 Motivation Problem

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"Percent of" Short Cut

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Compatible Numbers to Simplify Percent Problems

# Compatible Numbers to Simplify Percent Problems

By now, you have probably recognized that some percents are equivalent fractions with which we are very familiar. When these percents occur with "compatible numbers" (numbers that simplify or multiply easily), we may calculate the percent problems mentally.

Example:   100% is the whole, so 100% of 782 is 782 since 1(782) = 782.

Example:   50% is one-half, so 50% of 84 is 42 since ½ (84) = 42.

Example:   25% is one-fourth, so 25% of 20 is 5 since ¼ (20) = 5.

Example:   10% is one-tenth (one place value less), so 10% of 36.5 is 3.65 since 0.1(36.5) = 3.65.

The shortcut is even more useful by realizing that due to the Commutative Property of Multiplication , "28% of 50" must have the same final answer as "50% of 28".

This is due to the fact that the multiplication  must have the same answer as  since  .

So 100%, 50%, 25,% and 10% are not only easy percents to use when the numbers are compatible; they are also easy bases to take a percentage of, since 40% of 25 must have the same value as 25% of 40 (solution ). These are not the same problem, but they have the same arithmetic answer. Since when we multiply the fraction forms, we can use the commutative property in the numerator and the arithmetic becomes identical.

Note: Here are some basic percent-fraction equivalences that should be memorized for use with mental estimation and compatible numbers. ## Self Check Problems

Work these problems mentally.

Sandy has a credit card balance of \$960. If the interest rate is 12½%, how much interest would Sandy owe?

Solution Jamie has a \$50,000 CD in Lake Region Bank. The APR (annual percentage rate) is 2.8%. How much interest will Jamie receive at the end of one year?

Solution ### Joke or Quote

Three percent exceeds 2 percent by 50 percent, not by 1 percent.

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