11/18-19 Multiply Fractions & Decimals #42 LT: I will learn to multiply mixed numbers, fractions, and decimals. Today’s Plan: -Warm up & correct homework.

11/18-19 Multiply Fractions & Decimals #42LT: I will learn to multiply mixed numbers, fractions, and decimals.

Today’s Plan:-Warm up & correct homework-Lesson-Assignment

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

Warm UpWrite each number as an improper fraction.

1. 13

2 73

2. 78

1 15 8

3. 25

3 17 5

4. 23

6 203

5. 38

5 438

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.

2 1 3

Multiply

Simplify 10 2 3

16 32

32 3

5

5(3) + 1 3= =1 35 16

3

Multiply. Write the answer in simplest form.

B.

–3 5 8

Multiply. Write the answer in simplest form.

Multiply

Simplify

–15 8

–1 7 8

–3 • 5 8

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.

A model of is shown. Notice that to multiply fractions, you multiply the numerators and multiply the denominators.

3 5 • 2

3

35

•

•

=

= 6 15

23

If you place the first rectangle on top of the second, the number of green squares represents the numerator, and the number of total squares represents the denominator.

To simplify the product, rearrange the six green squares into the first two columns. You can see that this is .2

5

=

= 2 5

6 15

A fraction is in lowest terms, or simplest form, when the numerator and denominator have no common factors.

Helpful Hint

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.

Multiply numerators. Multiply denominators.

1 2

3 7

4

Write as an improper fraction.

= 31(1) 7(2)

31 ÷ 14 = 2 R3 = or 231 14

3 14

Additional Example 2C: Multiplying Fractions

C.

Multiply. Write the answer in simplest form.

1 2

3 7

4 = 31 17 2

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

7 9

3 5

2 = 13 75 9

2(–0.51)

Multiply.

Product is negative with 2 decimal places.

2 • (–0.51) = –1.02

(–0.4)(–3.75)Product is positive with 3 decimal places.

(–0.4) • (–3.75) = 1.500

You can drop the zeros after the decimal point.

= 1.5

Additional Example 3: Multiplying Decimals

A.

B.

00

3.1 (0.28)

Multiply.

Product is positive with 3 decimal places.

3.1 • (0.28) = 0.868

(–0.4)(–2.53)Product is positive with 3 decimal places.

(–0.4) • (–2.53) = 1.012

Try This: Example 3

A.

B.

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)=

4. Evaluate 2 (x) for x = .

1.

Lesson Quiz: Part 1

Multiply.

–1.034

2. 5 8

2 3

–

1 7

9

3. –0.47(2.2)

1 2 24

5

– 5 12

1 2 7

Assignment

Pg 124

18-24 even and 36-56 even