November 14

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