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RATIO

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A ratio is a comparison of two quantities.

Ratios can be written in several ways. 7

to 5, 7:5, and name the same ratio.7 5

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Additional Example 1: Writing Ratios in Simplest Form

Write the ratio 15 bikes to 9 skateboards in simplest form.

159

53

The ratio of bikes to skateboards is , 5:3, or 5 to 3.

=

15 ÷ 39 ÷ 3

Write the ratio as a fraction.

= = Simplify.

53

bikesskateboards

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Check It Out! Example 1

Write the ratio 24 shirts to 9 jeans in simplest form.

249

83

The ratio of shirts to jeans is , 8:3, or 8 to 3.

=shirtsjeans

24 ÷ 39 ÷ 3

Write the ratio as a fraction.

= = Simplify.

83

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When simplifying ratios based on measurements, write the quantities with the same units, if possible.

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Write the ratio 3 yards to 12 feet in simplest form.

First convert yards to feet.

9 feet12 feet

=3 yards12 feet

34

=9 ÷ 312 ÷ 3

=

There are 3 feet in each yard.

Additional Example 2: Writing Ratios Based on Measurement

3 yards = 3 ● 3 feet

= 9 feet Multiply.

Now write the ratio.

Simplify.

The ratio is , 3:4, or 3 to 4.34

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Write the ratio 36 inches to 4 feet in simplest form.

First convert feet to inches.

36 inches48 inches

=36 inches4 feet

34

=36 ÷ 1248 ÷ 12

=

There are 12 inches in each foot.

Check It Out! Example 2

4 feet = 4 ● 12 inches

= 48 inches Multiply.

Now write the ratio.

Simplify.

The ratio is , 3:4, or 3 to 4.34

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Ratios that make the same comparison are equivalent ratios. Equivalent ratios represent the same point on the number line. To check whether two ratios are equivalent, you can write both in simplest form.

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Additional Example 3: Determining Whether Two Ratios Are Equivalent

Simplify to tell whether the ratios are equivalent.

1215

B. and 2736

327

A. and 218

Since ,

the ratios are

equivalent.

19

= 19

19

=3 ÷ 327 ÷ 3

327

=

19

=2 ÷ 218 ÷ 2

218

=

45=

12 ÷ 315 ÷ 3

1215

=

34=

27 ÷ 936 ÷ 9

2736

=

Since ,

the ratios are not

equivalent.

45 3

4

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Check It Out! Example 3

Simplify to tell whether the ratios are equivalent.

1449

B. and 1636

Since ,

the ratios are

equivalent.

15

= 15

15

=3 ÷ 315 ÷ 3

315

=

15

=9 ÷ 945 ÷ 9

945

=

27

=14 ÷ 749 ÷ 7

1449

=

49=

16 ÷ 436 ÷ 4

1636

=

Since ,

the ratios are not

equivalent.

27 4

9

315

A. and 945

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Additional Example 4: Earth Science Application

At 4°C, four cubic feet of silver has the same mass as 42 cubic feet of water. At 4°C, would 20 cubic feet of silver have the same mass as 210 cubic feet of water?

4 ÷ 242 ÷ 2

?= 20 ÷ 10210 ÷ 10

221

= 221

442

?= 20210

Since ,

210 cubic feet of water would have the same mass at 4°C as 20 cubic feet of silver.

221

= 221

Divide.

Simplify.

ft3 silverft3 water

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Check It Out! Example 4

At 4°C, two cubic feet of silver has the same mass as 21 cubic feet of water. At 4°C, would 105 cubic feet of water have the same mass as 10 cubic feet of silver?

?= 10 ÷ 5105 ÷ 5

221

221

= 221

221

?= 10105

Since ,

105 cubic feet of water would have the same mass at 4°C as 10 cubic feet of silver.

221

= 221

Divide.

ft3 silver ft3 water

Simplify.

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COMPARISON BETWEEN RATIOS AND RATE

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