Find the unit rate: 1 1/2 pounds in 1/2 box. How many pounds per 1 box?
Exact division: first quantity ÷ second quantity
CCSS 7.RP.A.1 · complex fraction reasoning
Unit Rates with Fractions Worksheet Generator
Practice the Grade 7 step beyond whole-number unit rates: divide one fractional quantity by another and express the exact amount per one unit. The generator keeps every rate rational and simplified instead of converting silently to rounded decimals.
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Unit Rates with Fractions
Unit rates with fractions · Grade 7 standard · Seed 261601
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Find the unit rate: 1 1/2 miles in 1 3/4 hour. How many miles per 1 hour?
Exact division: first quantity ÷ second quantity
3.
Find the unit rate: 1 1/2 miles in 2/3 hour. How many miles per 1 hour?
Exact division: first quantity ÷ second quantity
4.
Find the unit rate: 3/4 miles in 5/6 hour. How many miles per 1 hour?
Exact division: first quantity ÷ second quantity
5.
Find the unit rate: 1 1/4 miles in 1 3/4 hour. How many miles per 1 hour?
Exact division: first quantity ÷ second quantity
6.
Find the unit rate: 2/3 miles in 1/2 hour. How many miles per 1 hour?
Exact division: first quantity ÷ second quantity
7.
Find the unit rate: 1 1/4 cups in 1 3/4 batch. How many cups per 1 batch?
Exact division: first quantity ÷ second quantity
8.
Find the unit rate: 1/2 cups in 3/4 batch. How many cups per 1 batch?
Exact division: first quantity ÷ second quantity
9.
Find the unit rate: 2/3 miles in 4/5 hour. How many miles per 1 hour?
Exact division: first quantity ÷ second quantity
10.
Find the unit rate: 1 3/4 cups in 5/6 batch. How many cups per 1 batch?
Exact division: first quantity ÷ second quantity
Exact-construction rule: fraction unit rates stay rational, graph coordinates come from known equations, and money applications use integer cents. No answer key depends on a hidden rounding convention.
How to find a unit rate when the numbers are fractions
A unit rate tells you how much of one quantity there is for one of the other, so it is the first quantity divided by the second. When both quantities are fractions, divide by multiplying by the reciprocal of the second fraction, then simplify. The answer stays a simplified fraction or mixed number when the exact rate is not a whole number, and the units tell you which quantity is 'per one'.
Worked examples
- One half cup of sugar per one quarter hour: 1/2 ÷ 1/4 = 1/2 × 4 = 2, so the rate is 2 cups per hour.
- A walker covers 3/4 mile in 1/2 hour: 3/4 ÷ 1/2 = 3/4 × 2 = 3/2, so the speed is 1 1/2 miles per hour.
- 2/3 of a pizza is eaten in 1/6 hour: 2/3 ÷ 1/6 = 2/3 × 6 = 4, so 4 pizzas per hour.
- A mixed number: 1 1/2 cups of flour make 3/4 of a batch. Write 1 1/2 as 3/2, then 3/2 ÷ 3/4 = 3/2 × 4/3 = 2, so 2 cups of flour per whole batch.
Common slips
- Dividing in the wrong order. For 3/4 mile in 1/2 hour, 1/2 ÷ 3/4 = 2/3 gives hours per mile, not miles per hour. Check that the rate reads 'miles per hour'.
- Forgetting to flip the second fraction. 3/4 ÷ 1/2 is not 3/8; it is 3/4 × 2 = 3/2.
- Converting a mixed number wrongly. 1 1/2 is 3/2, not 11/2.
- Leaving the units off, which makes it easy to apply the reciprocal to the wrong quantity.
How to use this worksheet
Ask students to write the division sentence with units before they compute, then to say the finished rate in a full sentence such as '2 cups of sugar per hour'. The answer key shows the simplified fraction or mixed number, so students can compare both the number and the units.
Common Core connection
- 7.RP.A.1 · Compute unit rates associated with ratios of fractions, including rates with unlike units.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Classroom note 1
Treat the unit rate as a division problem: first quantity divided by second quantity.
Classroom note 2
Model it: one half cup per one quarter hour is one half divided by one quarter, which is one half times four, or 2 cups per hour.
Classroom note 3
Keep units attached so the reciprocal is applied to the correct quantity.
Classroom note 4
Answers stay as simplified fractions or mixed numbers when the exact rate is not a whole number.
Continue the 7.RP progression
Move to another Grade 7 representation or application
Questions people ask
Do these problems include mixed numbers?
Standard and challenge modes include improper fractions that display as mixed numbers, while foundation mode stays with familiar proper fractions.
Are decimal approximations used?
No. The rate is simplified exactly as a rational number.
Why does dividing by a fraction give the unit rate?
A unit rate asks how much per one. Dividing the first quantity by the second scales the second quantity down to 1, and the matching amount of the first quantity is the rate.