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αAπΣ∞∂θ√x²≠∫÷≤%+−½αβΔλφ³≈∑°
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  3. Grade 7/
  4. Unit 2/
  5. Unit Rates with Fractions
Grade 7 · Unit 2Topic 1 of 3~22 min

Unit Rates with Fractions

Find a per-one rate even when the quantities are fractions.

All topics in this unit
αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
Step 1 · Learn

Walkthrough

Read this first — it covers the idea in plain language with a worked example.

A unit rate is 'per one'

A unit rate tells you how much of one quantity goes with exactly one of another — like miles per hour or cost per pound.

When the numbers are fractions

  1. 1Write the rate as a fraction (a complex fraction).
  2. 2Divide the top by the bottom — multiply by the reciprocal.
  3. 3Simplify to get the rate per one.
Worked example

A person walks 1/2 mile in 1/4 hour. What is the speed in miles per hour?

  1. →Set up the rate: (1/2) ÷ (1/4).
  2. →Multiply by the reciprocal: 1/2 × 4/1 = 4/2 = 2.
  3. →The unit rate is 2 miles per hour.
αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
Step 2 · Watch

Video walkthrough

Watch the main video, then check the second take if you want another explanation.

Khan Academy

Determining Rates with Fractions

Turn a ratio of fractions into a clean unit rate.

Watch on YouTube
Other

Rates and Unit Rates

A refresher on cost-per-item and speed rates.

Watch on YouTube
αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
Step 3 · Practice

Practice

Try a worksheet or work through some problems before the quiz.

Khan Academy

Rates with fractions

Open resource
Math Worksheets 4 Kids

Unit rate worksheets

Open resource
πΣ√≠≤+αβΔπΣx²θ÷+
Step 4 · Check

Quick check

A couple of questions to make sure this topic stuck. Retake as many times as you want.

Unit Rates with Fractions

Question 1 of 2

Medium

You read 1/3 page in 1/6 minute. What is your rate in pages per minute?

αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
←Back toUnit 2 overview→Next up · Topic 2 of 3Proportional Relationships & k