Basic Mathematics for College Students

 

 

Solve a proportion to find an unknown term.

Suppose that we know three of the four terms in the following proportion.

In mathematics, we often let a letter represent an unknown number. We call such a

letter a variable.To find the unknown term, we let the variable xrepresent it in the

proportion and we can write:

If the proportion is to be true, the cross products must be equal.

Find the cross products for and set them equal.

To simplify the right side of the equation, do the

multiplication:.

On the left side of the equation, the unknown number xis multiplied by 20. To

undo the multiplication by 20 and isolate x, we divide both sides of the equation by 20.

We can simplify the fraction on the left side of the equation by removing the

common factor of 20 from the numerator and denominator. On the right side, we

perform the division indicated by the fraction bar.

Since the product of any number and 1 is that number, it follows that the

numerator on the left side can be replaced by x.

Since the quotient of any number and 1 is that number, it follows that on the left

side of the equation can be replaced with x. Therefore,

x 6

x

1

x

1

 6

x 1

To simplify the left side of the equation, remove the common

factor of 20 in the numerator and denominator.

To simplify the right side of the equation, do the division: 120 20 6.

x 20

1

20

1

 6

x 20

20



120

20

5  24  120

x 20  120

x

5 

24

x 20  5  (^2420)
x
5



24

20

?

5



24

20

3

432 Chapter 5 Ratio, Proportion, and Measurement

Self Check 5

Determine whether 6, 11 and

54, 99 are proportional.

Now TryProblem 37

EXAMPLE (^5) Determine whether 3, 7 and 36, 91 are proportional.
StrategyWe will use the given pairs of numbers to write two ratios and form a
proportion. Then we will find the cross products.
WHYIf the cross products are equal, the proportion is true, and the numbers are
proportional. If the cross products are not equal, the proportion is false, and the
numbers are not proportional.
Solution
The pair of numbers 3 and 7 form one ratio and the pair of numbers 36 and 91 form
a second ratio. To write a proportion, we set the ratios equal. Then we find the cross
products.
One cross product is 273 and the other is 252.
Since the cross products are not equal, the numbers are not proportional.

3

7



36

91

3  91  273 7  36  252