**Understanding Percent Problems**

- the base ( B ) or whole or total amount, a standard used for comparison
- the portion ( P ) or part being compared with the base
- the rate ( R ) or percent, a percent number

**Identify the Parameters:**

*Example*: What is 20% of 280?

- is indicates the portion (or percent) P to be found.
- % indicate the percent rate R, here R = 30%
- of indicates the base B which is equal to 280.

**Find the Missing Percentage from Two Given Numbers**

The next three sample sentences are all forms of the same problem. In each sentence the percent R is unknown. We know this because neither of the other two numbers has a % symbol attached.

- 7 is what percent of 12?
- Find what percent 7 is of 12.
- What percent of 12 is 7?

**Finding the Missing Percent**

To find the missing percent when given two numbers, do the following:

- Write a fraction with the two numbers. The number after the word “of” is always the denominator, and the other number is the numerator.
- Simplify the fraction (if possible).
- Change the fraction to a decimal.
- Express the decimal as a percent.

EXAMPLE

Now let`s solve this problem: What percent of 12 is 7?

SOLUTION

- Write a fraction with the two numbers, the bigger is usually the base or denominator:

\[\frac{7}{12}\] - Simplify the fraction (if possible):

\[\frac{7}{12}\]is at its lowest terms since 7 is a prime number. - Change the fraction to a decimal:

7÷12 = 0.58

Express the decimal as a percent:

We can say that 58% of 12 is 7. When you find the percentage, remember to include the % symbol with your answer.