Name 4.14.1Multiplication Multiplication

PatternsPatternsLearning Target:Learning Target: Find products involving multiples of 10 Find products involving multiples of 10and powers of 10.and powers of 10.Success Criteria:Success Criteria: • I can explain how to multiply a number by a power of 10.• I can explain how to multiply a number by a power of 10.• I can explain how to find a product involving multiples of 10.• I can explain how to find a product involving multiples of 10.

Explore and Grow

Chapter 4 ⎜ Lesson 1 139

Complete the table. Find the value of each expression.

Patterns Explain how to multiply any number by a power of 10.

Power Expression Value

8 × 101

8 × 100

8 × 103

8 × 104

What patterns do you notice?

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Think and Grow: Understand Multiplicative ComparisonThink and Grow: Use Patterns to Find Products

140

Find the product.

1. 1. 78 × 104 = 2. 2. 20 × 400 =

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Example Find 46 × 103.

Example Find 40 × 600.

Use a multiplication fact and look for a pattern.

4 × 6 = 24 Multiplication fact

4 × 60 = 4 × (6 × 10) = (4 × 6) × 10 = 24 × 10 = 240

4 × 600 = 4 × (6 × 100) = (4 × 6) × 100 = 24 × 100 = 2,400

40 × 600 = (4 × 10) × (6 × 100) = (4 × 6) × (10 × 100) = 24 × 1,000 =

So, 40 × 600 = .

One Way: One Way: Use powers and look forUse powers and look fora pattern.a pattern.

46 × 101 = 46 × 10 = 460

46 × 102 = 46 × 100 = 4,600

46 × 103 = 46 × 1,000 =

Another Way: Another Way: Use place value.Use place value.

46 × 103 = 46 × 1,000

= 46 thousands

=

So, 46 × 103 = .

Notice the pattern: In each product, the number of zeros after 46 is the same as the exponent.

Notice the pattern: In each product, the number of zeros after 24 is equal to the number of zeros in the factors.

Remember, every time you multiply a number by 10, the number shifts one position to the left in a place value chart.

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Chapter 4 ⎜ Lesson 1 141

Name

Find the product.

Find the missing factor.

12. 12. A heart pumps about 2,000 gallons of blood each day. How many gallons of blood does the heart pump in 7 days?

13. 13. Number Sense Which expressions are equal to 24,000?

240 × 100 30 × 800

400 × 600 24 × 1,000

14. 14. Logic When you multiply any whole number by 100, what do you know about the digits in the product?

15. 15. DIG DEEPER Show how to find 20 × 103 using the Associative Property of Multiplication.

3. 3. 11 × 103 =

9. 9. 30 × = 15,000

6. 6. 104 × 60 =

4. 4. 40 × 70 =

10. 10. × 103 = 54,000

7. 7. 206 × 102 =

5. 5. 300 × 90 =

11. 11. 500 × = 40,000

8. 8. 15 × 200 =

Apply and Grow: Practice

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Think and Grow: Modeling Real Life

142

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about 300,000 guests each month. The attendance at a water park is 2,280,000 guests in 1 year. Which park has a greater attendance in 1 year?

18. 18. A whale’s brain weighs 103 times as much as a platypus’s brain. The whale’s brain weighs 9,000 grams. How many grams does theplatypus’s brain weigh?

17. 17. Your heart beats 120,000 times each day. In 1 week, a professional athlete’s heart beats 607,000 times. How many more times does your heart beat in 1 week compared to the athlete?

Example A black bear consumes 12,000 calories each day for 30 days. A grizzly bear consumes 400,000 calories in 30 days. Which bear consumes more calories in 30 days?

Multiply 12,000 and 30 to find the number of calories the black bear consumes in 30 days. Use a multiplication fact and a pattern.

12 × 3 = Multiplication fact

The multiplication fact is 12 × 3 = 36. The factors 12,000 and 30 have

a total of zeros. So, the product has zeros after 36.

12,000 × 30 =

The black bear consumes calories in 30 days.

Compare the numbers of calories the bears consume in 30 days.

The bear consumes more calories in 30 days.

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Name Homework & Practice 4.14.1

Learning Target:Learning Target: Find products involving Find products involving multiples of 10 and powers of 10.multiples of 10 and powers of 10.

143Chapter 4 ⎜ Lesson 1

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Example Find 125 × 103.

Use powers and look for a pattern.

125 × 101 = 125 × 10 = 1,250

125 × 102 = 125 × 100 = 12,500

125 × 103 = 125 × 1,000 =

So, 125 × 103 = .

Find the product.

1. 1. 37 × 104 =

4. 4. 800 × 700 =

2. 2. 400 × 90 =

5. 5. 867 × 103 =

3. 3. 100 × 900 =

6. 6. 12 × 6,000 =

125,000

125,000

Notice the pattern: In each product, the number of zeros after 125 is the same as the exponent.

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144

10. 10. Reasoning Do 50 × 8,000 and 50 × 9,000 have the same number of zeros in their products? Explain.

12. 12. Modeling Real Life A hummingbird flutters its wings 80 times in 1 second. A bumblebee flutters its wings 7,800 times in 1 minute. Which animal flutters its wings more times in 1 minute?

11. 11. DIG DEEPER The product of a number and twice that number is 180,000. Write the multiplication equation.

13. 13. DIG DEEPER In 1 day, the blood in your body travels a total of 12,000 miles. This is about 4 times the distance across the United States from coast to coast. About how many miles is the distance across the United States?

Review & Refresh

Classify the triangle by its sides.

15.15. 16.16.

Find the missing factor.

7. 7. × 102 = 3,000 8. 8. × 500 = 450,000 9. 9. 80 × = 640,000

14.14.

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