Basic Mathematics for College Students

Determine whether proportions are true or false.

Since a proportion is an equation, a proportion can be true or false. A proportion is
true if its ratios (or rates) are equal and false if it its ratios (or rates) are not equal.
One way to determine whether a proportion is true is to use the fraction simplifying
skills of Chapter 3.

2

5.2 Proportions 429

EXAMPLE (^1) Write each statement as a proportion.
a.22 is to 6 as 11 is to 3.
b.1,000 administrators is to 8,000 teachers as 1 administrator is to 8 teachers.
StrategyWe will locate the word asin each statement and identify the ratios (or
rates) before and after it.
WHYThe word astranslates to the = symbol that is needed to write the statement
as a proportion (equation).
Solution
a.This proportion states that two ratios are equal.



b.This proportion states that two rates are equal.

1,000 administrators is to8,000 teachers as1 administrator is to8 teachers



When proportions involve rates, the units are often written outside of the
proportion, as shown below:

=

Administrators

 Teachers

1 

8

1,000

8,000

Administrators 

Teachers

1 administrator

8 teachers

1,000 administrators

8,000 teachers

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩ ⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩

11

3

22

6

⎧⎪⎨⎪⎩ ⎧⎪⎨⎪⎩

Recall that the word “to”is used to

separate the numbers being compared.

22 is to 6 as 11 is to 3.

Self Check 1

Write each statement as a

proportion.

a.16 is to 28 as 4 is to 7.

b.300 children is to 500

adults as 3 children is to

5 adults.

Now TryProblems 17 and 19

EXAMPLE (^2) Determine whether each proportion is true or false by
simplifying.
a. b.
StrategyWe will simplify any ratios in the proportion that are not in simplest
form. Then we will compare them to determine whether they are equal.
WHYIf the ratios are equal, the proportion is true. If they are not equal, the
proportion is false.
Solution
a.On the left side of the proportion , the ratio is in simplest form. On the
right side, the ratio can be simplified.
Since the ratios on the left and right sides of the proportion are equal, the
proportion is true.
Factor 21 and 56 and then remove the common
factor of 7 in the numerator and denominator.

21

56



3  7

1

7

1

 8



3

8

21

56

3

8

3

8 

21

56

30

4



45

12

3

8



21

56

Self Check 2

Determine whether each

proportion is true or false

by simplifying.

a. b.

Now TryProblem 23

30

24



28

16

4

5



16

20