Middle School Math Quiz: Multiplying And Dividing Rational Numbers
3 questions · exam conditions
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Multiplying And Dividing Rational NumbersQuestion 1 of 3

A recipe calls for 34\frac{3}{4} cup of flour, but Sarah only has 16\frac{1}{6} cup. She decides to make a proportionally smaller batch by dividing all ingredients by the same factor. If she uses all her flour, by what factor should she divide the other ingredients?

29\frac{2}{9}
418\frac{4}{18}
4.54.5
92\frac{9}{2}
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Middle School Math Quiz

Middle School Math Quiz: Multiplying And Dividing Rational Numbers

Practice Multiplying And Dividing Rational Numbers 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 And Dividing Rational Numbers, 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 recipe calls for 34\frac{3}{4} cup of flour, but Sarah only has 16\frac{1}{6} cup. She decides to make a proportionally smaller batch by dividing all ingredients by the same factor. If she uses all her flour, by what factor should she divide the other ingredients?

  1. 29\frac{2}{9}
  2. 418\frac{4}{18}
  3. 4.54.5 (correct answer)
  4. 92\frac{9}{2}
Explanation: Sarah needs to find what factor to divide by, which means finding 3/41/6=34×61=184=4.5\frac{3/4}{1/6} = \frac{3}{4} \times \frac{6}{1} = \frac{18}{4} = 4.5. This means the original recipe is 4.5 times larger than what she can make, so she divides all ingredients by 4.5. Choice A gives the ratio 1/63/4\frac{1/6}{3/4} instead. Choice B is the same as A in different form. Choice D gives the reciprocal as an improper fraction.

Question 2

Consider the expression (−0.4)×(−1.25)÷(−0.8)(-0.4) \times (-1.25) \div (-0.8). When computed from left to right, what is the final result?

  1. −0.625-0.625 (correct answer)
  2. 0.6250.625
  3. −0.4-0.4
  4. 0.40.4
Explanation: Following order of operations left to right: (−0.4)×(−1.25)=0.5(-0.4) \times (-1.25) = 0.5. Then 0.5÷(−0.8)=−0.6250.5 \div (-0.8) = -0.625. The key is tracking signs carefully: negative times negative gives positive, then positive divided by negative gives negative. Choice B misses the final negative sign. Choice C makes an error in the initial multiplication. Choice D combines both sign errors.

Question 3

The product of three rational numbers is −1235-\frac{12}{35}. Two of the numbers are 25\frac{2}{5} and −37-\frac{3}{7}. What is the third number?

  1. 22 (correct answer)
  2. −2-2
  3. 12\frac{1}{2}
  4. −12-\frac{1}{2}
Explanation: Let the third number be xx. Then 25×(−37)×x=−1235\frac{2}{5} \times \left(-\frac{3}{7}\right) \times x = -\frac{12}{35}. First: 25×(−37)=−635\frac{2}{5} \times \left(-\frac{3}{7}\right) = -\frac{6}{35}. So −635×x=−1235-\frac{6}{35} \times x = -\frac{12}{35}, which gives x=−12/35−6/35=−1235×35−6=2x = \frac{-12/35}{-6/35} = \frac{-12}{35} \times \frac{35}{-6} = 2. Choice B mishandles the double negative. Choice C uses wrong arithmetic. Choice D combines both errors.