## Percents

The term percent means per hundred or divide by one hundred. It can be substituted for the term hundredth in fractions and decimals. For example, 56/100 = 56% and 0.23 = 23%. A good model for percents is a square grid divided into 100 equal parts. Twelve of the 100 parts in the square below are shaded to show 12 hundredths (12/100, 0.12) or 12%.

Money is another good model for percent because there are 100 cents in a dollar. Thirty-seven cents (\$0.37) is 37 hundredths (37/100) or 37% of a dollar. Six cents (\$0.06) is 6 hundredths (6/100) or 6% of a dollar.

You can also use a meter stick to model percent. There are 100 centimeters in a meter, so 5 centimeters is 5 hundredths (0.05) or 5% of a meter. Twenty-three centimeters is 23 hundredths (0.23) or 23% of a meter. Provide students with many opportunities to see the relationship between percents, fractions, and decimals.

As a prerequisite to computing with percents, an understanding of how to change fractions, decimals, and percents to satisfy a problem needs to be acquired.

• To change a decimal to a percent, multiply by 100 and write a % sign after the number.
0.45 ---> 0.45 100 ---> 45%
• To change a percent to a decimal, delete the % sign and divide by 100.
87% ---> 87 ÷ 100 ---> 0.87
• To change a fraction to a percent, divide the numerator by the denominator, then change the decimal quotient to a percent.
2/5 ---> 2 ÷ 5 ---> 0.4 ---> 40%
When students have a firm grasp of the concept of percents, they can proceed to calculate with percents. Percents are commonly used when computing tips, discounts, and taxes. To find the amount of a tip, discount, or tax, you can use the formula A = p x r where A is the amount of the tip, discount, or tax; p is the original price; and r is the rate or percent of the tax, tip, or discount. Look at this example.

"A coat is on sale for 20% off the original price of \$85. What is the amount of the discount?" In this problem you know the regular price and the rate or percent of the discount. You need to find the amount of the discount. (When computing with percent, remember to change the percent to a fraction or decimal.)

 A = p r A = \$85 20% A = \$85 0.20 A = \$85 0.20 A = \$17

Now that you know the discount is \$17, you can find the sale price of the coat by subtracting \$17 from \$85. The sale price of the coat is \$68.00. Sometimes when you work with percents, you know the original price and the amount of the tip, discount, or tax, but you need to find the rate or percent of the tax, tip, or discount. You can use the same formula to find the rate or percent of the tax, tip, or discount. Here is an example.

"The Montagues went out to dinner and the bill came to \$80. Ms. Montague left a tip of \$12.00. What percent of the bill was the tip?"

 A = p x r \$12 = \$80 x r \$12/\$80 = r 0.15 = r 15% = r

In this final example, the amount and percent of the tax, tip, or discount is given, but you need to find the original price.

"If the state meal tax is 8% and you paid \$3.60 in tax for your meal, what was the cost of your meal before tax?" Use the same formula again.

 A = p r \$3.60 = p 8% \$3.60 = p 0.08 \$3.60/0.08 = p \$45 = p

The formula used above can be adapted to calculate simple interest on a loan. Look at this example.

"Tony borrowed \$800 at 12% for 3 years. How much interest did he pay?

 Interest (I )= principal (p) x rate (r) x time (t) I = p r t I = \$800 12% x 3 yr I = \$800 0.12 x 3 I = \$288

The secret to solving these problems is to recognize what information is given and what information is missing and then substitute appropriately into the equation.