3-5 Multiplying Decimals Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

3-5 Multiplying Decimals

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson Quizzes


Warm UpMultiply.

27,840

754,400

38,060120,700

14,112

62,760

1. 87 320

2. 943 800

3. 3,806 10

4. 1,207 100

5. 72 196

6. 120 523


Problem of the Day

Carmen and Rita sold homemade oatmeal cookies. After 8 days, they had sales totaling $70. Each day, their sales were $0.50 higher than the previous day. What were their sales on the first day?

$7.00


Learn to multiply decimals by whole numbers and by decimals.


Additional Example 1: Science Application

Something that weighs 1 lb on Earth weighs 0.17 lb on the Moon. How much would a 4 lb dumbbell weigh on the Moon?

Multiply 4 by 0.17, since 1 pound on Earth is 0.17 pound on the Moon.

17 4

68

Multiply as you would with whole numbers.

4 0.17


Additional Example 1 Continued


0.17 40.68

Place the decimal point by adding the number of decimal places in the numbers multiplied.

A 4 lb dumbbell on Earth weighs 0.68 lb on the Moon.

2 decimal places+ 0 decimal places

2 decimal places


Check It Out: Example 1


Multiply 7 by 0.17, since 1 pound on Earth is 0.17 pound on the Moon.

17 7119

Multiply as you would with whole numbers.

7 0.17


Check It Out: Example 1 Continued


0.17 71.19

Place the decimal point by adding the number of decimal places in the numbers multiplied.

A 7 lb dumbbell on Earth weighs 1.19 lb on the Moon.

2 decimal places+ 0 decimal places

2 decimal places


You can use a decimal grid to model multiplication of decimals.

Helpful Hint


Additional Example 2A: Multiplying a Decimal by a Decimal

Find the product.

0.3 0.4

Multiply. Then place the decimal point.

0.3

0.4

1 decimal place

+ 1 decimal place

2 decimal places 0.12


Additional Example 2B: Multiplying a Decimal by a Decimal

0.07 0.8


0.07 0.8

2 decimal places + 1 decimal place3 decimal places; use a placeholder zero

0.056

Estimate the product. 0.8 is close to 1.

0.07 1 = 0.07

0.056 is close to the estimate of 0.07. The answer is reasonable.


Additional Example 2C: Multiplying a Decimal by a Decimal

1.34 2.5


1.34

2.52 decimal places

+ 1 decimal place

3 decimal places

670

Estimate the product. Round each factor to the nearest whole number.

1 3 = 3

3.350 is close to the estimate of 3. The answer is reasonable.

26803.350


Check It Out: Example 2A

Find the product.

0.5 0.2


0.5

0.21 decimal place

+ 1 decimal place



Check It Out: Example 2B

0.03 0.9


0.03

0.92 decimal places

+ 1 decimal place3 decimal places; use a placeholder zero

0.027

Estimate the product. 0.9 is close to 1.

0.03 1 = 0.03

0.027 is close to the estimate of 0.03. The answer is reasonable.


Check It Out: Example 2C

3.80 3.3


3.80

3.32 decimal places

+ 1 decimal places

3 decimal places

1140

Estimate the product. Round each factor to the nearest whole number.

4 3 = 12

12.54 is close to the estimate of 12. The answer is reasonable.

1140012.540


Additional Example 3A: Evaluating Decimal Expressions

Evaluate 5x for the value of x.

x = 3.062

3.062

53 decimal places

+ 0 decimal places

3 decimal places15.310

Substitute 3.062 for x. 5x = 5(3.062)

These notations all mean multiply 3 times x.

3 • x 3x 3(x)

Remember!


Additional Example 3B: Evaluating Decimal Expressions


x = 4.79

4.79

52 decimal places

+ 0 decimal places




Check It Out: Example 3A


x = 2.012

2.012

53 decimal places

+ 0 decimal places




Check It Out: Example 3B


x = 6.22

6.22

52 decimal places

+ 0 decimal places




Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson QuizFind each product.

1. 0.8 0.07

2. 0.006 0.07

Evaluate 8x for each value of x.0.00042

0.056

21.64 6.432

$87.40

3. x = 2.705 4. x = 0.804

5. “Pick your own” peaches sell for $0.95 per pound. You picked 92 pounds of peaches. How much were you charged?


1. Identify the product.

0.29 0.01

A. 0.29

B. 0.029

C. 0.0029

D. 0.00029



2. Identify the product.

0.052 0.03

A. 1.0056

B. 0.1056

C. 0.0156

D. 0.00156



3. Evaluate 4x for x = 5.325.

A. 21

B. 21.2

C. 21.28

D. 21.3



4. Evaluate 9x for x = 0.012.

A. 10.8

B. 1.08

C. 0.108

D. 0.0108



5. Strawberry lemonade costs $0.89 per packet. Karen bought 58 packets of strawberry lemonade for a picnic. How much did she pay for it?

A. $51.62

B. $51.86

C. $52.54

D. $52.93


3-5 Multiplying Decimals Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

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