ReviewNotes

Grade 5 Fraction Word Problems

Each problem is a situation, not a calculation. You have to decide what to add, what to subtract, and in which order — the arithmetic is the easy part.

What this problem type covers

Adding and subtracting fractions and mixed numbers inside real situations. The harder bands work backwards from two weighings of a container, and use the overlap of two groups — adding two fractions counts the overlap twice, which is the idea being tested.

Example problems

One example from each difficulty band, with worked solutions.

These problems are generated automatically. The answers are derived as each problem is built and are checked by tests, but mistakes are still possible — please tell us if you find one.

  1. 1 · ★1
    Someone drank 3/10 L of juice yesterday and 3/5 L today. How much did they drink over the two days?
    • ①2/5
    • ②7/10
    • ③9/10
    • ④1
    • ⑤3/10
    Show solution
    ③9/10
    1. Add the two lengths: 3/10 + 3/5
    2. Put them over a common denominator and add the numerators.
    3. Rewrite an improper fraction as a mixed number.
    4. The answer is 9/10.
  2. 2 · ★2
    From 77/15 kg of flour, 23/4 kg was used for bread and 111/12 kg for biscuits. How much flour is left?
    • ①42/3
    • ②443/60
    • ③213/15
    • ④24/5
    • ⑤511/20
    Show solution
    ④24/5
    1. Add what was used: 23/4 + 111/12
    2. Subtract that from the total: 77/15 − (used)
    3. Use a common denominator.
    4. What is left is 24/5.
  3. 3 · ★3
    A can full of oil weighs 513/20 kg. After half the oil is poured out, it weighs 31/4 kg. How much does the empty can weigh?
    • ①4/5
    • ②22/5
    • ③44/5
    • ④17/20
    • ⑤9/10
    Show solution
    ④17/20
    1. Half the water was used, so the drop in weight is half the water.
    2. Doubling the remaining weight 31/4 counts the bucket twice and the water once in full.
    3. So (bucket) = 31/4 × 2 − 513/20
    4. That gives 17/20.
  4. 4 · ★4
    1/4 of the students like football and 1/6 like baseball, while 2/3 of them like neither. What fraction of the students like both? Give your answer in lowest terms.
    • ①2/3
    • ②1/12
    • ③1/4
    • ④1/3
    • ⑤1/6
    Show solution
    ②1/12
    1. Since 2/3 like neither, the fraction liking at least one is 1 − 2/3 = 1/3.
    2. Adding 1/4 and 1/6 counts the students who like both twice.
    3. (both) = 1/4 + 1/6 − 1/3
    4. In lowest terms that is 1/12.
  5. 5 · ★5
    1/2 of the residents like A and 5/8 like B. 3/4 of them like A or B, and 15 residents like both. How many residents are there in total?
    • ①48
    • ②120
    • ③15
    • ④40
    • ⑤20
    Show solution
    ④40
    1. Since 3/4 like A or B, (both) = (A) + (B) − 3/4.
    2. That works out to 3/8 of the total.
    3. Those are 15 people, so 3/8 of the total is 15.
    4. The total is 40.

Where people usually go wrong

  • Adding numerators and denominators straight across. 1/4 + 3/5 is not 4/9 — the fractions have to be put over a common denominator first.
  • Subtracting only one of the two amounts used. If two amounts were taken away, both come off the total.
  • Forgetting to double when half of something was removed. The drop in weight is half the contents, so the remaining weight has to be doubled before subtracting.
  • Treating "neither" as the answer to "both". The fraction liking neither has to be turned into the fraction liking at least one first: 1 minus neither.
  • Adding the two group fractions and stopping. That counts everyone in the overlap twice, which is exactly what the question is about.

Practice these in your own notebook

Load 200 problems into your account in one click — split into five sets by difficulty. Solve them, then gather just the ones you got wrong into a new set and work through those again.

You will be asked to sign in first. It is free.