Evaluating Algebraic Expressions 2-4 Multiplying Rational Numbers Warm Up Write each number as an...

$: Evaluating Algebraic Expressions 2-4 Multiplying Rational Numbers Warm Up Write each number as an improper fraction. 1. 1 3 2 7 3 2. 7 8 1 15 8 3. 2 5.$
Evaluating Algebraic Expressions

2-4 Multiplying Rational Numbers

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



Warm Up

Hanna and Elizabeth drove to Niagara Falls

for vacation. Hannah drove miles and

Elizabeth drove 106.44 miles. How far did

they drive together?

34

98



1(6) 8(7)=

Multiply. Write the answer in simplest form.

6 7

Simplify.3 28

=

1 8

=1(6) 8(7)

Multiply numerators.

Multiply denominators.

Look for common factors: 2. 3

4

Additional Example 1A: Multiplying Fractions



–2(9) 3(2)=

=–2(9) 3(2)

3

1

Simplify.–3=

Multiply numerators.

Multiply denominators.

Look for common factors: 2, 3.

1 2

2 3

–

1

–1

Additional Example 1B: Multiplying FractionsMultiply. Write the answer in simplest form.

4

Write 4 as an improper fraction.12

1 2

2 3

– 4 9 2

2 3

–=



3(5) 5(8)=


5 8

Simplify.3 8

=

3 5

=3(5) 5(8)

Multiply numerators.Multiply denominators.

Look for common factors: 5.1

1

Partner Share! Example 1A



–7(4) 8(7)=

=–7(4) 8(7)

1

2

Simplify.

Multiply numerators.Multiply denominators.

Look for common factors: 4, 7.

4 7

7 8

–

1

–1

1 2= –


Partner Share! Example 1B



To multiply a fraction by an integer, first write the integer as a fraction with a denominator of 1. Then multiply as you would with two fractions.



Joy completes of her painting each day.

How much of her painting does she complete in a 7 day week?

Write the integer 7 as a fraction.

1 20

Additional Example 2: Application

=

(7) = 1 20

Multiply numerators and denominators.

1 20

71

1 • 7 20 • 1

= 7 20

Joy completes of her painting in a 7-day week. 7 20



Mark runs mile each day. What is the total

distance Mark runs in 5 days?

Write the integer 5 as a fraction.

1 7

Partner Share! Example 2

=

(5) = 1 7

Multiply numerators and denominators.

1 7

51

1 • 5 I7 • 1

= 5 7

Mark runs mile in 5 days. 5 7



To multiply decimals, first multiply as you would with integers. The number of decimal places in the product is equal to the sum of the number of decimal places in the factors.



Multiply.

0 decimal places2

B. (–0.4)(–3.75)

–3.75 0.4

Additional Example 3: Multiplying Decimals

A. 2(–0.51)

1.500

–0.51 2 decimal places–1.02 0 + 2 = 2 decimal places.

2 decimal places1 decimal place2 + 1 = 3 decimal places

or 1.5



Multiply.

1 decimal place3.1

B. (–0.4)(–2.53)

–0.4

–2.53

Partner Share! Example 3

A. 3.1(0.28)

1.012

0.28 2 decimal places0.868 1 + 2 = 3 decimal places

1 decimal place

2 decimal places1 + 2 = 3 decimal places



4. Evaluate 2 (x) for x = .

1.

Lesson Review!Multiply.

–1.034

2. 5 8

2 3

–

1 7

9

3. –0.47(2.2)

1 2 2

45

– 5 12

1 2 7

Edgar runs mile each day. What is the total distance that Edgar runs in a 7-day week?

5.8 9

6 miles2 9

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