november 14
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November 14, 2012
Today:
Warm-Up: Review Fractions & GCFDecimals: +, -, x, ÷
STAR MathKhan Academy: Nov. 10th & 17
Topics
Warm-Up:
Khan Academy Help: Dividing Fractions Word Probs.
Warm-Up:
3. Which Fraction is larger: 4/6 or 7/10?
4. 2/5 + 7/8 = 5. 3 3/7 + 2 3/8 =
6. 6/11 - 5/12 =
7. 3 2/7 - 2 1/8 =
8. 8/15 • 3/11 =
9. 3 2/7 • 2 1/8 =
10. 8/15 ÷ 3/11 =
11. 3 2/7 ÷ 2 1/8 =
12. Find the Prime Factorization of 60
13. Simplify, using GCF: 144/150
Decimals: Objectives
1. Read decimals2. Write decimals3. Compare the size of
decimals to one another
4. Convert fractions to decimals
5. Convert decimals to fractions
6. Add decimals7. Subtract decimals8. Multiply decimals9. Divide decimals10. Round decimals to
nearest tenth11. Round decimals to
nearest hundredth
Decimals: Definition
A decimal is a fraction with a denominator that is a multiple of 10. The decimal (.) is used to indicate place value. Examples:
Caution: each decimal expression with a value less than 1 is preceded by a leading
zero to emphasize the presence of a decimal. For example, .7 is correctly
written as 0.7
3 equals 0.3 stated as "three tenths"
1018
equals 0.18 stated as "eighteen hundredths"100
Decimals: Place values
Decimals: Reading
Reading1. Read the whole number on the left2. Read the decimal point as the
word “and”3. Read the decimal fraction on the
rightExample: 8.3 = “eight and three
tenths” 4.06 = “four and six
hundredths” 0.5 = “five tenths
Write as follows
1. The whole number (if none, then write a zero - (“0”)
2. The decimal point to indicate the place of value
3. The decimal fraction portion of the numberExamples: “Seven and five tenths” = 7.5“One hundred twenty-five thousandths” = 0.125
Decimals: Writing
Decimals: Comparing Values
Zeros do not change the value of the number whether added at the beginning or the end, but they are unsafe as trailers.
Ex: .7 is the same numerical value as 0.712.6250 is the same value as 12.625but, 30.0 can be misinterpreted as 300!
Use leading zeros; AVOID trailing zeros
Decimals: Comparing Values (cont’d)
Zeros added within a decimal number change the value dramatically
Example: 0.375 is NOT the same as 0.0375
2.025 is NOT the same as 20.025
Decimals: Comparing Values (cont’d)
Different whole numbers If whole numbers are present and
different, whole numbers are compared to determine largest
Example: 4.8 is greater than 2.9
Same or no whole number The number in the tenths place
determines largest Example: 0.45 is larger than 0.37
Same or no whole number, and the number in the tenths place is the same
The decimal with the highest number in the hundredths place is the largest
Examples: 0.67 is larger than 0.66 0.17 is larger than 0.14 0.09 is larger than 0.08
Decimals: Comparing Values (cont’d)
Decimals: Adding and Subtracting
Place the numbers in the columns so the decimals are lined up. Add or subtract from left to right. Examples:
Safety Point: Zeros may be added to help line up decimals – don’t include in final answer!
16.4 21.8+ 3.0
.7 .750+ .324
.7 - .050
Place decimal correctly!Multiply numbers; in the product (answer),
count decimal places right to left equal to the total decimal places in the numbers being multiplied. Example: 1.2
3.2 24 36 384. = 3.84
x
Decimals: Multiplying
.7 x .050
Decimals: Multiplying (cont’d)
Add zeros where needed to ensure correct placement of decimal in answer Example: 0.11 x .33
0.110.33
33 33
0363. = 0.0363
x .12 x .14
Multiplying by 10, 100, 1,000 can be done by moving decimal to the right one space for each zero in the number by which multiplying Example: 1.6 x 10 = 1.6 = 16
5.2 x 100 = 5.20 = 520
Multiplying by Decimal Movement
.7 • 10 =
.8 • 100 =
Decimals: Dividing
Same as for whole numbers
Example: = 27 divided by 9
QuotientDivisor Dividend
9 27
Decimals: Dividing a Decimal
To divide by a whole number, place decimal in quotient directly above decimal in dividend
3.55 17.5
- 15 25- 25
0
8 22.3
4 35.7
. 0.3 6.96
Decimals: Dividing by a Decimal
Move the decimal in the divisor to the right until the number is a whole number. Then move the decimal in the dividend the same number of spaces. 23.2
3 69.6
- 6 9- 9
6
-6
0
.8 12.1
Class Work:
Decimal Handout:Every Other ProblemGirls: Begin with First ProblemGents: Begin with Second Problem
Decimals: Changing from Fractions
Rewrite fraction in division formatDivide the numerator by the denominator
and add zeros as neededMethod can be used to compare fraction
size
0.42
5 2.05
1 1
0.333... and 0.166...3 6
1 1 is larger than 3 6
Therefore