Pre-Algebra

7-1 Ratios and Proportions7-1 Ratios and Proportions

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

7-1 Ratios and Proportions

Warm UpWrite each fraction in lowest terms.

Pre-Algebra

7-1 Ratios and Proportions

1416

1.

972

3.

2464

2.

45120

4.

78

38

18

38

Pre-Algebra

7-1 Ratios and Proportions

Problem of the Day

A magazine has page numbers from 1 to 80. What fraction of those page numbers include the digit 5?

1780

Pre-Algebra

7-1 Ratios and Proportions

Learn to find equivalent ratios to create proportions.

Pre-Algebra

7-1 Ratios and Proportions

Vocabulary

ratioequivalent ratioproportion

Pre-Algebra

7-1 Ratios and Proportions

Relative density is the ratio of the density of a substance to the density of water at 4°C. The relative density of silver is 10.5. This means that silver is 10.5 times as heavy as an equal volume of water.

The comparisons of water to silver in the table are ratios that are all equivalent.

42 g31.5 g21 g10.5 gSilver

4 g3 g2 g1 gWater

Comparisons of Mass of Equal Volumesof Water and Silver

Pre-Algebra

7-1 Ratios and Proportions

Ratios can be written in several ways. A colon is

often used. 90:3 and name the same ratio.

Reading Math

90 3

Pre-Algebra

7-1 Ratios and Proportions

A ratio is a comparison of two quantities by division. In one rectangle, the ratio of shaded squares to unshaded squares is 7:5. In the other rectangle, the ratio is 28:20. Both rectangles have equivalent shaded areas. Ratios that make the same comparison are equivalent ratios.

Pre-Algebra

7-1 Ratios and Proportions

Additional Example 1: Finding Equivalent Ratios

Find two ratios that are equivalent to each given ratio.

B.

1854

13

12848

83

A. =927

=9 • 227 • 2

=9 ÷ 927 ÷ 9

927

= Two ratios equivalent

to are and . 927

1854

13

Two ratios equivalent

to are and . 6424

12848

83

=64 • 224 • 2

=64 ÷ 824 ÷ 8

6424

=

6424

=

Multiply or divide the numerator and denominator by the same nonzero number.

Pre-Algebra

7-1 Ratios and Proportions

Try This: Example 1

Find two ratios that are equivalent to each given ratio.

B.

1632

24

6432

42

A. =816

=8 • 216 • 2

=8 ÷ 416 ÷ 4

816

= Two ratios equivalent

to are and . 816

1632

24

Two ratios equivalent

to are and . 3216

6432

42

=32 • 216 • 2

=32 ÷ 816 ÷ 8

3216

=

3216

=

Multiply or divide the numerator and denominator by the same nonzero number.

Pre-Algebra

7-1 Ratios and Proportions

Ratios that are equivalent are said to be proportional, or in proportion. Equivalent ratios are identical when they are written in simplest form.

Pre-Algebra

7-1 Ratios and Proportions

Additional Example 2: Determining Whether Two Ratios are in Proportion

Simplify to tell whether the ratios form a proportion.

1215

B. and 2736

327

A. and 218

Since ,

the ratios are in

proportion.

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

in proportion.

45 3

4

Pre-Algebra

7-1 Ratios and Proportions

Try This: Example 2

Simplify to tell whether the ratios form a proportion.

1449

B. and 1636

Since ,

the ratios are in

proportion.

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

in proportion.

27 4

9

315

A. and 945

Pre-Algebra

7-1 Ratios and Proportions

Additional Example 3: 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 210 cubic feet of water have the same mass as 20 cubic feet of silver?

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

Pre-Algebra

7-1 Ratios and Proportions

Try This: Example 3

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

Pre-Algebra

7-1 Ratios and Proportions

Lesson Quiz: Part 1

85

85

= ; yes

Find two ratios that are equivalent to each given ratio.

415

1.

821

2.

1610

3.

3624

4.

Simplify to tell whether the ratios form a proportion.

830

1245

Possible answer: ,

1642

2463

Possible answer: ,

and 32 20

and 28 18

32

149

; no

Pre-Algebra

7-1 Ratios and Proportions

Lesson Quiz: Part 2

5. Kate poured 8 oz of juice from a 64 oz bottle. Brian poured 16 oz of juice from a 128 oz bottle. What ratio of juice is missing from each bottle? Are the ratios proportional?

864

16128

and ; yes, both equal 1 8