A percent is a mathematical relationship between two quantities where one quantity is a particular portion of the other quantity.

This relationship is always defined within the context of being out of 100. You can determine what percent a quantity is of another quantity in two ways:

**Notice that the proportion is actually the same thing as the algebraic expression. **

- The only difference is that A, or original quantity, is switched to the other side of the equation by division, which is the first step for the algebraic expression when A and B are known quantities.
- The variable A usually represents a larger number than the variable B, but this may not always be the case.
- It is often easier to use the proportion method than the algebraic expression for many students.

**Example**

Percentages can be represented as a number followed by the % sign, a fraction, or a decimal, but they all mean the same thing.

One other method of solving percentage problems will involve you simply multiplying whichever value you have by the percentage represented as a decimal.

This method is often even easier than using either the Algebraic Expression or Proportion methods defined above.

Review this chart of percentages, decimals, and reduced fractions from 1% to 100%.

- What is 60% as both a decimal and a fraction?
- What is 30% of 200?
- What is the result of increasing 40 by 40%?
- A television is on sale for 70% off. The original price of the television was $1,000. What is the sale price of the television?
- Fruit tree A produces 20% fewer fruits than fruit tree B. If fruit tree A produces 100 fruits in a year, how many fruits will fruit tree B produce?

**Answers to Practice Problems**

- 0.6 and 3/5
- 60
- 56
- $300
- 125

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