Chapter 08 of 10

Percents & Proportions

How can a comparison out of one hundred describe part of a whole?

A percent is a rate per one hundred. Fractions, decimals, and percents can name the same quantity, while proportions and unit rates help solve missing-part, missing-whole, and percent-change situations.

01

The big ideas

Understand these before you worry about speed.

Convert among three equivalent forms

Divide numerator by denominator to make a decimal. Multiply a decimal by 100 to make a percent; divide a percent by 100 to return to a decimal.

Example38=0.375=37.5%\displaystyle \frac{3}{8}=0.375=37.5\%.

Find a percent of a quantity

Convert the percent to a decimal and multiply by the whole. The word of usually signals multiplication.

Example35%\displaystyle 35\% of 80\displaystyle 80 is 0.35(80)=28\displaystyle 0.35(80)=28.

Use a proportion for missing parts or wholes

Match part to whole in both ratios, then solve the missing value. Keep the units and the order consistent.

Examplex60=25100\displaystyle \frac{x}{60}=\frac{25}{100} gives x=15\displaystyle x=15.

Percent change compares with the original

Find the amount of increase or decrease, divide that change by the original value, and multiply by 100 percent.

ExampleFrom 40\displaystyle 40 to 50\displaystyle 50 is 1040⋅100%=25%\displaystyle \frac{10}{40}\cdot100\%=25\% increase.
02

Worked example

Follow the reason for each step—not just the symbols.

Problem

A $48\displaystyle \$48 jacket is discounted by 25%\displaystyle 25\%. What is the sale price?

  1. Convert the percent to a decimal: 25%=0.25\displaystyle 25\%=0.25.
  2. Find the discount: 0.25($48)=$12\displaystyle 0.25(\$48)=\$12.
  3. Subtract the discount from the original price: $48−$12\displaystyle \$48-\$12.
Answer$36\displaystyle \$36
03

Try it yourself

Work on paper first. Open each answer only when you are ready to check.

1

Write 0.62\displaystyle 0.62 as a percent and simplified fraction.

Check answer62%\displaystyle 62\% and 3150\displaystyle \frac{31}{50}
2

Find 18%\displaystyle 18\% of 250\displaystyle 250.

Check answer45\displaystyle 45
3

21\displaystyle 21 is 35%\displaystyle 35\% of what number?

Check answer60\displaystyle 60
4

A price rises from $80\displaystyle \$80 to $92\displaystyle \$92. Find the percent increase.

Check answer15%\displaystyle 15\%
04

Practice and tools

Use the resource that matches what you need next.

Worksheet

Percent Problems

Find a percent, a part, or a whole.

Open resource Worksheet

Percent Increase & Decrease

Apply percent change to real situations.

Open resource Calculator

Percent Change Calculator

Compare absolute and relative change step by step.

Open resource Worksheet

Proportions

Solve missing-value proportional relationships.

Open resource