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Grade 7 Math · Operations with Fractions and Integers

Grade 7 Operations with Fractions and Integers Practice Test

Build Grade 7 Math skills with five 10-question practice tests on integer operations, fraction addition, subtraction, multiplication, division, mixed numbers, equations, order of operations, and applications.

Operations with Fractions and Integers Practice Tests

These Grade 7 Math practice tests help students add, subtract, multiply, and divide integers, fractions, and mixed numbers. Students also apply order of operations, solve equations, simplify results, and use rational number operations in distance, time, recipes, money, and measurement problems.

Skills covered

  • Adding and subtracting positive and negative integers
  • Multiplying and dividing integers and applying positive and negative sign rules
  • Adding and subtracting fractions with common and unlike denominators
  • Multiplying and dividing fractions, mixed numbers, and zero
  • Applying order of operations with integers and fractions
  • Solving one-step equations and modeling real-world situations with rational operations

How to use these practice tests

For integer operations, track the signs before calculating. For fraction addition and subtraction, use a common denominator. For fraction division, multiply by the reciprocal. Follow the order of operations, simplify the final result, and use estimation or substitution to check whether the answer is reasonable.

For more Grade 7 Math practice, return to the Grade 7 Math category.

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Grade 7 Operations with Fractions and Integers Practice Tests

A 10-question Grade 7 Math practice test on integer operations, fraction addition, subtraction, multiplication, division, mixed numbers, order of operations, equations, and applications.

Apply sign rules, common denominators, reciprocal multiplication, order of operations, simplification, and estimation to solve each problem.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

Evaluate 6−2(34+12)6-2\left(\frac{3}{4}+\frac{1}{2}\right).

Please select an answer first.

Correct answer: A

The correct answer is 72\frac{7}{2}.

  1. Identify the operation: Determine whether the problem requires integer signs, a common denominator, a reciprocal, multiplication, division, or order of operations.
  2. Calculate carefully: First add inside parentheses: 34+12=54\frac{3}{4}+\frac{1}{2}=\frac{5}{4}. Then 6−2⋅54=6−52=726-2\cdot\frac{5}{4}=6-\frac{5}{2}=\frac{7}{2}.
  3. Check the result: Confirm the sign, simplify the fraction, and estimate or substitute when possible.

First add inside parentheses: 34+12=54\frac{3}{4}+\frac{1}{2}=\frac{5}{4}. Then 6−2⋅54=6−52=726-2\cdot\frac{5}{4}=6-\frac{5}{2}=\frac{7}{2}.

2. QuestionMultiple choice

Evaluate 56+13⋅(−3)\frac{5}{6}+\frac{1}{3}\cdot(-3).

Please select an answer first.

Correct answer: B

The correct answer is −16-\frac{1}{6}.

  1. Identify the operation: Determine whether the problem requires integer signs, a common denominator, a reciprocal, multiplication, division, or order of operations.
  2. Calculate carefully: Multiply first: 13⋅(−3)=−1\frac{1}{3}\cdot(-3)=-1, then 56−1=−16\frac{5}{6}-1=-\frac{1}{6}.
  3. Check the result: Confirm the sign, simplify the fraction, and estimate or substitute when possible.

Multiply first: 13⋅(−3)=−1\frac{1}{3}\cdot(-3)=-1, then 56−1=−16\frac{5}{6}-1=-\frac{1}{6}.

3. QuestionMultiple choice

A hiker walks 34\frac{3}{4} mile, rests, and walks 1231\frac{2}{3} miles more. How far does the hiker walk?

Please select an answer first.

Correct answer: C

The correct answer is 25122\frac{5}{12} miles.

  1. Identify the operation: Determine whether the problem requires integer signs, a common denominator, a reciprocal, multiplication, division, or order of operations.
  2. Calculate carefully: Add the distances: 34+53=912+2012=2912=2512\frac{3}{4}+\frac{5}{3}=\frac{9}{12}+\frac{20}{12}=\frac{29}{12}=2\frac{5}{12}.
  3. Check the result: Confirm the sign, simplify the fraction, and estimate or substitute when possible.

Add the distances: 34+53=912+2012=2912=2512\frac{3}{4}+\frac{5}{3}=\frac{9}{12}+\frac{20}{12}=\frac{29}{12}=2\frac{5}{12}.

4. QuestionMultiple choice

A tank is 78\frac{7}{8} full and loses 14\frac{1}{4} of the tank. What fraction remains?

Please select an answer first.

Correct answer: D

The correct answer is 58\frac{5}{8}.

  1. Identify the operation: Determine whether the problem requires integer signs, a common denominator, a reciprocal, multiplication, division, or order of operations.
  2. Calculate carefully: Subtract the amount lost: 78−14=78−28=58\frac{7}{8}-\frac{1}{4}=\frac{7}{8}-\frac{2}{8}=\frac{5}{8}.
  3. Check the result: Confirm the sign, simplify the fraction, and estimate or substitute when possible.

Subtract the amount lost: 78−14=78−28=58\frac{7}{8}-\frac{1}{4}=\frac{7}{8}-\frac{2}{8}=\frac{5}{8}.

5. QuestionMultiple choice

Solve x−35=110x-\frac{3}{5}=\frac{1}{10}.

Please select an answer first.

Correct answer: A

The correct answer is x=710x=\frac{7}{10}.

  1. Identify the operation: Determine whether the problem requires integer signs, a common denominator, a reciprocal, multiplication, division, or order of operations.
  2. Calculate carefully: Add 35=610\frac{3}{5}=\frac{6}{10} to both sides: x=110+610=710x=\frac{1}{10}+\frac{6}{10}=\frac{7}{10}.
  3. Check the result: Confirm the sign, simplify the fraction, and estimate or substitute when possible.

Add 35=610\frac{3}{5}=\frac{6}{10} to both sides: x=110+610=710x=\frac{1}{10}+\frac{6}{10}=\frac{7}{10}.

6. QuestionMultiple choice

Solve −2x=65-2x=\frac{6}{5}.

Please select an answer first.

Correct answer: B

The correct answer is x=−35x=-\frac{3}{5}.

  1. Identify the operation: Determine whether the problem requires integer signs, a common denominator, a reciprocal, multiplication, division, or order of operations.
  2. Calculate carefully: Divide both sides by −2-2: x=65÷(−2)=−35x=\frac{6}{5}\div(-2)=-\frac{3}{5}.
  3. Check the result: Confirm the sign, simplify the fraction, and estimate or substitute when possible.

Divide both sides by −2-2: x=65÷(−2)=−35x=\frac{6}{5}\div(-2)=-\frac{3}{5}.

7. QuestionMultiple choice

Evaluate (−4)2−3⋅5(-4)^2-3\cdot5.

Please select an answer first.

Correct answer: C

The correct answer is 11.

  1. Identify the operation: Determine whether the problem requires integer signs, a common denominator, a reciprocal, multiplication, division, or order of operations.
  2. Calculate carefully: Evaluate the exponent and product first: (−4)2−3⋅5=16−15=1(-4)^2-3\cdot5=16-15=1.
  3. Check the result: Confirm the sign, simplify the fraction, and estimate or substitute when possible.

Evaluate the exponent and product first: (−4)2−3⋅5=16−15=1(-4)^2-3\cdot5=16-15=1.

8. QuestionMultiple choice

A recipe needs 23\frac{2}{3} cup of sugar per batch. How much is needed for 3 batches?

Please select an answer first.

Correct answer: D

The correct answer is 22 cups.

  1. Identify the operation: Determine whether the problem requires integer signs, a common denominator, a reciprocal, multiplication, division, or order of operations.
  2. Calculate carefully: Multiply the amount per batch by 3: 3⋅23=23\cdot\frac{2}{3}=2 cups.
  3. Check the result: Confirm the sign, simplify the fraction, and estimate or substitute when possible.

Multiply the amount per batch by 3: 3⋅23=23\cdot\frac{2}{3}=2 cups.

9. QuestionMultiple choice

Which expression correctly represents subtracting 56\frac{5}{6} from −13-\frac{1}{3}?

Please select an answer first.

Correct answer: A

The correct answer is −13−56-\frac{1}{3}-\frac{5}{6}.

  1. Identify the operation: Determine whether the problem requires integer signs, a common denominator, a reciprocal, multiplication, division, or order of operations.
  2. Calculate carefully: The phrase subtract 56\frac{5}{6} from −13-\frac{1}{3} means start with −13-\frac{1}{3} and subtract 56\frac{5}{6}.
  3. Check the result: Confirm the sign, simplify the fraction, and estimate or substitute when possible.

The phrase subtract 56\frac{5}{6} from −13-\frac{1}{3} means start with −13-\frac{1}{3} and subtract 56\frac{5}{6}.

10. QuestionMultiple choice

A student has 56\frac{5}{6} hour for two tasks and spends 14\frac{1}{4} hour on the first. How much time remains?

Please select an answer first.

Correct answer: B

The correct answer is 712\frac{7}{12} hour.

  1. Identify the operation: Determine whether the problem requires integer signs, a common denominator, a reciprocal, multiplication, division, or order of operations.
  2. Calculate carefully: Subtract: 56−14=1012−312=712\frac{5}{6}-\frac{1}{4}=\frac{10}{12}-\frac{3}{12}=\frac{7}{12}.
  3. Check the result: Confirm the sign, simplify the fraction, and estimate or substitute when possible.

Subtract: 56−14=1012−312=712\frac{5}{6}-\frac{1}{4}=\frac{10}{12}-\frac{3}{12}=\frac{7}{12}.

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Frequently asked questions about Grade 7 Operations with Fractions and Integers

What topics are covered?

The page covers integer addition, subtraction, multiplication, division, exponents, fraction addition, subtraction, multiplication, division, mixed numbers, order of operations, equations, and applications.

How should students avoid errors?

Track signs, use common denominators for addition and subtraction, multiply by reciprocals when dividing fractions, follow operation order, simplify, and check with estimation or substitution.

How many questions are on this page?

The page includes five mini tests with 10 questions each, for 50 Grade 7 Operations with Fractions and Integers questions in total.