•
Multiply each term in the ratio by this quotient: $30 × 3 = $90; 30 × 4 = $120;
$30 × 5 = $150.
The money is divided thus: $90, $120, and $150.
To simplify any complicated ratio of two terms containing fractions, decimals, or percents, you only
need to divide the first term by the second. Reduce the answer to its lowest terms, and write the
fraction as a ratio. For example, simplify the ratio
5
6
7
8
:
.
Solving Proportion Problems
A proportion indicates the equality of two ratios. For example, 2:4 = 5:10 is a proportion. This is
read, “2 is to 4 as 5 is to 10.” The two outside terms (2 and 10) are the extremes, and the two inside
terms (4 and 5) are the means. Proportions are often written in fractional form. For example, the
proportion 2:4 = 5:10 can be written as
2
4
5
10
=
.
In any proportion, the product of the means equals the product of the extremes. If the proportion is
in fractional form, the products can be found by cross-multiplication. For example, in the proportion
2
4
5
10
=
, 4 × 5 = 2 × 10.
5
6
7
8
5
6
7
8
20
21
20
21
:
:
→
÷
=
=
Master the™ Civil Service Exams

Chapter 16: Percentages, Ratios, and Proportions
259
Many problems in which three terms are given and one term is unknown can be solved using pro-
portions. To solve such problems, follow these three steps:
1.
Formulate the proportion very carefully according to the facts given. (If any term is
misplaced, the solution will be incorrect.) Any symbol can be written in place of the
missing term.
2.
Determine by inspection whether the means or the extremes are known. Multiply the
pair that has both terms given.
3.
Divide this product by the third term given to find the unknown term.
Try this example problem:
The scale on a map shows that 2 centimeters represent 30 miles of actual length. What is
the actual length of a road that is represented by 7 centimeters on the map?
In this problem, the map lengths and the actual lengths are in proportion; that is, they have equal
ratios. If
m
stands for the unknown length, the proportion is
2
7
30
=
m
. As the proportion is written,
m
is an extreme and is equal to the product of the means, divided by the other extreme:
m
= 7 × 30 ÷ 2 = 210 ÷ 2 = 105.
Therefore, 7 cm on the map represent 105 miles.
It’s time to practice using the rules you’ve learned about ratios and proportions. Work through the
exercises carefully and then compare your answers with the answer keys and explanations that follow.

260
PART V: Arithmetic Ability
EXERCISE 1
Directions:
Choose the correct answer to the following ratio and proportion problems.
1.
The ratio of 24 to 64 is
A.
8:3
B.
24:100
C.
3:8
D.
64:100
2.
A football team won 8 games and lost 3.
The ratio of games won to games played is
A.
8:11
B.
3:11
C.
8:3
D.
3:8
3.
The ratio of
1
4
to
3
5
is
A.
1 to 3
B.
3 to 20
C.
5 to 12
D.
3 to 4
4.
If there are 16 boys and 12 girls in a class,
the ratio of the number of girls to the
number of children in the class is
A.
3 to 4
B.
3 to 7
C.
4 to 7
D.
4 to 3
5.
259 is to 37 as
A.
5 is to 1
B.
63 is to 441
C.
84 is to 12
D.
130 is to 19
Master the™ Civil Service Exams
SHOW YOUR WORK HERE

Chapter 16: Percentages, Ratios, and Proportions
261
exercises
EXERCISE 2
Directions:
Choose the correct answer to the following ratio and proportion problems.

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- Spring '18
- Peter Lee
- Physics, Federal government of the United States, Civil service, United States civil service