A ratio preserves order
A ratio can be written with words, a colon, or a fraction. The order matters: 3 red marbles to 5 blue marbles is different from 5 blue to 3 red.
ExampleThe ratio of red marbles to blue marbles is or .
Chapter 01 of 10
Ratios & Rates
How can two quantities be compared in a way that scales?
A ratio compares quantities by division. A rate compares quantities with different units, and a unit rate tells the amount for exactly one unit. These ideas describe prices, speeds, recipes, maps, and countless real situations.
The big ideas
Understand these before you worry about speed.
Equivalent ratios scale together
Multiply or divide both quantities by the same nonzero number. A ratio table makes the shared scale factor visible.
Example. Each pair compares the quantities in the same relationship.
A unit rate has a denominator of one
Divide both quantities by the second quantity to find the amount per one unit. Always attach units so the result has meaning.
Example miles in hours is miles per hour.
Tables and graphs show rate patterns
Equivalent-ratio pairs form a table in which each output is the same multiple of its input. When graphed, the points lie on a straight line through the origin.
ExampleAt per pound, connects pounds to cost .
Worked example
Follow the reason for each step—not just the symbols.
Problem
Five notebooks cost . At the same rate, what do eight notebooks cost?
- Find the unit price: per notebook.
- Multiply the unit price by : .
- Check that the larger number of notebooks produces a proportionally larger cost.
Answer
Try it yourself
Work on paper first. Open each answer only when you are ready to check.
1
Simplify the ratio .
Check answer
2
A car travels miles in hours. Find its unit rate.
Check answer
miles per hour3
Complete the equivalent ratio: .
Check answer
4
Three cups of flour make cookies. How many cups are needed for cookies?
Check answer
cupsPractice and tools
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