Student Progress Chart

Lesson Reflection

3-6

Math Learning Goal

Students will understand decimals.

Students will understand decimals by being able to do the following:

• Learn to write, compare, and order decimals using place value and number lines (3-1)

• Learn to estimate decimal sums, differences, products, and quotients (3-2)

• Learn to add and subtract decimals (3-3)• Learn to multiply and divide decimals by powers of ten and to

convert metric measurements (3-4)• Learn to write large numbers in scientific notation (3-5)

•Learn to multiply decimals by whole numbers and by decimals (3-6)

Today’s Learning Goal Assignment

Learn to multiply decimals by whole numbers and by decimals. Course 1

3-6 Multiplying Decimals

6th Grade Math HW

Page 122#10-25

Course 1

3-6 Multiplying Decimals

3-6 Multiplying Decimals

Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpMultiply.

27,840

754,400

38,060

Course 1

3-6 Multiplying Decimals

120,700

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

Course 1

3-6 Multiplying Decimals

Today’s Learning Goal Assignment

Learn to multiply decimals by whole numbers and by decimals. Course 1

3-6 Multiplying Decimals

Course 1

3-6 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?

4 0.17

0.17You can think of multiplication by a whole number as a repeated addition. 0.17

0.170.17+ _____0.68

Course 1

3-6 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?

You can also multiply as you would with whole numbers. Place the decimal point by adding the number of decimal places in the numbers multiplied.

0.17 4 _____0.68

2 decimal places + 0 decimal places

2 decimal places

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

Course 1

3-6 Multiplying Decimals

Try This: 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?

7 0.170.17 You can think of multiplication by a

whole number as a repeated addition.

0.170.170.17

+ _____1.19

0.170.17

0.17

Course 1

3-6 Multiplying Decimals

Try This: 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?

You can also multiply as you would with whole numbers. Place the decimal point by adding the number of decimal places in the numbers multiplied.

0.17 7 _____1.19

2 decimal places + 0 decimal places

2 decimal places

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

Course 1

3-6 Multiplying Decimals

Additional Example 2A: Multiplying a Decimal by a Decimal

Find the product.

A. 0.3 0.4Multiply. Then place the decimal point.

0.3

0.4

1 decimal place

+ 1 decimal place

2 decimal places 0.12

Course 1

3-6 Multiplying Decimals

Additional Example 2B: Multiplying a Decimal by a Decimal

B. 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.

Course 1

3-6 Multiplying Decimals

Additional Example 2C: Multiplying a Decimal by a Decimal

C. 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

Course 1

3-6 Multiplying Decimals

Try This: Example 2A

Find each product.

A. 0.5 0.2

Multiply. Then place the decimal point.

0.5

0.21 decimal place

+ 1 decimal place

2 decimal places 0.10

Course 1

3-6 Multiplying Decimals

Try This: Example 2B

B. 0.03 0.9

Multiply. Then place the decimal point.

0.03

0.9

2 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.

Course 1

3-6 Multiplying Decimals

Try This: Example 2C

C. 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

Course 1

3-6 Multiplying Decimals

Additional Example 3A: Evaluating Decimal Expressions

Evaluate 5x for each value of x.

A. 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!

Course 1

3-6 Multiplying Decimals

Additional Example 3B: Evaluating Decimal Expressions

B. x = 4.79

4.79

5

2 decimal places

+ 0 decimal places

2 decimal places 23.95

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

Course 1

3-6 Multiplying Decimals

Try This: Example 3A

Evaluate 5x for each value of x.

A. x = 2.012

2.012

5

3 decimal places

+ 0 decimal places

3 decimal places 10.060

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

Course 1

3-6 Multiplying Decimals

Try This: Example 3B

B. 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)

Lesson QuizFind each product.

1. 0.8

2. 0.006 0.07

Evaluate 8x for each value of x.

0.000420.056

Insert Lesson Title Here

21.64 6.432

Course 1

3-6 Multiplying Decimals

0.07

$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?