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3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals Estimating & Multiplying Decimals

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Page 1: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Estimating & Multiplying Decimals

Page 2: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

MA.6.A.1.2 Multiply…decimals efficiently.

MA.6.A.1.3 Solve real-world problems involving multiplication…of…decimals.

Also MA.6.A.1.1

Sunshine State Standards

Page 3: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Reading Decimal Place Value

How would you say the following decimals?

0.3

Page 4: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Reading Decimal Place Value

How would you say the following decimals?

0.3 three tenths

Page 5: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Reading Decimal Place Value

How would you say the following decimals?

0.3 three tenths

0.27

Page 6: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Reading Decimal Place Value

How would you say the following decimals?

0.3 three tenths

0.27 twenty-seven hundredths

Page 7: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Reading Decimal Place Value

How would you say the following decimals?

0.3 three tenths

0.27 twenty-seven hundredths

5.238

Page 8: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Reading Decimal Place Value

How would you say the following decimals?

0.3 three tenths

0.27 twenty-seven hundredths

5.238 five and two hundred

thirty-eight thousandths

Page 9: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

How do you determine place value for decimals?

Page 10: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

How do you determine place value for decimals?

When in doubt, place a one under the

decimal and a zero for each digit past the

decimal.

Page 11: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

How do you determine place value for decimals?

When in doubt, place a one under the

decimal and a zero for each digit past the

decimal.

0.375

Page 12: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

How do you determine place value for decimals?

When in doubt, place a one under the

decimal and a zero for each digit past the

decimal.

0.375

1

Page 13: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

How do you determine place value for decimals?

When in doubt, place a one under the

decimal and a zero for each digit past the

decimal.

0.375

1000

Page 14: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

How do you determine place value for decimals?

When in doubt, place a one under the

decimal and a zero for each digit past the

decimal.

0.375

1000

Read the whole number on top and the

number you see on the bottom as a “spit

number”

Page 15: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

How do you determine place value for decimals?

When in doubt, place a one under the

decimal and a zero for each digit past the

Decimal. 0.375

1000

Read the whole number on top and the

number you see on the bottom as a “spit

number” –

three hundred seventy-five thousandths

Page 16: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

How do you read the following decimals?

3.78

Page 17: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

How do you read the following decimals?

3.78 three and seventy-eight

hundredths

Page 18: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

How do you read the following decimals?

3.78 three and seventy-eight

hundredths

2.003

Page 19: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

How do you read the following decimals?

3.78 three and seventy-eight

hundredths

2.003 two and three thousandths

Page 20: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Model the following decimals:

0.18

Page 21: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Model the following decimals:

0.18

Page 22: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Model the following decimals:

0.18 · 3

Page 23: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Model the following decimals:

0.18 · 3

Page 24: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Model the following decimals:

0.18 · 3 = 0.54

Page 25: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Model the following decimal

0.3

Page 26: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Model the following decimal

0.3

Page 27: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Model the following decimals

0.3 · 0.70

Page 28: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Model the following decimals

0.3 · 0.70

Page 29: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Model the following decimals

0.3 · 0.70 = 0.21

Page 30: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying 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

Page 31: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Additional Example 1 Continued

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?

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

Page 32: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

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.

17 7119

Multiply as you would with whole numbers.

7 0.17

Page 33: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

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?

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

Page 34: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

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

Page 35: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Estimating Decimals

Page 36: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Estimating Decimals

Page 37: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

ClusteringWhat is clustering?

When would you use clustering to estimate the solution to a problem involving decimals?

Page 38: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

ClusteringNancy wants to cycle, ice skate, and water ski for

30 minutes each. About how many calories will

she burn in all? (Cycling – 165.5 calories, ice

skating – 177.5 calories, and water skiing – 171.5

calories.)

In this example , why would each of the three

addends (numbers being added) be rounded to

170? What operation could you use rather than

adding 170 plus 170 plus 170?

Page 39: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

RoundingWhen rounding a decimal, how do you know

which digit to look at?

Explain the rules for rounding a decimal.

If you rounded all the numbers “up”, how would your estimated answer compare to the actual answer to the problem?

Page 40: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Compatible NumbersWhat is a compatible number?

Given the expression 33.83 · 1.98, how does the estimated product compare to the actual product? Explain.

Given the expression 72.77 ÷ 26.14, why would you choose not to round the numbers to 73 and 26?

What would you use?

Page 41: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Estimating Decimals

Page 42: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Additional Example 2B: Multiplying a Decimal by a Decimal

0.07 0.8

Multiply. Then place the decimal point.

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.

Page 43: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Additional Example 2C: Multiplying a Decimal by a Decimal

1.34 2.5

Multiply. Then place the decimal point.

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

Page 44: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Check It Out: Example 2A

Find the product.

0.5 0.2

Multiply. Then place the decimal point.

0.5

0.21 decimal place

+ 1 decimal place

2 decimal places 0.10

Page 45: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Check It Out: Example 2B

0.03 0.9

Multiply. Then place the decimal point.

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.

Page 46: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Check It Out: Example 2C

3.80 3.3

Multiply. Then place the decimal point.

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

Page 47: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

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!

Page 48: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Additional Example 3B: Evaluating Decimal Expressions

Evaluate 5x for the value of x.

x = 4.79

4.79

52 decimal places

+ 0 decimal places

2 decimal places 23.95

Substitute 4.79 for x. 5x = 5(4.79)

Page 49: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Check It Out: Example 3A

Evaluate 5x for the value of x.

x = 2.012

2.012

53 decimal places

+ 0 decimal places

3 decimal places 10.060

Substitute 2.012 for x. 5x = 5(2.012)

Page 50: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Check It Out: Example 3B

Evaluate 5x for the value of x.

x = 6.22

6.22

52 decimal places

+ 0 decimal places

2 decimal places 31.10

Substitute 6.22 for x. 5x = 5(6.22)

Page 51: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Lesson Quiz

Find 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?

Page 52: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Page 53: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

1. Identify the product.

0.29 0.01

A. 0.29

B. 0.029

C. 0.0029

D. 0.00029

Lesson Quiz for Student Response Systems

Page 54: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

2. Identify the product.

0.052 0.03

A. 1.0056

B. 0.1056

C. 0.0156

D. 0.00156

Lesson Quiz for Student Response Systems

Page 55: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

3. Evaluate 4x for x = 5.325.

A. 21

B. 21.2

C. 21.28

D. 21.3

Lesson Quiz for Student Response Systems

Page 56: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

4. Evaluate 9x for x = 0.012.

A. 10.8

B. 1.08

C. 0.108

D. 0.0108

Lesson Quiz for Student Response Systems

Page 57: 3-4 Multiplying Decimals Estimating & Multiplying Decimals

3-4 Multiplying Decimals

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

Lesson Quiz for Student Response Systems