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11/30/09 Multiply & Divide Fractions #1

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11/30/09 Multiply & Divide Fractions #1

LT: I will learn to multiply and divide mixed numbers and fractions.

Fraction, Decimal, Percent Wheels

- Circle all fractions that are in lowest terms.
- Review the conversions & decorate your wheel.

Today’s Plan:

-Fraction, Decimal, Percent Wheel game

-Lesson

-Assignment

Learning Target: I will learn to multiply and divide mixed numbers and fractions.

11/30/09 Multiply & Divide Fractions #1

LT: I will learn to multiply and divide mixed numbers and fractions.

Fraction, Decimal, Percent Wheels

Today’s Plan:

-Fraction, Decimal, Percent Wheel game

-Lesson

-Assignment

Learning Target: I will learn to multiply and divide mixed numbers and fractions.

11/30/09 Multiply & Divide Fractions #1

LT: I will learn to multiply and divide mixed numbers and fractions.

Warm-up

Katie made a bookshelf that is 5 feet long. The first 6 books she put on it took up 8 inches of shelf space. About how many books should fit on the shelf?

45 books

Today’s Plan:

-Fraction, Decimal, Percent Wheel game

-Lesson

-Assignment

Learning Target: I will learn to multiply and divide mixed numbers and fractions.

RULES FOR MULTIPLYING TWO RATIONAL NUMBERS

If the signs of the factors are the same, the product is positive.

(+) • (+) = (+)

(–) • (–) = (+)

If the signs of the factors are different, the product is negative.

(+)•(–)=(–)

(–)•(+)=(–)

–8 • 6

7

–48

7

6 7

–6

Multiply. Write the answer in simplest form.

6 7

A.

–8

Multiply

Simplify

2 5

9(5) + 2 5

47 5

47 5

9

=

4

=

188 5

3 5

37

Try This: Example 1B

Multiply. Write the answer in simplest form.

2 5

9

4

B.

Multiply

Simplify

1(6) 8(7)

=

3

1(6) 8(7)

=

4

3 28

=

Additional Example 2A: Multiplying Fractions

Multiply. Write the answer in simplest form.

6 7

1 8

A.

Multiply numerators.

Multiply denominators.

Look for common factors: 2.

Simplest form

–2(9) 3(2)

=

–1

–2(9) 3(2)

3

=

1

1

–3

=

Additional Example 2B: Multiplying Fractions

Multiply. Write the answer in simplest form.

2 3

9 2

B.

–

Multiply numerators.

Multiply denominators.

Look for common factors: 2, 3.

Simplest form

3(5) 5(8)

=

1

3(5) 5(8)

=

1

3 8

=

Try This: Example 2A

Multiply. Write the answer in simplest form.

5 8

3 5

A.

Multiply numerators.

Multiply denominators.

Look for common factors: 5.

Simplest form

–7(4) 8(7)

=

–1

–7(4) 8(7)

1

=

1

2

1 2

= –

Try This: Example 2B

Multiply. Write the answer in simplest form.

4 7

7 8

B.

–

Multiply numerators.

Multiply denominators.

Look for common factors: 4, 7.

Simplest form

13(7) 5(9)

91 45

1 45

= or 2

Try This: Example 2C

Multiply. Write the answer in simplest form.

7 9

3 5

C.

2

Write as an improper fraction.

13 7

5 9

Multiply numerators.

Multiply denominators.

91 ÷ 45 = 2 R 1

1 8

Evaluate –3 x for the value of x.

18

18

–3 x

–3 (5)

–25 8

=

=

(5)

–125 8

=

5 8

= –15

Additional Example 4A: Evaluating Expressions with Rational Numbers

A. x = 5

Substitute 5 for x.

Write as an improper fraction.

–125 ÷ 8 = –15 R5

1 8

Evaluate –3 x for the value of x.

18

–3 x

18

2 7

27

=

–3

Substitute for x.

27

–25 8

=

–25 • 2

=

8 • 7

25 28

= –

Additional Example 4B: Evaluating Expressions with Rational Numbers Continued

2

B. x =

7

Write as an improper fraction.

1

Look for common factors: 2.

4

3 5

Evaluate –5 y for the value of y.

35

–5 y

6 7

Substitute for x.

67

35

=

–5

67

–28 5

=

–28 • 6

=

5 • 7

24 5

45

= –

, or – 4

Try This: Example 4A

67

A.

y =

Write as an improper fraction.

–4

Look for common factors: 7.

1

3 5

Evaluate –5 y for the value of y.

35

–5 y

35

=

–5 (3)

–28 5

(3)

=

–84 5

=

4 5

= –16

Try This: Example 4B

B. y = 3

Substitute 3 for y.

Write as an improper fraction.

–84 ÷ 5 = –16 R4

A number and its reciprocalhave a product of 1. To find the reciprocal of a fraction, exchange the numerator and the denominator. Remember that an integer can be written as a fraction with a denominator of 1.

2 5

2 5

1 3

1 3

2 15

2 15

÷

=

=

5 2

1 3

2 15

2•515 •2

Multiplication and division are inverse operations. They undo each other.

Notice that multiplying by the reciprocal gives the same result as dividing.

=

=

1 2

2 1

5 11

5 11

=

÷

•

2 1

5 11

=

•

10 11

=

Additional Example 1A: Dividing Fractions

Divide. Write the answer in simplest form.

1 2

5 11

A.

÷

Multiply by the reciprocal.

No common factors.

Simplest form

2 1

3 8

19 8

=

÷

÷

2

2

19 8

1 2

=

19 • 1

=

8 • 2

3 16

19 16

1

=

=

Additional Example 1B: Dividing Fractions

Divide. Write the answer in simplest form.

3 8

B.

2

2

÷

Write as an improper fraction.

Multiply by the reciprocal.

No common factors

19 ÷ 16 = 1 R 3

3 4

7 15

4 3

7 15

÷

=

•

7 • 4

=

28 45

15 • 3

=

Try This: Example1A

Divide. Write the answer in simplest form.

3 4

7 15

A.

÷

Multiply by the reciprocal.

No common factors.

Simplest form

22 5

3 1

2 5

4

÷ 3

÷

=

22 5

1 3

=

22 • 1

=

5 • 3

22 15

7 15

1

= or

Try This: Example1B

Divide. Write the answer in simplest form.

2 5

4

3

B.

÷

Write as an improper fraction.

Multiply by the reciprocal.

No common factors.

22 ÷ 15 = 1 R 7

5 1

5 4

4 5

•

=

1 4

254

=

5 • 5

6

=

=

1 • 4

Additional Example 3B: Evaluating Expressions with Fractions and Decimals

Evaluate the expression for the given value of the variable.

4 5

B.

k ÷ for k = 5

5÷

9 1

7 4

4 7

=

÷

9

9 • 7

=

1 • 4

3 4

=

15

Try This: Example 3B

Evaluate the expression for the given value of the variable.

4 7

B.

u ÷ , for u = 9

Write as in improper fraction and multiply by the reciprocal.

No common factors.

63 ÷ 4 = 15 R 3

Assignment

Pg 124 5-12