11/30/09 multiply & divide fractions #1

11/30/09 Multiply & Divide Fractions #1LT: I will learn to multiply and divide mixed numbers and fractions.

Today’s Plan:-Fraction, Decimal, Percent Wheel game-Lesson-Assignment

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

Fraction, Decimal, Percent Wheels

1. Circle all fractions that are in lowest terms.2. Review the conversions & decorate your

wheel.

11/30/09 Multiply & Divide Fractions #1LT: I will learn to multiply and divide mixed numbers and fractions.

Today’s Plan:-Fraction, Decimal, Percent Wheel game-Lesson-Assignment

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

Fraction, Decimal, Percent Wheels

11/30/09 Multiply & Divide Fractions #1LT: I will learn to multiply and divide mixed numbers and fractions.

Today’s Plan:-Fraction, Decimal, Percent Wheel game-Lesson-Assignment

Learning Target: 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

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

Multiply. Write the answer in simplest form.

Multiply

Simplify

–48 7

–6 6 7

–8 • 6 7

A.

4 2 5

Multiply

Simplify 37 3 5

47 5

4

188 5

9

9(5) + 2 5

= =2 5

9 47 5

Try This: Example 1B

B.

Multiply. Write the answer in simplest form.

1(6) 8(7)=

Multiply. Write the answer in simplest form.

6 7

Simplest form3 28

=

1 8

=1(6) 8(7)

Multiply numerators.

Multiply denominators.

Look for common factors: 2.3

4

Additional Example 2A: Multiplying Fractions

A.

–2(9) 3(2)=

=–2(9) 3(2)

3

1

Simplest form–3=

Multiply numerators.

Multiply denominators.

Look for common factors: 2, 3.

9 2

2 3

–

1

–1

Additional Example 2B: Multiplying Fractions

B.

Multiply. Write the answer in simplest form.

3(5) 5(8)=

Multiply. Write the answer in simplest form.

5 8

Simplest form3 8

=

3 5

=3(5) 5(8)

Multiply numerators.Multiply denominators.

Look for common factors: 5.1

1

Try This: Example 2A

A.

–7(4) 8(7)=

=–7(4) 8(7)

1

2

Simplest form

Multiply numerators.Multiply denominators.

Look for common factors: 4, 7.

4 7

7 8

–

1

–1

1 2= –

B.

Multiply. Write the answer in simplest form.

Try This: Example 2B

7 9

3 5

2C.

Multiply. Write the answer in simplest form.

Try This: Example 2C

Multiply numerators. Multiply denominators.

Write as an improper fraction.

13(7) 5(9)

91 ÷ 45 = 2 R 1 = or 291 45

1 45

13 75 9

A. x = 5

Evaluate –3 x for the value of x.1 8

Substitute 5 for x.

–3 x 18

–125 8

=

= –15 5 8

–125 ÷ 8 = –15 R5

Additional Example 4A: Evaluating Expressions with Rational Numbers

–25 8

= (5)

–3 (5) 18=

Write as an improper fraction.

–25 • 2 8 • 7

=

= – 25 28

27

Write as an improper fraction.

Substitute for x.2 7

1

4

27

Additional Example 4B: Evaluating Expressions with Rational Numbers Continued

B. x = –3 x 18

27

–25 8=

–3= 18

Look for common factors: 2.

Evaluate –3 x for the value of x.1 8

A. y =

–28 • 6 5 • 7=

67

Write as an improper fraction.

1

–4

–28 5

= 67

35–5= 6

7

–5 y 35

Try This: Example 4A

Look for common factors: 7.

= – 24 5 , or – 4 4

5

Evaluate –5 y for the value of y.3 5

Substitute for x.6 7

B. y = 3

Substitute 3 for y.

–5 y 35

–84 5=

= –16 4 5

–84 ÷ 5 = –16 R4

–28 5= (3)

Try This: Example 4B

Evaluate –5 y for the value of y.3 5

Write as an improper fraction.

35–5 (3)=

A number and its reciprocal have 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.

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

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

1 3

2 5

2 15

= 2 5

=÷2 15

1 3

= 1 3=

2 • 5 15 • 2

5 2

2 15

Additional Example 1A: Dividing Fractions

Divide. Write the answer in simplest form.

Multiply by the reciprocal.

5 11

÷ 1 2

5 11

•2 1

=

No common factors.

5 11

÷ 1 2

10 11=

A.

Simplest form

5 11

•2 1

=

Additional Example 1B: Dividing Fractions

Divide. Write the answer in simplest form.

B. 3 8

÷ 22

3 8

÷ 22 = 19 8

2 1÷ Write as an improper fraction.

Multiply by the reciprocal.

No common factors

= 19 8

1 2

19 • 18 • 2

=

3 16

=1 19 ÷ 16 = 1 R 319 16=

7 15

÷ 3 4

7 15

• 4 3

=7 15

÷ 3 4

28 45

=

Try This: Example1A

Divide. Write the answer in simplest form.

A.

Multiply by the reciprocal.

No common factors.

Simplest form

7 • 415 • 3

=

Write as an improper fraction.

2 5 ÷

Multiply by the reciprocal.

34

22 • 15 • 3

= No common factors.

22 ÷ 15 = 1 R 7

2 5 ÷ 34 = 22

53 1÷

B.

Divide. Write the answer in simplest form.

= 22 5

1 3

7 15= or 122

15

Try This: Example1B

k ÷ for k = 54 5

5 ÷ 5 4

= 5 1

•4 5

1 46

B.

5 • 51 • 4

= == 254

Additional Example 3B: Evaluating Expressions with Fractions and Decimals

Evaluate the expression for the given value of the variable.

u ÷ , for u = 9

Write as in improper fraction and multiply by the reciprocal.

9 • 71 • 4

= No common factors.

4 7

63 ÷ 4 = 15 R 3

= 9 19 ÷ 4

7

= 3 415

7 4

B.

Try This: Example 3B

Evaluate the expression for the given value of the variable.

Assignment

Pg 124 5-12