Middle School Math Quiz: Multiplying Fractions
7 questions · exam conditions
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Multiplying FractionsQuestion 1 of 7

A rectangular piece of fabric is 78\frac{7}{8} yard long and 23\frac{2}{3} yard wide. Sarah cuts off 37\frac{3}{7} of the total area for her project. How much area does she cut off?

14\frac{1}{4} square yard
14168\frac{14}{168} square yard
28\frac{2}{8} square yard
736\frac{7}{36} square yard
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Middle School Math Quiz

Middle School Math Quiz: Multiplying Fractions

Practice Multiplying 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 Multiplying 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 rectangular piece of fabric is 78\frac{7}{8} yard long and 23\frac{2}{3} yard wide. Sarah cuts off 37\frac{3}{7} of the total area for her project. How much area does she cut off?

  1. 14\frac{1}{4} square yard (correct answer)
  2. 14168\frac{14}{168} square yard
  3. 28\frac{2}{8} square yard
  4. 736\frac{7}{36} square yard
Explanation: First find the total area: 78×23=1424=712\frac{7}{8} \times \frac{2}{3} = \frac{14}{24} = \frac{7}{12} square yard. Then find 37\frac{3}{7} of this area: 37×712=2184=14\frac{3}{7} \times \frac{7}{12} = \frac{21}{84} = \frac{1}{4} square yard. Choice B is an unsimplified intermediate calculation. Choice C comes from incorrectly multiplying 78\frac{7}{8} by 37\frac{3}{7}. Choice D results from multiplying 23\frac{2}{3} by 37\frac{3}{7} directly.

Question 2

A machine produces widgets at a rate of 712\frac{7}{12} widgets per minute. If the machine operates at 47\frac{4}{7} of its normal capacity for 32\frac{3}{2} hours, how many widgets will it produce?

  1. 12\frac{1}{2} widget
  2. 3030 widgets (correct answer)
  3. 32\frac{3}{2} widgets
  4. 218\frac{21}{8} widgets
Explanation: First, find the reduced rate: 47×712=13\frac{4}{7} \times \frac{7}{12} = \frac{1}{3} widgets per minute. Convert time to minutes: 32×60=90\frac{3}{2} \times 60 = 90 minutes. Total widgets: 13×90=30\frac{1}{3} \times 90 = 30 widgets. Choice A comes from multiplying the fractions without converting time units. Choice C results from incorrect fraction multiplication. Choice D represents an intermediate calculation error.

Question 3

A water tank loses 16\frac{1}{6} of its water each day due to evaporation. If the tank starts with 45\frac{4}{5} of its capacity filled, what fraction of the tank's total capacity remains after 2 days?

  1. 23\frac{2}{3} of capacity
  2. 2045\frac{20}{45} of capacity
  3. 59\frac{5}{9} of capacity (correct answer)
  4. 12\frac{1}{2} of capacity
Explanation: Each day, 56\frac{5}{6} of the water remains (since 16\frac{1}{6} evaporates). After day 1: 45×56=2030=23\frac{4}{5} \times \frac{5}{6} = \frac{20}{30} = \frac{2}{3} of capacity. After day 2: 23×56=1018=59\frac{2}{3} \times \frac{5}{6} = \frac{10}{18} = \frac{5}{9} of capacity. Choice A represents the amount after only 1 day. Choice B is the unsimplified form of 23\frac{2}{3}. Choice D comes from incorrectly subtracting 16\frac{1}{6} twice from 45\frac{4}{5}.

Question 4

A bakery uses 35\frac{3}{5} cup of sugar for each batch of cookies. If they want to make 49\frac{4}{9} of their usual daily production, and their usual daily production is 7127\frac{1}{2} batches, how much sugar will they need?

  1. 22 cups of sugar (correct answer)
  2. 103\frac{10}{3} cups of sugar
  3. 53\frac{5}{3} cups of sugar
  4. 415\frac{4}{15} cups of sugar
Explanation: First find how many batches they'll make: 49×712=49×152=6018=103\frac{4}{9} \times 7\frac{1}{2} = \frac{4}{9} \times \frac{15}{2} = \frac{60}{18} = \frac{10}{3} batches. Then find the sugar needed: 103×35=3015=2\frac{10}{3} \times \frac{3}{5} = \frac{30}{15} = 2 cups. Choice B represents the number of batches, not cups of sugar. Choice C comes from incorrectly calculating 35×159\frac{3}{5} \times \frac{15}{9}. Choice D results from multiplying 49×35\frac{4}{9} \times \frac{3}{5} without considering the batch count.

Question 5

Jason reads 25\frac{2}{5} of a book on Monday and 38\frac{3}{8} of the remaining pages on Tuesday. What fraction of the entire book did Jason read on Tuesday?

  1. 38\frac{3}{8} of the book
  2. 640\frac{6}{40} of the book
  3. 940\frac{9}{40} of the book (correct answer)
  4. 3140\frac{31}{40} of the book
Explanation: After Monday, Jason has 1−25=351 - \frac{2}{5} = \frac{3}{5} of the book remaining. On Tuesday, he reads 38\frac{3}{8} of this remaining portion: 38×35=940\frac{3}{8} \times \frac{3}{5} = \frac{9}{40} of the entire book. Choice A incorrectly assumes Tuesday's reading is 38\frac{3}{8} of the whole book. Choice B comes from multiplying 25×38\frac{2}{5} \times \frac{3}{8}. Choice D represents the total read over both days (25+940\frac{2}{5} + \frac{9}{40}).

Question 6

A pizza is cut into equal slices. Alex eats 14\frac{1}{4} of the pizza, and then Ben eats 23\frac{2}{3} of what Alex ate. What fraction of the entire pizza did Ben eat?

  1. 23\frac{2}{3} of the pizza
  2. 1112\frac{11}{12} of the pizza
  3. 212\frac{2}{12} of the pizza
  4. 16\frac{1}{6} of the pizza (correct answer)
Explanation: When you see a fraction word problem with phrases like "of what someone ate," you're dealing with multiplication of fractions. The key is identifying what each fraction refers to. Let's work through this step by step. Alex eats 14\frac{1}{4} of the entire pizza. Then Ben eats 23\frac{2}{3} of what Alex ate - not 23\frac{2}{3} of the whole pizza, but 23\frac{2}{3} of Alex's portion. To find Ben's portion, multiply: 23×14=2×13×4=212=16\frac{2}{3} \times \frac{1}{4} = \frac{2 \times 1}{3 \times 4} = \frac{2}{12} = \frac{1}{6} So Ben ate 16\frac{1}{6} of the entire pizza. Looking at the wrong answers: Choice A (23\frac{2}{3}) is the trap of thinking Ben ate 23\frac{2}{3} of the whole pizza instead of 23\frac{2}{3} of Alex's portion. Choice B (1112\frac{11}{12}) comes from incorrectly adding 14+23=312+812=1112\frac{1}{4} + \frac{2}{3} = \frac{3}{12} + \frac{8}{12} = \frac{11}{12}, which would be the total amount eaten by both people, not just Ben's portion. Choice C (212\frac{2}{12}) is the unreduced form of the correct answer - while mathematically equivalent to 16\frac{1}{6}, it's not in simplest form. Remember: when you see "of what someone ate" or similar phrasing, you're multiplying fractions. Always reduce your final answer to simplest form, and double-check that you're answering the right question - what Ben ate, not what both people ate combined.

Question 7

A rectangular garden plot has dimensions 56\frac{5}{6} meters by 49\frac{4}{9} meters. If tomatoes are planted in 35\frac{3}{5} of the total area, what area is planted with tomatoes?

  1. 1254\frac{12}{54} square meters
  2. 29\frac{2}{9} square meters (correct answer)
  3. 415\frac{4}{15} square meters
  4. 60270\frac{60}{270} square meters
Explanation: First find the total area: 56×49=2054=1027\frac{5}{6} \times \frac{4}{9} = \frac{20}{54} = \frac{10}{27} square meters. Then find 35\frac{3}{5} of this area: 35×1027=30135=29\frac{3}{5} \times \frac{10}{27} = \frac{30}{135} = \frac{2}{9} square meters. Choice A represents an incorrect multiplication without simplification. Choice C comes from incorrectly multiplying 49×35\frac{4}{9} \times \frac{3}{5} directly. Choice D is the unsimplified form of the correct answer.