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Grade 5 math review pack

30 mixed questions from every topic in Grade 5, with an answer key and explanations. Great for the start of the year, before a test, or over the holidays.

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Grade 5 Math Review Pack

Name: ____________________Date: ____________Score: ____ / 30
  1. Number Sense
    Write in digits: five hundred nineteen thousand seven hundred fifty-three.
    Answer: ______________________
  2. Round $256{,}752$ to the nearest 1,000.
    Answer: ______________________
  3. Fractions
    Which sign makes this true? $\dfrac{1}{3} \; \square \; \dfrac{1}{6}$
    A. $<$B. $>$C. $=$
  4. A water tank holds 27 L. It is $\dfrac{1}{3}$ full. How many litres of water are in it?
    Answer: ______________________
  5. Decimals
    $73.44 \div 9$ = ?
    Answer: ______________________
  6. Round 80.220 to the nearest tenth.
    Answer: ______________________
  7. Percents
    What is $60\%$ of 560?
    Answer: ______________________
  8. Write $\dfrac{11}{20}$ as a decimal.
    Answer: ______________________
  9. Multiplication and Division
    $3{,}856 \div 7$ = ? Write a remainder like 12 R3.
    Answer: ______________________
  10. Ava has $\$728$ and buys 23 tickets at $\$30$ each. How many dollars are left?
    Answer: ______________________
  11. Factors and Primes
    What is the prime factorization of 420 using exponents?
    A. $2^{3} \times 3 \times 5 \times 7$B. $2^{2} \times 3 \times 5 \times 7$C. $2 \times 3 \times 5 \times 7$D. $2^{2} \times 3^{2} \times 5^{2} \times 7^{2}$
  12. What is the GCF of 16 and 20?
    Answer: ______________________
  13. Exponents, Squares and Cubes
    Which number is a perfect cube?
    A. 7B. 8C. 15D. 10
  14. $7^{5}$ = ?
    Answer: ______________________
  15. Integers
    $-11 \times (-10)$ = ?
    Answer: ______________________
  16. Order of Operations
    $2 \times (\square + 2)^2 = 98$. What number goes in the box?
    Answer: ______________________
  17. $\left[8+(9-5)^{2}\right] \times 3$ = ?
    Answer: ______________________
  18. Ratios and Rates
    7 apples cost $\$63$. What is the cost of one apple in dollars?
    Answer: ______________________
  19. Patterns and Algebra
    What is the greatest whole number x for which $7x + 5 < 61$?
    Answer: ______________________
  20. Solve: $6x + 8 = 62$
    Answer: ______________________
  21. Money and Financial Literacy
    3 books cost $\$56.36$ each, plus 13% sales tax on the total. What do you pay?
    A. $\$169.08$B. $\$182.08$C. $\$191.06$D. $\$63.69$
  22. Pack A: 2 for $\$2.88$. Pack B: 5 for $\$4.4$. Which has the lower price per item?
    A. Pack AB. Pack B
  23. Measurement
    What is the area of this parallelogram? (in cm²)
    Answer: ______________________
  24. A shape is a 11 cm by 3 cm rectangle with a triangle on top (base 11 cm, height 4 cm). What is the total area? (in cm²)
    Answer: ______________________
  25. Geometry
    Three angles meet at a point. Two are 144° and 120°. What is the third? (in degrees)
    Answer: ______________________
  26. Two angles of a triangle are 28° and 110°. What is the third angle? (in degrees)
    Answer: ______________________
  27. Data
    The mean of 7 test scores is 66. 6 of the scores are 52, 29, 76, 31, 84, 72. What is the last score?
    Answer: ______________________
  28. You roll two number cubes (1–6). What is the probability that the difference is 0? Simplify your answer.
    Answer: ______________________
  29. Contest Problems
    A car travels at 44 km/h for 4 h. How far does it go? (in km)
    Answer: ______________________
  30. How many different pairs can be chosen from 10 students?
    Answer: ______________________

Answer key

  1. 519753 — five hundred nineteen thousand seven hundred fifty-three = 519,753.
  2. 257000 — 256,752 is between 256,000 and 257,000. The next digit to the right is 7: round up to 257,000.
  3. B ($>$) — Common denominator 6: 1/3 = 2/6 and 1/6 = 1/6. Compare 2 and 1.
  4. 9 — 27 ÷ 3 = 9, then × 1 = 9 L.
  5. 8.16 — Divide as if there were no decimal point, then put the point straight above: 73.44 ÷ 9 = 8.16. Check: 8.16 × 9 = 73.44.
  6. 80.2 — Look at the digit after the tenth place: 2. Less than 5, so round down: 80.2.
  7. 336 — 1% of 560 is 5.6. 60% is 60 × 5.6 = 336.
  8. 0.55 — 11/20 = 55/100 = 0.55.
  9. 550 R6 — Divide place by place from the left. 7 × 550 = 3,850 and 3,856 − 3,850 = 6, so 3,856 ÷ 7 = 550 R6.
  10. 38 — 23 × 30 = 690. 728 − 690 = 38 dollars.
  11. B ($2^{2} \times 3 \times 5 \times 7$) — Factor tree: 420 = 2 × 2 × 3 × 5 × 7. Group equal primes with exponents: 2 × 2 × 3 × 5 × 7 = 2^2 × 3 × 5 × 7.
  12. 4 — Factors of 16: 1, 2, 4, 8, 16. Factors of 20: 1, 2, 4, 5, 10, 20. The greatest factor in both lists is 4.
  13. B (8) — 8 = 2 × 2 × 2, so it is a perfect cube.
  14. 16807 — 7^5 means 7 × 7 × 7 × 7 × 7 = 16,807. (Not 7 × 5!)
  15. 110 — 11 × 10 = 110. Same signs → positive: 110.
  16. 5 — Work backwards, undoing the operations in reverse BEDMAS order: 98 ÷ 2 = 49. √49 = 7. 7 − 2 = 5. Check: the box is 5.
  17. 72 — Brackets first: 9 − 5 = 4. Next brackets: 8 + 4² = 24. Now 24 × 3 = 72. So the answer is 72.
  18. 9 — Unit rate: 63 ÷ 7 = 9 dollars per apple.
  19. 7 — Solve 7x + 5 = 61: x = 8. x must be less than 8, so the greatest whole number is 7.
  20. 9 — Subtract 8: 6x = 54. Divide by 6: x = 9.
  21. C ($\$191.06$) — Subtotal: 3 × 56.36 = 169.08. Tax: 0.13 × 169.08 = 21.98. Total: 191.06.
  22. B (Pack B) — Unit price A: 2.88 ÷ 2 ≈ 1.44. Unit price B: 4.40 ÷ 5 ≈ 0.88. Pack B costs less per item.
  23. 12 — A parallelogram can be rearranged into a rectangle: A = base × height = 4 × 3 = 12 cm². (Use the height, not the slanted side.)
  24. 55 — Rectangle: 11 × 3 = 33. Triangle: 11 × 4 ÷ 2 = 22. Total 55 cm².
  25. 96 — Angles around a point add up to 360°: 360 − 144 − 120 = 96°.
  26. 42 — The angles of a triangle add up to 180°. 180 − 28 − 110 = 42°.
  27. 118 — Total of all 7 scores = 66 × 7 = 462. Known total = 344. Last score = 462 − 344 = 118.
  28. 1/6 — There are 6 × 6 = 36 equally likely outcomes. 6 of them work: 6/36 = 1/6.
  29. 176 — 4 h. Distance = 44 × 4 = 176 km.
  30. 45 — Ordered choices: 10 × 9 = 90. Each pair was counted 2 times, so divide by 2: 45.

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