Pre-Algebra · Grades 6 to 8
Ratios, rates and proportions
Compare amounts, find unit rates and solve proportions.
The idea
A ratio compares two amounts by division. A rate is a ratio with different units, such as miles per hour. A unit rate has a denominator of 1.
A proportion is an equation that says two ratios are equal. Cross-multiplication turns a proportion into a simple equation you can solve.
Worked examples
- How to Solve a Proportion Solve x/6 = 5/3 by cross-multiplication. Four steps with the reasons, plus the cross-multiplication mistakes that break the answer.
- How to Find a Unit Rate Find the speed for 180 miles in 3 hours. Three steps, the unit-rate reason, and the fraction and unit mistakes to avoid.
- How to Use the Order of Operations (PEMDAS) Work through 4 + 3 x 2^2 - 6 / 3 in four steps. See which operation goes first, why each step is allowed, and the order mistakes to avoid.
Practice this topic
3 problems with answers.