Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 7: Ratios, Proportions, and Percentages 89

Changing ratios to percentages is like changing fractions to a common denominator. Percentages
make it easier to compare different ratios, because they express everything as a part of 100.

When you need to change a ratio to a percentage, take your ratio, like^1520 , and set it equal to

the ratio P
100

. You’re saying 15 is to 20 as P is to 100, or 15 out of 20 is the same as P out of 100.

That’s a percentage. Use cross-multiplying to find P.

So 15 out of 20 is 75 percent.

The rule you want to remember is “part is to whole as percent is to 100” or
part
whole

%

100

. This

proportion can be used to solve almost all percent problems. Percentage problems come in three
basic types. One type asks a question like “what is 45 percent of 250?” The second type asks “15
is 30 percent of what number?” and the third is “29 is what percentage of 58?” The first type asks
you to find the part, the second asks you to find the whole, and the last asks for the percentage.

Suppose your town requires that a candidate receive at least 51% of the vote to be elected mayor.
If the population of the town is 1,288, what is the minimum number of votes a candidate must
receive to be elected?

You know the percentage and the whole, and you’re looking for the part of the population that
is required for election. Start with
part
whol e

%

100

 or p

1288

51

100

. Cross-multiply, and you’ll find that

the product of the means is 1,288 v 51 = 65,688 and the product of the extremes is 100p. The
product of the means is equal to the product of the extremes, so 100p = 65688, and dividing by
100 tells you p = 656.88. (Since no one can cast a fraction of a vote, round this to 657 votes.)

WORLDLY WISDOM

When you use the

part

whole

%

(^5100) rule, the important part is getting the numbers in the
right positions. Certain words in the problem can signal this for you. The word “of”
usually precedes the whole amount, and the word “is” can generally be found near the
part. Some people remember the rule as
is
of
%
100
(^5).
15
20 100
20 P 1,500
1,500
20
75
P
P