Math Review 3 Ratio Proportion

Topics: United States dollar, Income tax in the United States, Currency Pages: 46 (1999 words) Published: December 7, 2014
Contemporary Business
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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