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.

operation.

operation.

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)