Name

Chapter 9 ⎜ Lesson 8 465

9.89.8Compare Compare Factors and Factors and ProductsProductsLearning Target:Learning Target: Compare a product to each of its factors. Compare a product to each of its factors.

Success Criteria:Success Criteria: • I can determine whether a number is less than, greater than, • I can determine whether a number is less than, greater than,

or equal to 1.or equal to 1.• I can compare a product to each of its factors.• I can compare a product to each of its factors.• I can explain why a product is less than, greater than, or • I can explain why a product is less than, greater than, or

equal to each of its factors.equal to each of its factors.

Explore and Grow

Without calculating, order the rectangles by area from least to greatest. Explain your reasoning.

Construct Arguments Explain your strategy to your partner. Compare your strategies.

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Think and Grow: Understand Multiplicative Comparison

466

Think and Grow: Compare Factors and Products

Without calculating, tell whether the product is less than, greater than,or equal to each of its factors.

Show and GrowShow and GrowSSShhhhhhhhoowwwwww aannnndddddddd GGGrrrrrrroowwwwwwwSSSSSSSShhhhhhhhoooooooowwwwwwww aaaaaaaannnnnnnndddddddd GGGGGGGGrrrrrrrroooooooowwwwwwwwShow and GrowShow and Grow

Example Without calculating, tell whether the product 3 1 — 8

× 5 — 6

is less than, greater than, or equal to each of its factors.

Because 3 1

— 8

1, the product 3 1

— 8

× 5 — 6

is 5

— 6

.

Because 5 — 6

1, the product 3 1

— 8

× 5 — 6

is 3 1

— 8

.

Example Without calculating, tell whether the product

5

— 3

× 2 — 2

is less than, greater than, or equal to each of its factors.

Because 5 — 3

1, the product 5 — 3

× 2 — 2

is 2 — 2

.

Because 2 — 2

1, the product 5 — 3

× 2 — 2

is 5 — 3

.

1. 1. 8 × 3 — 10

2. 2. 4 — 4

× 5 2 — 3

3. 3. 4 — 3

× 1 — 6

Key Idea When you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.

5

— 3

× 2

— 2

= 5 × 2 — 3 × 2

= 10 — 6

shows you that

5 — 3

and 10 — 6

are equivalent. You canthink of this as multiplying by 1.

5 — 3

× 2 — 2

= 5 — 3

× 1

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467Chapter 9 ⎜ Lesson 8

Name

Apply and Grow: Practice

Without calculating, order the products from least to greatest.

Without calculating, tell whether the product is less than, greater than, or equal to each of its factors.

4. 4. 1 — 4

× 1 — 12

7. 7. 2 — 3

× 5

5. 5. 3 4 — 5

× 6 7 — 8

8. 8. 7 — 10

× 4 8 — 9

6. 6. 1 — 6

× 10 — 10

9. 9. 9 — 2

× 1 3 — 4

10. 10. 5 — 6

× 1 8 — 9

5

— 6

× 1 — 3

5

— 6

× 7 — 7

11. 11. 1 — 6

× 1 — 4

1

— 10

× 1 — 4

5 7

— 10

× 1 — 4

12. 12. Your

friend says that 1

— 2

× 8 is half as much

as 8. Is your friend correct? Explain.

13. 13. DIG DEEPER Without calculating, tell whether the product is less than,

greater than, or equal to 3 3 — 4

. Explain.

( 1 — 2 × 3 3 — 4 ) × 2 — 7

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Think and Grow: Modeling Real Life

468

wwo oowo wwowwwwwwwwrrrrrorrrrrrrr GGGGGw annnndhhhhhhhhoww a dddddddowwwwwwwwhhhhhohSSSS ow nd GGrrowGGGGGGGGrrrrrrrroooooooowwwwwwwwGGGGGGGGrrrrrrrroooooooowwwwwwwwaaaaaaaannnnnnnndddddddd aaaaaaaannnnnnnnddddddddSSSSSSSShhhhhhhhoooooooowwwwwwwwSSSSSSSShhhhhhhhoooooooowwwwwwwwS rShow and GrowShow and Grow14. 14. You practice playing the keyboard

for 3 1

— 2

hours. Your friend practices

playing the keyboard for 5

— 4

as many

hours as you. Does your friend practice for fewer hours, more hours, or the same number of hours as you?

16. 16. DIG DEEPER The Abraj Al-Bait Clock Tower is 6 — 10

kilometer tall.

Zifeng Tower is 3

— 4

as tall as the clock tower. Is Zifeng Tower shorter

than, taller than, or the same height as the Abraj Al-Bait Clock Tower? What is the height of each tower in meters?

15. 15. The original price of a telescope is $99.

The sale price is 4

— 5

of the original price.

An astrologist buys the telescope at its sale price and uses a half-off coupon. What fraction of the original price does the astrologist pay for the telescope?

Example Men’s shot put competitions use a shot with a mass of 7 1 —

4 kilograms. The mass of a bowling ball is 7 —

8 as much as the

mass of the shot. Is the mass of the bowling ball less than, greater than, or equal to the mass of the shot?

Write an expression to represent the mass of the bowling ball.

The mass of the bowling ball is 7 — 8

as much as the mass

of the shot, so multiply the mass of the shot by 7 — 8

.

7 1

— 4

× 7 — 8

Use the factor 7 — 8

to compare the masses.

Because 7 — 8

1, the product 7 1 — 4

× 7 — 8

is 7 1 — 4

.

So, the mass of the bowling ball is the mass of the shot.

Shot put is a track and fi eld throwing event that uses a heavy metal ball

called a shot.

You can also say that the

mass of the shot is times

as much as the mass of the bowling ball.

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Homework & Practice

Name 9.89.8

Learning Target:Learning Target: Compare a product to each Compare a product to each of its factors.of its factors.

469Chapter 9 ⎜ Lesson 8

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Example Without calculating, tell whether the product 1 — 3

× 6 — 7

is less than, greater than, or equal to each of its factors.

Because 1

— 3

< 1, the product 1

— 3

× 6 — 7

is 6

— 7

.

Because 6

— 7

< 1, the product 1

— 3

× 6 — 7

is 1 — 3

.

Without calculating, tell whether the product is less than, greater than, or equal to each of its factors.

Without calculating, order the products from least to greatest.

1. 1. 1 3 — 4

× 6

4. 4. 3 4 — 5

× 2 9 — 10

7. 7. 1 — 3

× 4 — 5

1

— 3

× 6 — 6

1

— 3

× 8 2 — 9

2. 2. 5 — 12

× 1 — 6

5. 5. 8 × 2 — 3

8. 8. 2 1 — 2

× 3 — 5

4 × 3 — 5

1

— 12

× 3 — 5

3. 3. 2 — 7

× 5 — 5

6. 6. 1 7 — 8

× 1 — 4

less than

less than

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470

Review & Refresh

Compare.

15. 15. 13.90 13.9 16. 16. 32.006 32.0614. 14. 40.5 40.13

12. 12. Modeling Real Life You snowboard

1 7 — 8

miles. Your friend snowboards 3 2

— 3

times as far as you. Does your friendsnowboard fewer miles, more miles, or the same number of miles as you?

9. 9. Logic Without calculating, use >,