Check the root.
The root checks.
Ratio and Proportion
One of the most important applications of fractional equations is ratio and proportion. A ratio
is a comparison of two like quantities by division. It is written by separating the quantities by
a colon or by writing them as a fraction. To write a ratio, the two quantities compared must be
of the same kind. For example, the ratio of to is written as : or
. Two unlike
quantities cannot be compared by a ratio. For example, 1 inch and 30 minutes cannot form a
ratio. However, two different units can be compared by a ratio if they measure the same kind
of quantity. For example, 1 minute and 30 seconds can form a ratio, but they must first be
converted to the same units. Since 1 minute equals 60 seconds, the ratio of 1 minute to 30
seconds is written 60 seconds:30 seconds, or
, which equals 2:1 or 2.
A proportion is a statement of equality between two ratios. For example, if a car travels 40 miles
in 1 hour and 80 miles in 2 hours, the ratio of the distance traveled is 40 miles:80 miles, or
, and the ratio of time is 1 hour:2 hours, or
. The proportion relating these
two ratios is:
40 miles:80 miles = 1 hour:2 hours
A proportion consists of four terms. The first and fourth terms are called the extremes of the
proportion; the second and third terms are called the means. If the letters a, b, c and d are used
to represent the terms in a proportion, it can be written in general form.