.
Make a guess about the number of factors 28 has, based on itsprime factorization: 22 � 71.
Use your guess to determine the number of factors each numberhas. Create a table to show what the factors are.
1. 98 2. 250
3. 36 4. 100
� 20 � 1 21 � 2 22 � 4
30 � 1 1 2 4
31 � 3 3 6 12
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Copyright © by Holt, Rinehart and Winston. 71 Holt MathematicsAll rights reserved.
Name Date Class
Ready to Go On? Skills InterventionDecimals and Fractions4-4
LESSON
Decimals and fractions can often be used to represent the samenumber. A number that contains both a whole number greater than
0 and a fraction, such as 2�23
�, is called a mixed number. A
terminating decimal, such as 0.84, has a finite number ofdecimal places. A repeating decimal, such as 0.555…, has ablock of one or more digits that repeats without end.
Writing Decimals as Fractions or Mixed NumbersWrite 4.8 as a fraction or mixed number.
What is the place value of the 8?
What number will you use as the denominator?
What will you use as the whole number?
Write the mixed number.
Writing Fractions as Decimals
Write �15
� as a decimal.
Divide 1 by 5. What number is the dividend?
5�1.�� Where should you add a zero?
�
What is the remainder?
�15
� � Is this a terminating decimal or a repeating decimal?
Comparing and Ordering Fractions and DecimalsOrder the fractions and decimals from least to greatest. 0.6, �
13
�, 0.49
�13
� � First, rewrite the fraction as a decimal. Is it a
terminating decimal or a repeating decimal?
Fill in the blank with �, �, �.
0.6 0.3_; 0.6 0.49; 0.49 0.3
_
The numbers in order from least to greatest are , , .
Vocabulary
mixed numberrepeating decimalterminating
decimal
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Amy’s batting average was 0.250. Today she got 3 hits in 4 times atbat. Now her average is 0.333. How many hits does she have?
Understand the Problem
1. How is batting average calculated?
Make a Plan
2. Amy’s average increased a lot in one day. Does that tell you shehad a lot of times at bat or just a few? Explain.
3. If Amy had only 1 hit in 4 times at bat before today, what wouldher batting average be after today’s game. How do you know?
4. How can you use guess and check to solve the problem?
Solve
5. Try 3. If Amy had 3 hits in 12 times at bat before today, whatwould her average be after today’s game? Show your work.
6. Keep trying. How many hits and times at bat did Amy havebefore today? How many hits does she have now?
Check
7. Show that your answer meets the conditions in the problem.
Copyright © by Holt, Rinehart and Winston. 72 Holt MathematicsAll rights reserved.
Name Date Class
Ready to Go On? Problem Solving InterventionDecimals and Fractions4-4
LESSON
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Copyright © by Holt, Rinehart and Winston. 73 Holt MathematicsAll rights reserved.
Name Date Class
Ready to Go On? Skills InterventionEquivalent Fractions4-5
LESSON
Fractions that represent the same value are equivalent fractions.
Finding Equivalent FractionsFind two equivalent fractions for �
23
�.
Look at the shaded areas of the rectangles and find equivalentfractions.
�23
� � �6
� � �9
�
So �23
� is equivalent to and .
Multiplying to Find Equivalent FractionsFind the missing number that makes the fractions equivalent.
�34
� � �2?0�
�34
••� � �
20� What number can you multiply 4 by to get 20?
So, �34
� is equivalent to �20
� .
A fraction is in simplest form when the GCF of the numerator andthe denominator is 1.
Writing Fractions in Simplest Form
Use the GCF to write �2206� in simplest form.
Is �2206� in simplest form? What is the GCF of 20 and 26?
�2206
��� � �� Divide 20 and 26 by their GCF.
So, �2206� written in simplest form is ��.
Vocabulary
equivalentfractions
simplest form
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Knowing how to find equivalent fractions can help you communicatemeasurements more clearly.
You measure a portable music player to the nearest �312� of an inch.
Its length is 5�382� in., and its width is 3�
2382� in. How can you report
those dimensions in a clearer way without changing their values?
Understand the Problem
1. What do you know and what are you asked to do?
Make a Plan
2. How can finding equivalent fractions help solve the problem?
Solve
3. List three simpler equivalent fractions for �382�. Which is the simplest?
4. List two simpler equivalent fractions for �2382�. Which is the simplest?
5. How would you report the measurements?
Check
6. Multiply the numerator and denominator by the same number to show that theequivalent fractions you found really are equivalent.
Copyright © by Holt, Rinehart and Winston. 74 Holt MathematicsAll rights reserved.
Name Date Class
Ready to Go On? Problem Solving InterventionEquivalent Fractions4-5
LESSON
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Name Date Class
Ready to Go On? Skills InterventionMixed Numbers and Improper Fractions4-6
LESSON
An improper fraction is a fraction in which the numerator isgreater than or equal to the denominator. When the numeratoris less than the denominator, the fraction is called a properfraction.
Astronomy Application
Pluto is �145� billion miles from the sun. Write �
145� as a mixed number.
Use the rectangles below as a model.
What size sections should you divide the rectangles into?
How many sections will you shade?
How many whole rectangles are shaded?
How many sections of the fourth rectangle are shaded?
There are squares shaded. Pluto is billion miles from the sun.
Writing Mixed Numbers as Improper Fractions
Write 3�27
� as an improper fraction.
In the mixed number 3�27
�, the whole number is ,
the numerator is and the denominator is .
3�27
� � �( • 3) �
� Multiply the whole number by the denominator.
Add the numerator. What number will you useas the denominator?
� ��� What operation should you perform first?
� �� Write the improper fraction.
Vocabulary
improper fractionproper fraction
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Copyright © by Holt, Rinehart and Winston. 76 Holt MathematicsAll rights reserved.
Name Date Class
Ready to Go On? Problem Solving InterventionMixed Numbers and Improper Fractions4-6
LESSON
You can use a number line to help compare and order mixednumbers and improper fractions numbers.
Match each improper fraction with a point on the number line.
�121� �
590� �
378� �
136�
Understand the Problem
1. Which point represents a greater number, C or D? Explain.
Make a Plan
2. Why would converting the improper fractions to mixed numbersmake it easier to compare them?
Solve
3. Convert each of the four improper fractions to a mixed number.
4. Which of the mixed numbers is represented by point D? Explain.
5. Which mixed number is represented by point A? Point B? Explain.
Check
6. The problem says to match the improper fractions. Whichimproper fractions go with which points?
4
A B C D
65
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Copyright © by Holt, Rinehart and Winston. 77 Holt MathematicsAll rights reserved.
Name Date Class
Ready to Go On? Quiz4B
LESSON
4-4 Decimals and FractionsWrite each decimal as a fraction.
1. 0.39 2. 0.7 3. 0.53 4. 0.3333…
Write each fraction as a decimal.
5. �45
� 6. �23
� 7. �58
� 8. �1230�
9. On a long distance run, George ran �35
� of the distance
in one hour while Brad ran 0.65 of the distance in the
same time. Who ran farther in one hour?
10. Sherri finished her homework in 0.4 hours. David
finished his homework in �12
� hour. Who finished their
homework first?
4-5 Equivalent FractionsWrite two equivalent fractions for each fraction.
11. �182� 12. �
2376� 13. �
1345� 14. �
16
�
Find the missing number that makes the fraction equivalent.
15. �160� � 16. �
146� � 17. �
37
� � 18. �56
� �15923
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4-5 Equivalent Fractions (continued)Write each fraction in simplest form.
19. �2315� 20. �
12050
� 21. �3459� 22. �
2450�
23. Melissa mowed �34
� of the front lawn. Write two fractions
that are equivalent to �34
�.
24. Kyle ate �38
� of a pizza. Write two fractions that are
equivalent to �38
�.
4-6 Mixed Numbers and Improper FractionsWrite each mixed number as an improper fraction.
25. 1�34
� 26. 2 �56
� 27. 1�38
� 28. 3 �13
�
Write each improper fraction as a mixed number.
29. �194� 30. �
285� 31. �
177� 32. �
287�
33. Tim spent thirteen quarter-hours working on his math
homework. Write �143� as a mixed number.
34. Robert is 5�152� feet tall. Express 5�
152� as an improper
fraction.
35. Mercedes can run a mile in �26809
� minutes. Express �26809
�
as a mixed number.
Ready to Go On? Quiz continued
4BSECTION
Name Date Class
MSM07C1_RTGO_ch04_062-088_B 6/17/06 5:28 PM Page 78 (Black plate)
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Name Date Class
Fractions with a denominator of 7 form an interesting pattern whenwritten as decimals.
Use your calculator to help you write �17
� as a decimal.
Describe the decimal you wrote.
Use your calculator to help you write �27
� as a decimal.
Compare the decimal equivalents of �17
� and �27
�. What patterns doyou notice?
Predict the decimal equivalent of �37
�. Remember that �37
� � �12
�, so since
the decimal equivalent of �12
� is 0.5, the decimal representation of �37
�
must begin with a digit that is less than 5.
Predict the decimal equivalents for �47
�, �57
�, and �67
�.
Describe how fractions with a denominator of 7 are related.
Look at the first four digits of the decimal equivalent of �17
�. How arethey related?
What do the last two digits of the decimal equivalent of �17
� have incommon?
You can use these characteristics to help you remember thedecimal equivalents for all fractions with a denominator of 7.
Ready to Go On? EnrichmentWhat is the Pattern When Dividing by 7?4B
SECTION
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Copyright © by Holt, Rinehart and Winston. 80 Holt MathematicsAll rights reserved.
Name Date Class
Ready to Go On? Skills InterventionComparing and Ordering Fractions4-7
LESSON
When comparing fractions, first check their denominators. Whenfractions have the same denominator, they are called likefractions. When two fractions have different denominators, theyare called unlike fractions. To compare unlike fractions, firstrename the fractions so they have the same denominator. This iscalled finding a common denominator.
Comparing Like FractionsCompare. Write �, �, or �.
�78
� �58
�
�78
� �58
�
Are the fractions like fractions or unlike fractions?
Which fraction has the larger numerator?
So, �78
� �58
�.
Ordering FractionsOrder the fractions from least to greatest.
�12
�, �35
�, �25
�
�12
••� � �� �
35
••� � �� �
25
••� � ��
Place the fractions on the number line.
The fractions in order from least to greatest are .
0 12–10
3–10
2–5
3–5
5–10
7–10
8–10
1–10
9–10
Vocabulary
like fractionsunlike fractionscommon
denominator
Multiply each denominator to make them allthe same.What is the common denominator?
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Copyright © by Holt, Rinehart and Winston. 81 Holt MathematicsAll rights reserved.
Ready to Go On? Problem Solving InterventionComparing and Ordering Fractions4-7
LESSON
Name Date Class
Sometimes you can use estimation and number sense to comparefractions that look complicated.
The table shows membership information for 3 after-school clubs. Which club hasthe largest fraction of sixth graders? Thesmallest fraction?
Understand the Problem
1. What fraction of the chess club members are in sixth grade?
Make a Plan
2. What three fractions will you compare?
3. Why is it a good idea to use estimation or number sense tocompare the fractions before dividing?
Solve
4. Without calculating exactly, which of the fractions is greater than �12
�? Explain.
5. Which fraction is greatest? How do you know?
6. Which fraction is least? How do you know?
Check
7. Answer the question that is being asked in the problem.
Club Total Members inMembers 6th Grade
Chess 29 13
Spanish 31 11
Writing 23 12
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Ready to Go On? Skills InterventionAdding and Subtracting with Like Denominators4-8
SECTION
Copyright © by Holt, Rinehart and Winston. 82 Holt MathematicsAll rights reserved.
Name Date Class
Home Economics Application
John uses �34
� cup of flour to make one batch of muffins. Find
how many cups of flour John will need to make five batches ofmuffins. Write your answer in simplest form.
�34
� � � � � Set up the addition problem.
�34
� � �34
� � �34
� � �34
� � �34
� � �4� When adding fractions, add the and
keep the the same.
� �4
� Write the improper fraction as a mixed number.
John will need �4
� cups of flour to make five batches of muffins.
Subtracting Like Fractions and Mixed NumbersSubtract. Write your answer in simplest form.
4�89
� � 2�59
� What should you subtract first?
�9
� What should you subtract second?
2�� Simplify the fraction.
Evaluating Expressions with Fractions
Evaluate the expression for x � �18
�. Write your answer in
simplest form.
x � 3�58
�
� 3�58
� What fraction will substitute into the equation for x?
Are the denominators the same?
� �8
� Add the fractions. Then add the whole numbers.
� 3�� Simplify your answer.
MSM07C1_RTGO_ch04_062-088_B 6/17/06 5:28 PM Page 82 (Black plate)
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Copyright © by Holt, Rinehart and Winston. 83 Holt MathematicsAll rights reserved.
Name Date Class
Ready to Go On? Problem Solving InterventionAdding and Subtracting with Like Denominators4-8
LESSON
You often need to add and subtract fractions when you work withcustomary measures.
Two pieces of wood are glued together and a slot cut into one of them. How far is it from the end of the long piece to the bottom of the slot?
Understand the Problem
1. What are you asked to find?
Make a Plan
2. How can you add and then subtract to find the answer?
3. How can you subtract and then add to find the answer?
4. Which method will you use?
Solve
5. Use the method you chose to solve the problem. What is thedistance to the bottom of the slot? Show your work.
Check
6. Estimate to check if your answer is reasonable.
1316
5
?
in. 916
3 in.
18
1 in.
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Ready to Go On? Skills InterventionEstimating Fraction Sums and Differences4-9
LESSON
Copyright © by Holt, Rinehart and Winston. 84 Holt MathematicsAll rights reserved.
Name Date Class
Estimating Fractions
Estimate each sum or difference by rounding to 0, �12
�, or 1.
A. �56
� � �112�
�56
� � �112� Think: What does �
56
� round to? What does �112� round to?
� � Round each fraction. Add.
�56
� � �112� is about .
B. �161� � �
35
�
�161� � �
35
� Think: What does �161� round to? What does �
35
� round to?
�� � �� � Round each fraction. Subtract.
�161� � �
35
� is about .
Home Economics ApplicationThe table shows the amount of milk the Baking Club usedin one week.
A. About how much milk did the Baking Club use onMonday and Wednesday?
4�49
� � 2�23
� Think: What does 4�49
� round to?
4�� � What does 2�23
� round to?
They used about gallons of milk.
B. About how much more milk did the Baking Club use on Fridaythan on Wednesday?
5�16
� � 2�23
� Think: What does 5�16
� round to? What does 2�23
� round to?
� �
They used about gallons more on Friday than on Wednesday.
Baking Club’sMilk Usage
AmountDay (gallons)
Monday 4�49
�
Wednesday 2�23
�
Friday 5�16
�
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Copyright © by Holt, Rinehart and Winston. 85 Holt MathematicsAll rights reserved.
Name Date Class
A model maker constructs 3 strips, A, B, and C, by gluing or cuttingas described below. Which strip is longest and which is shortest?
A. Three pieces are glued end to end. One is 3�38
� in. long, another is
1�176� in. long, and the third is 2�
14
� in. long.
B. Three pieces are glued end to end. Each is 2�196� in. long.
C. A 9-inch piece is shortened by cutting off 1�196� in.
Understand the Problem
1. What does the problem ask you to determine?
Make a Plan
2. What three expressions can you compare to solve the problem?
3. Why might estimation be a useful strategy?
4. Why might you round to the nearest �12
� instead of the nearestwhole number?
Solve
5. Fill in the blanks to show how you will round to the nearest �12
�.
3�38
� � 1�176� � 2�
14
� � �
3 • 2�196� 3 • 9 � 1�
196� 9 �
6. Estimate to tell which strip is longest and which is shortest. Explain.
Check
7. Go back and check your rounding, addition, and subtraction.
Ready to Go On? Problem Solving InterventionEstimating Fraction Sums and Differences4-9
LESSON
MSM07C1_RTGO_ch04_062-088_B 6/17/06 5:28 PM Page 85 (Black plate)
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4-7 Comparing and Ordering FractionsCompare. Write �, �, or � .
1. �45
� �56
� 2. �53
� �35
� 3. �37
� �57
� 4. �23
� �46
�
Order the fractions from least to greatest.
5. �23
�, �16
�, �34
� 6. �57
�, �34
�, �45
� 7. �49
�, �25
�, �47
�
8. A tortilla is cut into three pieces. Mary gets �12
�, Melissa
gets �13
�, and Marilyn gets �16
�. Who gets the largest piece
of tortilla?
4-8 Adding and Subtracting with Like DenominatorsAdd. Write each answer in simplest form.
9. �182� � �
1102� 10. �
94
� � �34
� 11. �1345� � �
375� 12. �
85
� � �95
�
Subtract. Write each answer in simplest form.
13. �2315� � �
1345� 14. �
79
� � �49
� 15. 2�176� � 1�
136� 16. �
134� � �
63
�
Evaluate each expression for x � �35
�. Write your answer insimplest form.
17. x � 4�15
� 18. 6�15
� � x 19. 5 �25
� � x 20. �65
� � x
Ready to Go On? Quiz4C
SECTION
Copyright © by Holt, Rinehart and Winston. 86 Holt MathematicsAll rights reserved.
Name Date Class
MSM07C1_RTGO_ch04_062-088_B 6/17/06 5:28 PM Page 86 (Black plate)
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Name Date Class
Ready to Go On? Quiz continued
4CSECTION
4-9 Estimating Fraction Sums and Differences
Round each fraction to the nearest �12
�.
21. �56
� 22. �16
� 23. �38
� 24. �13
�
Round each mixed number to the nearest �12
�.
25. 1�49
� 26. 3 �38
� 27. 2 �17
� 28. 3 �67
�
Round to the nearest �12
�. Add or subtract.
29. 1�38
� � 4 �15
� 30. 4 �78
� � 2�190� 31. 7�
29
� � 3�45
�
Use the table to answer the questions below.
32. Estimate the total rainfall for January through June to the
nearest �12
� inch.
33. Estimate. Did February have more, less, or about the sameamount of rain as April?
34. Estimate. Which month had more rain, January or June?
Month Jan Feb Mar Apr May Jun
Rainfall (in.) �58
� 1�56
� 3 �15
� 1�49
� 2 �78
� �255�
MSM07C1_RTGO_ch04_062-088_B 6/17/06 5:28 PM Page 87 (Black plate)
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Denise wants to make pasta sauce. Answer the questions based onthe recipes below.
1. Which sauce has more tomatoes? �23
� 1, so Sauce has more tomatoes.
2. Which sauce has more onions? �12
� �14
�, so Sauce has more onions.
3. How many cups of spices are in the recipe for PomodoroSauce?
4. Is there more basil or more parsley in Marinara Sauce? �12
� 1,so there is more
5. Order the spices in Marinara Sauce from least to greatest.
6. Denise wants to add �38
� can of whole tomatoes to the Pomodoro
Sauce. About how many cans of tomatoes would there be?
Marinara Sauce
1 can of whole tomatoes
�12
� cup of olive oil
�12
� tablespoon of dried basil
�14
� cup of diced onion
3 cloves of garlic
1 tablespoon of dried parsley
1�12
� tablespoons of dried oregano
Pomodoro Sauce
�23
� can of whole tomatoes
�12
� cup of olive oil
�14
� cup of fresh basil
�12
� cup of diced onion
�14
� cup of grated Parmesan cheese
�14
� cup of fresh parsley
�14
� cup of fresh oregano
Ready to Go On? EnrichmentRecipe Fractions4C
SECTION
Copyright © by Holt, Rinehart and Winston. 88 Holt MathematicsAll rights reserved.
Name Date Class