PART A - RATIOS AND PROPORTIONS
2-1. Defining Ratios and Proportions. You will find that a ratio can be expressed in four different
ways. For example, the side-slope ratio of 2-to-1 is normally used with soft clay. This ratio can be
expressed as follows: 2-to-1, 2:1, 2_1, or 2/1. The numbers 2 and 1, which are terms of the ratio, are
called the antecedent and the consequent, respectively. The antecedent is the same as the dividend or
numerator, and the consequent is the same as the divisor or denominator. Both terms of the ratio can be
multiplied or divided by the same number without changing the value of the ratio. In the ratio 12/3, for
example, the number 12 is divided by 3, giving the value of 4. This means that the ratio 12:3 is equal to
the ratio 4:1. Other examples are shown below.
Example 1: What is the ratio of 6:2? Set up the problem as a fraction, and perform the indicated
Solution: 6/2 = 3, or 3S1
Example 2: What is the ratio of 7:3? Set up the problem as a fraction, and perform the indicated
Solution: 7/3 = 2 1/3, or 2 1/3:1
a. A proportion is a statement of equality between two ratios. If the value of one ratio is equal
to the value of another ratio, they are said to be a proportion. For example, the ratio 3:6 is equal to the
ratio 4:8. Therefore, this relationship can be written in one of the following forms:
(1) 3:6 :: 4:8
(2) 3:6 = 4:8
(3) 3/6 = 4/8
b. In any proportion, the first and last terms are known as the extremes and the second and the
third terms are known as the means. If you look at the proportion example in the previous paragraph,
you note that the terms "3' and "8" are the extremes, while the terms "6" and "4" are the means.
c. When working proportions, you should remember that there are three rules which are used in
determining an unknown quantity. These rules can also be used to prove that the proportion is true.
(1) The first rule is that in any proportion the means' product equals the extremes' product.
See the following examples:
(a) 2:3 :: 6:9
(b) 2 x 9 = 18 (extremes' product)