1-2 Multiplying Rational Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

1-2 Multiplying Rational Numbers

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


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


Problem of the Day

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

55, 56, and 57


Learn to multiply fractions, mixed numbers, and decimals.


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



–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


2 1 3

Multiply.

Simplify. 10 2 3

16 3 2

32 3

5

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

3


Additional Example 1B: Multiplying a Fraction and an Integer


–3 5 8


Multiply.

Simplify.

–15 8

–1 7 8

–3 • 5 8

Check It Out: Example 1A


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



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

Caution!


1(6) 8(7)


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


–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



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

Check It Out: Example 2A


–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 –


Check It Out: Example 2B


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


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.


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


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


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


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


1. Multiply.

8

A. 1 C. 2

B. 1 D. 8


2 5

3 5

4 5

1 5

1 5


2. Multiply.

–

A. – C. –

B. – D. –


7 12

5 12

7 18

5 18

7 9

3 4


3. Multiply.

–0.39(3.2)

A. –1.238

B. –1.248

C. –1.428

D. –1.842



4. Sam cycles mile each day. What is the

total distance that Sam cycles in 5 days?

A. 7 miles C. 6 miles

B. 6 miles D. 4 miles


7 8

3 8

3 8

7 8

1-2 Multiplying Rational Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

Documents