2-6 ratios and proportions

2-6 Ratios and Proportions

Algebra 1 Glencoe McGraw-Hill Linda Stamper

A ratio is a comparison of two quantities measured in the same unit.

1210

students girlstudents boy

You can write a ratio in different ways.65

The order of the numbers in a ratio is very important. The first number in a ratio always names the quantity mentioned first.

5 to 6 5 : 6 65

A ratio compares

two quantities

by division!

An equation that states that two ratios are equal is a proportion.

0dandb where dc

ba

Cross Product PropertyIf two ratios are equal then their cross products are

also equal.

84

21

8 8

Determine whether each pair of ratios forms a proportion. Write yes or no (must show support work).

4.17.0

8.04.0

56.0 56.0

yes

2824

86

168 192

Determine whether each pair of ratios forms a proportion. Write yes or no (must show support work).

225.1

6.025.0

50.0 75.0

no

Example 1

Example 2

no

Solve the proportion.245

y10Write the cross products.

2410Multiply.

y5240 Solve

y48

Check

245

y10

24510

240

5y

5 5 240Do the

arithmetic work off to the side or

make a separate

column for this work!

48

When a proportion involves a variable, solving for the variable is called solving the proportion.

Solve the proportion.245

y10Write the cross products.

Multiply.Solve

You can not cross cancel through an equal sign.

//

5

125y125 y560

y12

245

y10

24510

60240

Check

5 5 12

Example 3

64

9x

6x36x6

6 6 6x

49

Solve the proportion. If necessary, round to the nearest hundredth.

You can simplify a fraction before you use cross products.

64

9x

32

9x

x3 3 3

6x

18

Example 4

14.07.

y5.1

07.y14.5.1

y07.210. 07 . 07 .

y3

Do the arithmetic work off to the side or make a separate column for this

work! 0.217210.07.

Example 5

n6.2

42.3

6.24n2.3

4.10n2.3 .23 .23

25.3n

Example 6

41x

125

4512x1220

21 21 x3

2

1x12

Solve the proportion. Example

775

72r

5772r

3514r7 14 14

3r

Example 8

62x

73

2x763

14x718

7 7 x7

32

1212x128 21r7

1414x732

7 7

Mrs. Jones travels 140 miles in 2.5 hours. At this rate, how far will she travel in 4 hours?

Start with a word ratio. 5.2

140

m5.24140

m5.2560

hoursmiles

Mrs. Jones will travel 224 miles in 4 hours.

4

.52 .52 m224

m

Write a proportion for the problem. Then solve.

Mrs. Jones travels 140 miles in 2.5 hours. At this rate, how long will it take her to travel 224 miles?

Write word ratio. 5.2140

2245.2h140

560h140

hoursmiles

Mrs. Jones will travel 224 miles in 4 hours.

h

401 401 4h

224

Example 9 A mechanic charged $92 for 4 hours of work. At this rate, how much will be charged for 6 hours?Example 10 Mr. Green used 3 gallons of paint to cover 1,350 sq ft. At this rate, how much paint will be needed to cover 1,800 sq. ft.?Example 11 The ratio of football players to cheerleaders in the NFL is 48 to 6. If there are 1,440 football players, how many cheerleaders are there?Example 12 Sue, the speed reader, can read 12 pages in 4.5 minutes. At that rate, how many pages will she read in 60 minutes?

Write a proportion for each problem. Then solve.

Example 9 The mechanic will charge $138 for 6 hours of work.Example 10 Mr. Green will need 4 gallons of paint.Example 11 There are 180 cheerleaders.Example 12 Sue will read 160 pages.

Example 9 A mechanic charged $92 for 4 hours of work. At this rate, how much will be charged for 6 hours?

492

d4692

d4552

hoursdollars

The mechanic will charge $138 for 6 hours of work.

6d

4 4 d138

Do the arithmetic work off to the side

or make a separate

column for this work!

Write a word ratio.

Sentence.

Example 10 Mr. Green used 3 gallons of paint to cover 1,350 sq ft. At this rate, how much paint will be needed to cover 1,800 sq. ft.?Write word ratio. 350,1

3

g350,1800,13

g350,1400,5

.ft .sqgallons

Mr. Green will need 4 gallons of paint.

800,1g

,3501 ,3501 g4

Example 11 The ratio of football players to cheerleaders in the NFL is 48 to 6. If there are 1,440 football players, how many cheerleaders are there?Write word ratio. 6

48

440,16c48

640,8c48

rscheerleadeplayers

There are 180 cheerleaders.

c440,1

84 84 180c

Example 12 Sue, the speed reader, can read 12 pages in 4.5 minutes. At that rate, how many pages will she read in 60 minutes?

5.412

p5.46012

p5.4720

minutespages

Sue will read 160 pages.

60p

.54 .54 p160

2-A11 Pages 109-110 #9-33,41-48.