Course 3

2-4 Multiplying Rational Numbers

2-4 Multiplying Rational Numbers

Course 3

Warm Up

Problem of the Day

Lesson Presentation

Course 3

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

Course 3

2-4 Multiplying Rational Numbers

Problem of the Day

The sum of three consecutive integers is 168. What are the three integers?

55, 56, and 57

Course 3

2-4 Multiplying Rational Numbers

Learn to multiply fractions, mixed numbers, and decimals.

Course 3

2-4 Multiplying Rational Numbers

Notice that multiplying a fraction by a whole number is the same as multiplying the whole number by just the numerator of the fraction and keeping the same denominator.

1 4

3 4

1 4

+ + =

Repeated addition

1 4 3 3

4= =

Multiplication3 • 1

414

Course 3

2-4 Multiplying Rational Numbers

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.

(+) • (+) = (+) or (–) • (–) = (+)

(+) • (–) = (–) or (–) • (+) = (–)

Course 3

2-4 Multiplying Rational Numbers

–8 6 7

Multiply. Write the answer in simplest form.

Multiply.

Simplify.

–48 7

=

–6 6 7

=

–8 • 6 7

=

To write as a mixed

number, divide:

Helpful Hint

–48 7

–487 = –6 R6

6 7= –6

Additional Example 1A: Multiplying a Fraction and an Integer

Course 3

2-4 Multiplying Rational Numbers

2 1 3

Multiply.

Simplify. 10 2 3=

16 3=2

32 3=

5

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

3

Multiply. Write the answer in simplest form.

Additional Example 1B: Multiplying a Fraction and an Integer

Course 3

2-4 Multiplying Rational Numbers

–3 5 8

Multiply. Write the answer in simplest form.

Multiply.

Simplify.

–15 8

=

–1 7 8

=

–3 • 5 8

=

Check It Out: Example 1A

Course 3

2-4 Multiplying Rational Numbers

4 2 5

Multiply.

Simplify. 37 3 5

=

47 5

= 4

188 5

=

9

9(5) + 2 5

= =2 5

9 47 5

Check It Out: Example 1B

Multiply. Write the answer in simplest form.

Course 3

2-4 Multiplying Rational Numbers

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

Caution!

Course 3

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 2A: Multiplying Fractions

Course 3

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.

9 2

2 3

–

1

–1

Additional Example 2B: Multiplying Fractions

Multiply. Write the answer in simplest form.

Course 3

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 2A

Course 3

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 2B

Course 3

2-4 Multiplying Rational Numbers

Multiply.

Product is negative with 2 decimal places.

2 • (–0.51) = –1.02

B. (–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. 2(–0.51)

00

Course 3

2-4 Multiplying Rational Numbers

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

Check It Out: Example 3

A.

B.

Course 3

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 as an improper fraction.

1 20

Additional Example 4: Application

=

(7) = 1 20

Multiply.

1 20

71

1 • 7 20 • 1

= 7 20

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

Course 3

2-4 Multiplying Rational Numbers

Mark runs mile each day. What is the total

distance Mark runs in a 5-day week?

Write as an improper fraction.

1 7

Check It Out: Example 4

=

(5) = 1 7

Multiply.

1 7

51

1 • 5 I7 • 1

= 5 7

Mark runs mile in a 7-day week. 5 7

Course 3

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