Middle School Math Quiz: Unit Rate With Fractions

4 questions · exam conditions

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Unit Rate With FractionsQuestion 1 of 4

A printer uses $\frac{7}{8}$ of an ink cartridge to print $1\frac{3}{4}$ reports. How much of an ink cartridge is needed per report?

\frac{1}{2}

of a cartridge per report

\frac{7}{14}

of a cartridge per report

2

cartridges per report

\frac{49}{32}

of a cartridge per report

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Middle School Math Quiz

Middle School Math Quiz: Unit Rate With Fractions

Practice Unit Rate With Fractions in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Unit Rate With Fractions, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A printer uses $\frac{7}{8}$ of an ink cartridge to print $1\frac{3}{4}$ reports. How much of an ink cartridge is needed per report?

$\frac{1}{2}$ of a cartridge per report (correct answer)
$\frac{7}{14}$ of a cartridge per report
$2$ cartridges per report
$\frac{49}{32}$ of a cartridge per report

Explanation: Convert

1\frac{3}{4}

\frac{7}{4}

reports. Find ink per report:

\frac{\frac{7}{8}}{\frac{7}{4}} = \frac{7}{8} \times \frac{4}{7} = \frac{4}{8} = \frac{1}{2}

cartridge per report. Choice B simplifies to

\frac{1}{2}

but is presented in unreduced form to confuse students. Choice C inverts the division incorrectly. Choice D results from multiplying instead of dividing the fractions.

Question 2

A garden hose fills $\frac{2}{5}$ of a swimming pool in $2\frac{2}{5}$ hours. At this rate, what fraction of the pool can be filled in one hour?

$\frac{2}{12}$ of the pool per hour
$\frac{1}{6}$ of the pool per hour (correct answer)
$\frac{24}{25}$ of the pool per hour
$6$ pools per hour

Explanation: Convert

2\frac{2}{5}

\frac{12}{5}

hours. Find the unit rate:

\frac{\frac{2}{5}}{\frac{12}{5}} = \frac{2}{5} \times \frac{5}{12} = \frac{2}{12} = \frac{1}{6}

of the pool per hour. Choice A shows the unreduced fraction form. Choice C results from multiplying the fractions instead of dividing. Choice D incorrectly inverts the entire calculation and gives an unrealistic answer.

Question 3

A machine produces $3\frac{3}{5}$ widgets in $\frac{4}{5}$ of a minute. What is the production rate in widgets per minute?

$4\frac{1}{2}$ widgets per minute (correct answer)
$\frac{36}{25}$ widgets per minute
$2\frac{4}{5}$ widgets per minute
$\frac{144}{100}$ widgets per minute

Explanation: Convert

3\frac{3}{5}

\frac{18}{5}

widgets. Find the unit rate:

\frac{\frac{18}{5}}{\frac{4}{5}} = \frac{18}{5} \times \frac{5}{4} = \frac{18}{4} = \frac{9}{2} = 4\frac{1}{2}

widgets per minute. Choice B results from incorrectly computing

\frac{18}{5} \times \frac{4}{5}

. Choice C comes from subtracting

\frac{4}{5}

from

3\frac{3}{5}

. Choice D represents an incorrect decimal conversion.

Question 4

A water pump can fill $\frac{5}{8}$ of a tank in $1\frac{1}{3}$ hours. At this constant rate, how many tanks can the pump fill in one hour?

$\frac{15}{32}$ tank per hour (correct answer)
$\frac{32}{15}$ tanks per hour
$\frac{5}{32}$ tank per hour
$\frac{8}{15}$ tank per hour

Explanation: Convert

1\frac{1}{3}

\frac{4}{3}

hours. Find the unit rate:

\frac{\frac{5}{8}}{\frac{4}{3}} = \frac{5}{8} \times \frac{3}{4} = \frac{15}{32}

tank per hour. Choice B incorrectly inverts the final answer. Choice C results from multiplying the fractions incorrectly (

\frac{5}{8} \times \frac{1}{4}

). Choice D comes from incorrectly converting the mixed number to

\frac{5}{3}