Working with Percentages and Proportions
When working with percentages, it is often helpful to think of them in terms of ratios
and proportions. For instance, if someone asks you, â€œWhat is 10% of 40?â€ you could
simply change 10% into a decimal (0.1) and multiply it by 40 to get 4. But what if you
were asked, â€œ5% of what number is 10?â€ Thatâ€™s a little trickier. To do this calculation, it
is convenient to use a proportion.
PROCEDURE: To use percentages in a proportion, first put your known percentage in
a ratio with 100. Then create an equivalent ratio, leaving the place for your
unknown quantity blank. Crossmultiply the known numerator with the known
denominator. Divide the product with your remaining known value. The result is
your unknown quantity.
SAMPLE PROBLEM: 25% of what number is 4?
Step 1: Put your percentage in a
ratio with 100.

Step 2: Create an equivalent ratio, leaving
the space for the unknown quantity blank.

Step 3: Crossmultiply the known
numerator with the known
denominator.

Step 4: Divide the product with the remaining
known quantity.

25% of 16 is 4.
