Pre-Algebra
Ratios and rates
Rates and unit rates
20 practice questions
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Theory + worked examples
Rates and Unit Rates
California Pre-Algebra • Standard 6.RP.2 • Ratios & Rates
Rates and Unit Rates is a topic in Ratios & Rates in the California Common Core State Standards. It is aligned to Standard 6.RP.2, which requires students to compute unit rates and use them to compare and solve problems.
A rate compares quantities with different units; a unit rate gives the amount per single unit.
Theory
A rate compares two quantities with different units; a unit rate is the amount per one unit.
Divide to find a unit rate — “per 1.”
Rates and unit rates.
Finding a unit rate.
Unit rate:
\[\text{unit rate}=\dfrac{\text{quantity }A}{\text{quantity }B}\]
Unit rates make comparisons easy.
How to find a unit rate
- Write the rate as a fraction.
- Divide to make the denominator \(1\).
- Attach the units (per unit).
- Compare unit rates to decide the better deal.
Example 1 — Unit price
\(\$6\) for \(4\) apples. Find the unit price.
Solution
Divide.
| \(\dfrac{6}{4}\) | \(=\) | \(\$1.50\text{ per apple}\) |
Example 2 — Speed
A car goes \(180\) miles in \(3\) hours. Find the speed.
Solution
Miles per hour.
| \(\dfrac{180}{3}\) | \(=\) | \(60\text{ mph}\) |
Example 3 — Compare
Which is cheaper: \(\$5\) for \(2\) lb or \(\$9\) for \(4\) lb?
Solution
Compare unit prices: \(\$2.50\) vs \(\$2.25\).
| \(2.25\) | < | \(2.50\) |
Example 4 — Use a rate
At \(50\) mph, how far in \(4\) hours?
Solution
Multiply rate by time.
| \(50\cdot4\) | \(=\) | \(200\text{ mi}\) |
Common pitfalls
A unit rate is per one unit — divide.
Keep the units attached.
Lower unit price is the better buy.
Frequently asked questions
What is a rate?
A comparison of quantities with different units.
What is a unit rate?
The amount per one unit.
\(\$6\) for \(4\) apples?
\(\$1.50\) each.
\(180\) miles in \(3\) hours?
\(60\) mph.
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