📐 Ratios & Proportional Relationships
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Unit Rates with Fractions

A unit rate compares a quantity to exactly 1 — even when fractions are involved.

A unit rate tells you how much of one quantity corresponds to exactly one unit of another. When the quantities involve fractions, you divide the fraction by another fraction — which means multiplying by the reciprocal.

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Unit Rate = Quantity ÷ Number of Units

Unit Rate=quantitynumber of units\text{Unit Rate} = \frac{\text{quantity}}{\text{number of units}}
🚴Cyclist with fractional distance
A cyclist rides ¾ of a mile in ½ an hour. What is the unit rate (miles per hour)?

Unit rate = (3/4) ÷ (1/2) = (3/4) × (2/1) = 6/4 = 1.5 miles per hour.
34÷12=34×21=64=32=1.5 mph\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = \frac{3}{2} = 1.5 \text{ mph}

How to find a unit rate with fractions:

1Write the rate as a fraction: (quantity) / (units)
2Divide the fraction by multiplying by the reciprocal of the denominator
3Simplify the resulting fraction
4Label with the correct units (per hour, per mile, etc.)
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Remember This!

Dividing by a fraction is the same as multiplying by its reciprocal. Flip the second fraction, then multiply straight across.

✏️ Try It!

A recipe uses 2/3 cup of sugar for 1/4 of a batch. How many cups of sugar are needed per full batch?

Practice with CalcVerse
⚖️Unit Rate & Ratio Solver
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