PERCENT PROBLEMS

Concept: There are three basic elements in a percent problem: base x rate = part. In a percent problem, one of the three elements is missing. To find the missing element set up a proportion using the base, part and rate.

To find the missing number in a proportion, cross multiply and divide the product by the third number.

Steps for Solving Percent Problems

Step 1 | Set up the proportion, using the base, part, and rate.
Step 2 | Substitute the known elements into the proportion.
Step 3 | Cross multiply.
Step 4 | Divide the product by the third number.
Step 5 | The dividend becomes the fourth term, replacing the X in the denominator of the first number of the equation.
Step 6 | The dividend also becomes the answer.

Example 2% of a number is 0.7. What is the number?

Step 1 | Set up the proportion, using the base, part, and rate. |
Step 2 | Substitute the known elements into the proportion. |
=
0.7 2% base 100%
Step 3 | Cross multiply. (0.7 x 100 = 70) |
=
0.7 2% base 100%
Step 4 | Divide the product by the third number. | 70 2 = 35
Step 5 | The dividend becomes the fourth term, replacing the X in the denominator of the first number of the equation. |
=
0.7 2% 35 100%
Step 6 | The dividend also becomes the answer. | 35

Vocabulary
Base: The base is the whole amount. In the example above, the base is the missing number.
Part: The part is a piece of the whole or base. In the example above, the part is 0.7.
Rate: The rate is always followed by a percent sign. The rate tells the relationship of the part to the base. In the example above, the rate is 2%.