Basic Mathematics for College Students

We can translate percent sentences to percent

equations and solve to find the base.

Caution!Sometimes the calculations to solve a

percent problem are made easier if we write the

percent as a fraction instead of a decimal.This is

the case with percents that have repeating

decimal equivalents such as , , and

16 23 %.

33 13 % 66 23 %

is of

8.2 x Translate.

Now, solve the percent equation.

Write the percent as a fraction:.

To isolate xon the right side of the equation, divide

both sides by. Then remove the common factor of

in the numerator and denominator.

On the left side, the fraction bar indicates division.

On the left side, write 8.2 as a fraction. Then use the

rule for dividing fractions: Multiply by the reciprocal of

, which is.

Do the multiplication.

Thus, 8.2 is 33 13 %of 24.6.

24.6x

31 31

8.2

1



3

1

x

8.2

1

3

x

31 31

8.2

1

3



1

3

1

x

1

3

1

8.2 33 31 % 31

1

3

x

33 13 %

8.2 33 13 % what number?

574 Chapter 6 Percent

Percent sentences involve a comparison of

numbers. The relationship between the base

(the standard of comparison, the whole), the

amount(a part of the base), and the percent is:

or

Partpercentwhole

Amountpercentbase

is of

Amount percent base

(part) (whole)

8 12.5% 64.

The percent equation method

We can translate percent sentences to percent

equations and solve to find the amount.

Caution! When solving percent equations,

always write the percent as a decimal (or

fraction) before performing any calculations.

is of

x  45%  120 Translate.

Now, solve the percent equation.

Write 45% as a decimal.

Do the multiplication.

Thus, 54 is 45% of 120.

x 54

x0.45 120

What number 45% 120?

We can translate percent sentences to percent

equations and solve to find the percent.

is of

12  x  192 Translate.

Now, solve the percent equation.

To isolate xon the right side of the equation, divide

both sides by 192. Then remove the common factor

of 192 in the numerator and denominator.

On the left side, divide 12 by 192.

To write 0.0625 as a percent, multiply it by 100 by

moving the decimal point two places to the right,

and then insert a % symbol.

Thus, 12 is 6.25% of 192.

06.25%x

0.0625x

12

192



x 192

1

192

1

12 x 192

12 what percent 192?