Therefore, 0.2 = 2/9.
PERCENTAGE
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
n = 5.636363...
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%.
100n = 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.
RATIO AND PROPORTION
You can use ratio and proportion to solve problems
quickly and reduce the chances of error.
Ratio
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.
Proportion
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
