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

or

2 = 4

5

10

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

EXTREMES.

(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.

(extreme)

25 mg = 250 mg

(mean)

(mean)

1 ml

10 ml

(extreme)

(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:

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

for X.

(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

ratio.

(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

in mg/ml).

(3) Step 3. Cross multiply means and extremes.

(4) Step 4. Solve for X.

MD0913

1-9

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