The value of the ratio on the right must always equal the value of the ratio on the left. A
proportion may be written with the double colon, or proportion sign (::), or with the sign
of equality (=).
2:5 :: 4:10
2 = 4
a. Parts of a Proportion. In a proportion, there are four numbers. The two
middle numbers are known as MEANS and the two end numbers are known as
(1) Example: You find a 10-ml vial of Aminophylline in supply labeled "25 mg
per ml." Thus, there are 250 mg of drug in this 10-ml vial.
25 mg = 250 mg
(2) Notice that when you multiply the two extremes and the two means, the
products are equal. For example: 25 x 10 = 250 x 1.
25 10 = 250
Multiply the extremes:
1 250 = 250
Multiply the means:
RULE: In a proportion, the product of the means is always
equal to the product of the extremes.
b. Solving Problems with Proportions. Using the above rule of proportion
and knowing the value of three parts of a proportion, then the fourth unknown part, call it
"X," can be found. When confronted with a calculation, use the following steps to solve
(1) Step 1. State problem in "if-then" form.
(2) Step 2. Convert the problem to an equation.
(a) Known information (labeled strength, and so forth) should be your IF
(b) The unknown ratio including X will be your THEN ratio.
(c) Put like units on the same side of each ratio. (For example, if the left
side of the equation is expressed in mg/ml, then the right side must also be expressed
(3) Step 3. Cross multiply means and extremes.
(4) Step 4. Solve for X.