Unit 4: Proportions

Proportions can be applied to almost every health care profession in one way or another. In addition to on-the-job applications, proportions provide a simple and quick method for solving many every day math problems, such as measurement conversions, recipe conversions and increasing or decreasing the amounts of ingredients.

Proportions are two or more equivalent ratios or fractions in which the terms of the first ratio have the same part-to-whole relationship as the second ratio. The example we use to best explain this is box to gloves.

Each ratio is separated by two colons. Example:

1 box : 100 gloves :: 2 box : 200 gloves

This is an example of a proper proportion. For every 1 box there are 100 gloves. In order to be a proper proportion, this ratio must stay the same for every increasing amount.

For example, 1 box : 100 gloves :: 3 box : 400 gloves is not a proper proportion. If there are 3 boxes, there should be 300 gloves in order for the proportion to be accurate. If there are 400 gloves, there must be 4 boxes.

We often use proportions in medicine to solve for a missing number, which we usually value as x. In order to find the missing number, we label proportions the following way:

In the above picture, there are no numbers listed, but the values that they highlight are what's important. Let's say we have the following proportion:

20 mg : 40 tablets :: x mg : 15 tablets

In order to solve for x we must multiply the means as well as the extremes and separate them by an = sign. In a true proportion, the multiplied means are equal to the multiplied extremes.

So, the equation work would look like:

20 x 15 = 40x ------------> 20 x 15 = 300 ------------> 300 = 40x ------------> divide both sides by 40 to get x alone ------------> x = 7.5

Remember to label after solving for x! Is our answer 7.5 tablets or 7.5 mg? Check back to the original problem to see what x was labeled. The proper answer would be 7.5 mg