# Math Review 3 Ratio Proportion

**Topics:**United States dollar, Income tax in the United States, Currency

**Pages:**46 (1999 words)

**Published:**December 7, 2014

Mathematics With Canadian Applications

Tenth Edition

S. A. Hummelbrunner • Kelly Halliday • K. Suzanne Coombs PowerPoint Presentation by P. Au

Math Review 3

Ratio, Proportion,

and Percent

Copyright © 2015 Pearson Canada Inc.

03-1

Objectives

After completing chapter three, the

student will be able to:

❶ Use ratios and proportions to solve allocation and

equivalence problems

❷ Convert percents, common fractions, and decimals

❸ Find percents and percent bases to solve business

problems.

❹ Find rates and original quantities for increase and

decrease problems

Copyright © 2015 Pearson Canada Inc.

03-2

Objectives

After completing chapter three, the

student will be able to:

❺ Use proportions and currency cross rate

tables to convert currency

❻ Use index numbers and the Consumer Price

Index to compute purchasing power of the

Canadian dollar

❼ Use federal income tax brackets and tax

rates to calculate federal income taxes

Copyright © 2015 Pearson Canada Inc.

03-3

Ratios

• A ratio is a comparison of the relative values

of numbers or quantities

• When two or more ratios are equivalent, a

proportion equating the ratios can be set up

• Business information is often based on a

comparison of related quantities stated in the

form of a ratio

Copyright © 2015 Pearson Canada Inc.

03-4

Ratios

• Can be written in the following ways:

(a) by using the word “to,” such as in “5 to 2”;

(b) by using a colon, such as in “5 : 2”;

(c) as a common fraction, such as “5/2”;

(d) as a decimal, such as “2.50”;

(e) as a percent, such as “250%.”

• When comparing more than two numbers or quantities, using the colon is preferred

– 5 kg : 3 kg : 2 kg we usually drop the units of measure

–5:3:2

– The numbers appearing in a ratio are called the terms of the ratio Copyright © 2015 Pearson Canada Inc.

03-5

Reducing Ratios to Lowest Terms

• The procedure used to reduce ratios to lowest

terms is the same as that used to reduce fractions

to lowest terms

• When a ratio is expressed by an improper fraction

that reduces to a whole number, the denominator

“1” must be written to indicate that two quantities

are being compared

80 : 35 = (16 x 5) : (7 x 5) = 16 : 7 (5 is a common factor) 81 : 54 : 27 = (3 x 27) : (2 x 27) : (1 x 27) = 3 : 2 : 1

Copyright © 2015 Pearson Canada Inc.

03-6

Equivalent Ratios in Higher Terms

• Multiply each term of a ratio by the same

number

• Higher-term ratios are used to eliminate

decimals from the terms of a ratio

• 1.25 : 3.75 : 7.5

= 125 : 375 : 750

= (1 x 125) : (3 x 125) : (6 x 125)

=1:3:6

Copyright © 2015 Pearson Canada Inc.

03-7

Allocation Involving Ratios

• Allocate 660 in the ratio of 3:2

Method A

Method B

Total Number of Parts is

Total

of Parts is

3 + 2 Number

=5

3+2=5

Total Number of Parts is

Total

of Parts is

3 + 2 Number

=5

3+2=5

Value of Each Part is

660 ÷ 5 = 132

Value of Each Part is

3

x 132

660

÷ 5 = 396

132

2 x 132 = 264

3 x 132 = 396

2 x 132 = 264

Copyright © 2015 Pearson Canada Inc.

03-8

Proportions

• When

two ratios are equal, they form a

proportion

• 2:3 = 4:6

• x:5 = 7:35

are proportions

– If one of the four terms is unknown, the

proportions form a linear equation in one variable

Copyright © 2015 Pearson Canada Inc.

03-9

Proportions

• Solve the proportion 2 : 5 = 8 : x

Original Form

Simplified

technique

called cross

multiplication

Change to

fractional form

and multiply by

the LCD 5x

Copyright © 2015 Pearson Canada Inc.

03-10

Proportions

• If your car can travel 385 km on 35 L of

gasoline, how far can it travel on 24 L?

– Let the distance travelled on 24 L be n km

Known ratio

Copyright © 2015 Pearson Canada Inc.

03-11

The Meaning of Percent

• The easiest method of comparing the two

quantities is to use fractions with denominator

100

– The preferred form of writing such fractions is...

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