Evaluating Algebraic Expressions

2-4 Multiplying Rational Numbers

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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

Evaluating Algebraic Expressions

2-4 Multiplying Rational Numbers

NS1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.

California Standards

Evaluating Algebraic Expressions

2-4 Multiplying Rational Numbers

Evaluating Algebraic Expressions

2-4 Multiplying Rational Numbers

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

Evaluating Algebraic Expressions

2-4 Multiplying Rational Numbers

–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

–=

Evaluating Algebraic Expressions

2-4 Multiplying Rational Numbers

3(5) 5(8)=

Multiply. Write the answer in simplest form.

5 8

Simplify.3 8

=

3 5

=3(5) 5(8)

Multiply numerators.Multiply denominators.

Look for common factors: 5.1

1

Check It Out! Example 1A

Evaluating Algebraic Expressions

2-4 Multiplying Rational Numbers

–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= –

Multiply. Write the answer in simplest form.

Check It Out! Example 1B

Evaluating Algebraic Expressions

2-4 Multiplying Rational Numbers

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.

Evaluating Algebraic Expressions

2-4 Multiplying Rational Numbers

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

Evaluating Algebraic Expressions

2-4 Multiplying Rational Numbers

Mark runs mile each day. What is the total

distance Mark runs in 5 days?

Write the integer 5 as a fraction.

1 7

Check It Out! 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

Evaluating Algebraic Expressions

2-4 Multiplying Rational Numbers

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.

Evaluating Algebraic Expressions

2-4 Multiplying Rational Numbers

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

Evaluating Algebraic Expressions

2-4 Multiplying Rational Numbers

Multiply.

1 decimal place3.1

B. (–0.4)(–2.53)

–0.4

–2.53

Check It Out! 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

Evaluating Algebraic Expressions

2-4 Multiplying Rational Numbers

4. Evaluate 2 (x) for x = .

1.

Lesson QuizMultiply.

–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