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3-5. Multiplying Decimals. Course 1. Warm Up. Problem of the Day. Lesson Presentation. 3-5. Multiplying Decimals. Course 1. Warm Up Multiply. 1. 87  320. 27,840. 2. 943  800. 754,400. 3. 3,806  10. 38,060. 4. 1,207  100. 120,700. 5. 72  196. 14,112.

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3-5

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3-5

Multiplying Decimals

Course 1

Warm Up

Problem of the Day

Lesson Presentation

3-5

Multiplying Decimals

Course 1

Warm Up

Multiply.

1.87  320

27,840

2. 943  800

754,400

3. 3,806  10

38,060

4. 1,207  100

120,700

5. 72  196

14,112

6. 120  523

62,760

3-5

Multiplying Decimals

Course 1

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

3-5

Multiplying Decimals

Course 1

Learn to multiply decimals by whole numbers and by decimals.

3-5

Multiplying Decimals

Course 1

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.

4  0.17

17

Multiply as you would with whole numbers.

 4

68

3-5

Multiplying Decimals

Course 1

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?

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

0.17

2 decimal places

 4

+ 0 decimal places

0.68

2 decimal places

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

3-5

Multiplying Decimals

Course 1

Check It Out: Example 1

Something that weighs 1 lb on Earth weighs 0.17 lb on the Moon. How much would a 7 lb dumbbell weigh on the Moon?

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

7  0.17

17

Multiply as you would with whole numbers.

 7

119

3-5

Multiplying Decimals

Course 1

Check It Out: Example 1 Continued

Something that weighs 1 lb on Earth weighs 0.17 lb on the Moon. How much would a 7 lb dumbbell weigh on the Moon?

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

0.17

2 decimal places

 7

+ 0 decimal places

1.19

2 decimal places

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

3-5

Multiplying Decimals

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

Course 1

3-5

Multiplying Decimals

Multiply. Then place the decimal point.

1 decimal place

+ 1 decimal place

2 decimal places

Course 1

Additional Example 2A: Multiplying a Decimal by a Decimal

Find the product.

0.3  0.4

0.3

0.4

0.12

3-5

Multiplying Decimals

Multiply. Then place the decimal point.

2 decimal places

+ 1 decimal place

3 decimal places; use a placeholder zero

Estimate the product. 0.8 is close to 1.

Course 1

Additional Example 2B: Multiplying a Decimal by a Decimal

0.07  0.8

0.07  1 = 0.07

0.07

 0.8

0.056

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

3-5

Multiplying Decimals

2 decimal places

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

Multiply. Then place the decimal point.

3 decimal places

+ 1 decimal place

Course 1

Additional Example 2C: Multiplying a Decimal by a Decimal

1.34  2.5

1  3 = 3

1.34

2.5

670

2680

3.350

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

3-5

Multiplying Decimals

Multiply. Then place the decimal point.

1 decimal place

+ 1 decimal place

2 decimal places

Course 1

Check It Out: Example 2A

Find the product.

0.5  0.2

0.5

0.2

0.10

3-5

Multiplying Decimals

Multiply. Then place the decimal point.

2 decimal places

+ 1 decimal place

3 decimal places; use a placeholder zero

Estimate the product. 0.9 is close to 1.

Course 1

Check It Out: Example 2B

0.03  0.9

0.03  1 = 0.03

0.03

0.9

0.027

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

3-5

Multiplying Decimals

2 decimal places

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

Multiply. Then place the decimal point.

3 decimal places

+ 1 decimal places

Course 1

Check It Out: Example 2C

3.80  3.3

4  3 = 12

3.80

3.3

1140

11400

12.540

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

3-5

Multiplying Decimals

Remember!

These notations all mean multiply 3 times x.

3 •x3x3(x)

3 decimal places

+ 0 decimal places

3 decimal places

Substitute 3.062 for x.

Course 1

Additional Example 3A: Evaluating Decimal Expressions

Evaluate 5x for the value of x.

x = 3.062

5x = 5(3.062)

3.062

5

15.310

3-5

Multiplying Decimals

2 decimal places

+ 0 decimal places

2 decimal places

Substitute 4.79 for x.

Course 1

Additional Example 3B: Evaluating Decimal Expressions

Evaluate 5x for the value of x.

x = 4.79

5x = 5(4.79)

4.79

5

23.95

3-5

Multiplying Decimals

3 decimal places

+ 0 decimal places

3 decimal places

Substitute 2.012 for x.

Course 1

Check It Out: Example 3A

Evaluate 5x for the value of x.

x = 2.012

5x = 5(2.012)

2.012

5

10.060

3-5

Multiplying Decimals

2 decimal places

+ 0 decimal places

2 decimal places

Substitute 6.22 for x.

Course 1

Check It Out: Example 3B

Evaluate 5x for the value of x.

x = 6.22

5x = 5(6.22)

6.22

5

31.10

3-5

Multiplying Decimals

Course 1

Insert Lesson Title Here

Lesson Quiz

Find each product.

1. 0.8

2. 0.006  0.07

Evaluate 8x for each value of x.

 0.07

0.056

0.00042

3.x = 2.7054.x = 0.804

6.432

21.64

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

\$87.40