1. Unit 21
Proportion

2. Basic Principles of Proportion Problems
A proportion is an equation that states that two ratios are equal.
Proportions are written with an equal sign between two ratios.
For example: 1:2 = 3:6.

3. Basic Principles of Proportion Problems
The first and last numbers of the proportion are called the extremes, and the two middle numbers are called the means.
For a proportion to be a true proportion, the product of the means must equal the product of the extremes.
If one factor in a true proportion is unknown, the missing factor can be found because the product of the means must equal the product of the extremes.

4. Basic Principles of Proportion Problems
Cross-multiplication can be used to solve proportions.
Proportions can be used while preparing solutions.
Any percent can be converted to a ratio.

5. Proportion
Example: How many grams (g) of boric acid crystals are needed to prepare 500 milliliters (mL) of a 5% boric acid solution?
First calculate that a 5% boric acid solution equals 0.05 or 5/100 or 5:100 or 1:20.
This means there is 1 g of boric acid crystals in every 20 mL of solution.

6. Proportion Set up a proportion: Multiply the means: 20 x X = 20X
Multiply the extremes:
1 x 500 = 500

7. Proportion Write as means equals extremes: 20X = 500
Divide both sides by 20 to find X:
Write the answer: X = 25 g (Use 25 g of boric acid.)

8. Practical Problem
A public health nurse calculates that it costs $1.30 for every 2.5 miles he drives his car.
If he travels 382 miles in 1 week, how much does it cost him to drive his car?

9. Practical Problem Set up the proportion and cross-multiply:
It costs the nurse $ to drive his car for 1 week.