# ## Use Percent

Setting Up Percent Problems
Remind students that a percent is a ratio of a number to 100. A percent tells what part of 100 is being considered. To solve percent problems, either proportions or equations can be used. Students already know how to solve proportions and equations. If n is the percent, x is the part, and w is the whole, students can write and solve a proportion, using part-to-whole ratios. The percent equation is set up as “whole × percent = part.” Students can write the equation using either the decimal form or the fraction form of the percent.

w × 0.01n = x or w × = x

Find a Percent of a Number
In these types of problems the percentage and the whole are known and the part is the unknown. Having students do many exercises of the type “Find 40% of 230” allows them to become skilled in finding a percent of a number before applying those skills to problem solving.

Example: Find 40% of 230.

 Using a Proportion  = 100x = 40 × 230 = x = 92 Using Decimals in an Equation w × 0.01n = x 230 × 0.40 = x 92 = x Using Fractions in an Equation w × = x 230 × = x 92 = x

Solution: 40% of 230 is 92.

Finding a Percent
In these types of problems the part and the whole are known and the percent is the unknown. Having students do many exercises of the type “What percent of 250 is 40?” or “40 is what percent of 250?” allows them to become skilled in finding a percent before applying their skills to problem solving.

Example: 40 is what percent of 250?

 Using a Proportion  = 250n = 40 × 100 = n = 16 Using Decimals in an Equation w × 0.01n = x 250 × 0.01n = 40 (250 × 0.01)n = 40 = n = 16 Using Fractions in an Equation w × = x 250 × = 40 = = 40 × n = 16

Solution: 40 is 16% of 250.

Finding a Number When a Percent Is Known
In these types of problems the part and the percentage are known and the whole is the unknown. Having students do many exercises of the type “40% of what number is 25?” or “25 is 40% of what number?” allows them to become skilled in finding the whole when the part and percent are known before applying their skills to problem solving.

Example: 25 is 40% of what number?

 Using a Proportion  = 40w = 100 × 25 = w = 62.5 Using Decimals in an Equation w × 0.01n = x w × 0.40 = 25 = w = 62.5 Using Fractions in an Equation w × = x w × = 25 w × × = 25 × w = 62.5

Solution: 25 is 40% of 62.5.

Estimating With Percents
Remind students that, when estimating, their estimates may vary. Estimating with percents can be done in the same way as estimating with decimals. Numbers are rounded in order to make computation easier. Sometimes percents can be estimated mentally.

Example:

Estimate a 15% tip on a bill of \$37.50.
Round \$37.50 to \$40 and find 15% of \$40, or \$6.

Example:

Estimate a 15% tip on a bill of \$37.50.
Think: 15% = 10% + of 10%
10% of \$37.50 is about \$3.80 and of \$3.80 is \$1.90, so 15% is about \$5.70.

Sometimes estimating with percents is more easily done by using fractions. As students gain experience and confidence in converting between percents, decimals, and fractions, they may find this method easier.

Example:

An \$84 coat is on sale for 33% off. Estimate how much you save by buying the coat on sale. Then estimate the sale price.
33% is about and \$84 can be rounded to \$90. of \$90 is \$30. You save about \$30.
\$84 − \$30 = \$54. The sale price is about \$54.

Example:

A \$1,199 computer is on sale for 75% of its regular price. Estimate the sale price.
75% is and \$1,199 is close to \$1,200. of \$1,200 is \$300, so of \$1,200 is 3 × \$300, or \$900.
The sale price is about \$900.

Teaching Model 18.1: Find a Number When a Percent Is Known