Calculate Unit Rates With Fractions | Worksheet - Free Printable

Let's solve each problem on the worksheet "Calculate Unit Rates With Fractions" step by step. The goal is to find the unit rate (e.g., gallons per day, pounds per bucket, etc.) and express it as a simplified fraction, mixed number, or whole number.

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Problem 1

> $ \frac{1}{2} $ of a gallon of orange juice every 3 days
> → gallons per day

We want to divide $ \frac{1}{2} $ gallon by 3 days:

$$
\frac{1/2}{3} = \frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}
$$

✔ Answer: $ \frac{1}{6} $ gallons per day

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Problem 2

> 80 pounds of concrete for $ \frac{1}{4} $ of a cubic foot
> → pounds per cubic foot

Divide 80 pounds by $ \frac{1}{4} $:

$$
80 \div \frac{1}{4} = 80 \times 4 = 320
$$

✔ Answer: 320 pounds per cubic foot

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Problem 3

> 2 buckets hold $ \frac{1}{5} $ of a gallon
> → gallons per bucket

Divide $ \frac{1}{5} $ gallon by 2 buckets:

$$
\frac{1/5}{2} = \frac{1}{5} \div 2 = \frac{1}{5} \times \frac{1}{2} = \frac{1}{10}
$$

✔ Answer: $ \frac{1}{10} $ gallons per bucket

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Problem 4

> 40 apple trees in $ \frac{1}{2} $ of an acre
> → trees per acre

Divide 40 trees by $ \frac{1}{2} $ acre:

$$
40 \div \frac{1}{2} = 40 \times 2 = 80
$$

✔ Answer: 80 trees per acre

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Problem 5

> 4 pots hold $ \frac{1}{3} $ of a pound of soil
> → pounds per pot

Divide $ \frac{1}{3} $ pound by 4 pots:

$$
\frac{1/3}{4} = \frac{1}{3} \div 4 = \frac{1}{3} \times \frac{1}{4} = \frac{1}{12}
$$

✔ Answer: $ \frac{1}{12} $ pounds per pot

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Problem 6

> $ \frac{1}{2} $ of a kilometer in $ \frac{1}{4} $ of an hour
> → kilometers per hour

Divide $ \frac{1}{2} $ km by $ \frac{1}{4} $ hr:

$$
\frac{1/2}{1/4} = \frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times \frac{4}{1} = \frac{4}{2} = 2
$$

✔ Answer: 2 kilometers per hour

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Problem 7

> $ \frac{1}{4} $ of a mile in $ \frac{1}{2} $ of an hour
> → miles per hour

Divide $ \frac{1}{4} $ mile by $ \frac{1}{2} $ hour:

$$
\frac{1/4}{1/2} = \frac{1}{4} \div \frac{1}{2} = \frac{1}{4} \times \frac{2}{1} = \frac{2}{4} = \frac{1}{2}
$$

✔ Answer: $ \frac{1}{2} $ miles per hour

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Problem 8

> $ \frac{1}{3} $ of a cup of sugar for $ \frac{1}{4} $ of a batch of cookies
> → cups per batch

Divide $ \frac{1}{3} $ cup by $ \frac{1}{4} $ batch:

$$
\frac{1/3}{1/4} = \frac{1}{3} \div \frac{1}{4} = \frac{1}{3} \times \frac{4}{1} = \frac{4}{3} = 1\frac{1}{3}
$$

✔ Answer: $ 1\frac{1}{3} $ cups per batch

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Problem 9

> $ \frac{1}{5} $ of a bag of lawn seed for $ \frac{3}{5} $ of an acre
> → bags per acre

Divide $ \frac{1}{5} $ bag by $ \frac{3}{5} $ acre:

$$
\frac{1/5}{3/5} = \frac{1}{5} \div \frac{3}{5} = \frac{1}{5} \times \frac{5}{3} = \frac{5}{15} = \frac{1}{3}
$$

✔ Answer: $ \frac{1}{3} $ bags per acre

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Problem 10

> $ \frac{1}{2} $ of a batch of cookies uses $ \frac{3}{4} $ of a cup of butter
> → cups per batch

Divide $ \frac{3}{4} $ cup by $ \frac{1}{2} $ batch:

$$
\frac{3/4}{1/2} = \frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = \frac{3}{2} = 1\frac{1}{2}
$$

✔ Answer: $ 1\frac{1}{2} $ cups per batch

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Problem 11

> $ \frac{1}{2} $ of an hour to travel $ \frac{3}{4} $ of a mile
> → miles per hour

Divide $ \frac{3}{4} $ mile by $ \frac{1}{2} $ hour:

$$
\frac{3/4}{1/2} = \frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = \frac{3}{2} = 1\frac{1}{2}
$$

✔ Answer: $ 1\frac{1}{2} $ miles per hour

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Problem 12

> $ \frac{1}{2} $ of a pint of icing for $ \frac{1}{4} $ of a dozen donuts
> → pints per dozen

Divide $ \frac{1}{2} $ pint by $ \frac{1}{4} $ dozen:

$$
\frac{1/2}{1/4} = \frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times \frac{4}{1} = \frac{4}{2} = 2
$$

✔ Answer: 2 pints per dozen

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $ \frac{1}{6} $ gallons per day |
| 2 | 320 pounds per cubic foot |
| 3 | $ \frac{1}{10} $ gallons per bucket |
| 4 | 80 trees per acre |
| 5 | $ \frac{1}{12} $ pounds per pot |
| 6 | 2 kilometers per hour |
| 7 | $ \frac{1}{2} $ miles per hour |
| 8 | $ 1\frac{1}{3} $ cups per batch |
| 9 | $ \frac{1}{3} $ bags per acre |
| 10 | $ 1\frac{1}{2} $ cups per batch |
| 11 | $ 1\frac{1}{2} $ miles per hour |
| 12 | 2 pints per dozen |

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🔍 Key Concept:

To calculate unit rates with fractions, you divide the quantity by the unit of time or measure using division of fractions:
$$
\text{Unit Rate} = \frac{\text{Quantity}}{\text{Time or Measure}}
$$
And remember: dividing by a fraction is the same as multiplying by its reciprocal.

Let me know if you'd like this formatted into a printable answer sheet!