Therefore, 0.2 = 2/9.

Example: Convert 5.63 to a fraction and reduce to

Percentage is the expression of numbers in

lowest terms.

hundredths. The percent sign

is used to show

percentage. Three terms apply to percentage

Solution: Let

problems-- *base, rate, *and *percentage. *The base is the

number upon which a percent is calculated. The rate is

Multiply both sides by 100, since there are two

the amount of the percent. The percentage is the result

repeating digits.

of the calculations made with the base and rate. For

example, 2% of 5.00 equals .50. The rate is 2%.

100*n *= 563.636363...

The base is 5.00. The percentage is .50.

Subtract the original equation from the new equation.

Percentage is calculated as a decimal fraction.

Therefore, the rate must be a decimal fraction. For

example, 2% and 25% are equal to 2/100 and 25/100,

respectively. Convert these to 0.02 and 0.25,

respectively. Write a rate of 100% as 1.00, 225% as

Solve for *n *and reduce to lowest terms.

2.25, and so on.

You can use ratio and proportion to solve problems

quickly and reduce the chances of error.

Hence, 5.63 = 57/11.

For the previous problem we could have kept the

A ratio is a method of comparing two numbers or

integer portion as an integer and converted the repeating

values in fractional form. For example, a fast frigate

decimal to a fraction.

has a top speed of 30 knots and a cargo ship has a top

speed of 15 knots. You can easily compare their speeds.

Example: Convert -38.054 to a fraction and reduce

This comparison can be written as 30:15 and 30/15.

to lowest terms.

This makes the fractional form easier to calculate. To

Solution: We will retain -38 and work with .

simplify the comparison, you reduce the fraction 30/15

to its simplest form of 2/l. Now, you can use this

fraction form of a comparison very easily when

calculating.

Comparison by a ratio is limited to quantities of the

same kind. To express the ratio between 6 feet and 3

yards, both quantities must be in like terms. The proper

Therefore, -38.054 = -38 2/37.

forms of this ratio would be either 2 yards:3 yards or 6

feet:9 feet. Mathematically, like terms cancel each

Example: Convert -12.637 to a fraction.

other. The yards or feet would cancel each other and

Solution:

the resulting ratio would read 2:3 or 6:9.

Closely related to the study of ratio is the subject

of proportion. The term *proportion *is defined as a

relation of equality. A proportion is nothing more than

an equation of two ratios that are equal to each other.

Hence, -12.637 = -12 631/990.

Proportion can be written in three different ways, as

shown in the following examples:

Example 1: 15:20::3:4

14-6