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Three Quarters of 24: Why Fraction-of-a-Quantity Sums Go Wrong

9 October 2026 · by Larry

A child can shade three quarters of a circle without a pause, then meet "What is 3/4 of 24?" and hand back 6, or 8, or 32. The picture was fine. The sum is a different job.

This is the third idea hiding inside the word "fraction": not a piece of a shape, and not a point on a line, but something you do to a number. We touched on it in fractions: when they suddenly stop making sense. Here is the sum on its own, because it is where a lot of marks go.

What the sum is really asking

"3/4 of 24" means: cut 24 into 4 equal groups, then take 3 of those groups. So there are two steps, always in the same order.

So 3/4 of 24 is 18. The bottom number says how many equal parts to make. The top number says how many of them to keep.

Four slips, and the answer each one gives

1. Stopping after the first step. The child divides 24 by 4, gets 6, and writes it down. They have found one quarter, not three quarters. The giveaway is an answer that is the same whatever the top number was: 1/4 of 24, 2/4 of 24 and 3/4 of 24 all "come out" as 6.

2. Dividing by the top number. The child sees a 3 and divides by 3: 24 ÷ 3 = 8. It is a natural mistake, because the top number is the one we say first ("three quarters"). The giveaway is that 3/4 of 24 comes out smaller than 2/3 of 24 would, or that two different fractions give the same answer.

3. Answering with what is left. Say a question reads: "Mei has 24 stickers. She gives away 3/4 of them. How many does she have left?" The child correctly finds 18, and writes 18 as the answer. But 18 is what she gave away. What she has left is 24 − 18 = 6. Here the arithmetic is right and the answer is still wrong, because the child stopped at the number they were proud of finding.

4. Using the wrong whole. This one shows up when a question has two steps. "Ben had $48. He spent 1/4 of it on a book and 1/3 of the rest on lunch. How much did he have left?" The book costs 48 ÷ 4 = $12, which leaves $36. The lunch is 1/3 of the $36, not of the $48: $36 ÷ 3 = $12. A child who takes 1/3 of $48 gets $16 and is off from that point on. The question never says "of what" out loud, and the child has to supply it.

A five-minute check

Ask these aloud, with a pencil only if needed. Each one is picked to expose one slip.

  1. "What is 1/4 of 12?" (3.) If this is wrong, the child is missing the first step, and nothing below matters yet.
  2. "What is 3/4 of 12?" (9.) If the answer is 3, that is slip 1. If it is 4, that is slip 2.
  3. "What is 2/3 of 18?" (12: 18 ÷ 3 = 6, then 6 × 2.) A different fraction, so a memorised answer cannot carry them.
  4. "What is 5/6 of 30?" (25: 30 ÷ 6 = 5, then 5 × 5.) A top number that is not 1, 2 or 3, so the habit of "just do one more step" cannot be guessed.
  5. "There are 12 buttons. A quarter are red. How many are not red?" (9.) This is the left-over question, and it shows whether the child reads the last line of a problem.

Where it first goes wrong tells you what to fix. A wrong first answer is a missing idea. A wrong fifth answer is a reading habit.

What helps

Use real things for two minutes. Twelve buttons, coins or dried beans. Make four equal piles and slide three of them across. The child can see that "of" means "take that many of the equal groups", and that the division is only how you find the size of a group. Fractions of a set are exactly where children who are fine with fractions of a shape come unstuck, and holding the set makes the rule something they can see.

Draw it as a bar. Draw one bar to stand for 24, split it into 4 equal parts, shade 3. Write 6 in each part. The picture does the sum, and it stops slips 1 and 2 because there is nowhere to put the wrong number. This is the beginning of the bar model that schools use later; there is more in the guide to bar models.

Say the two steps aloud. "Divide by the bottom to get one part. Multiply by the top to get the parts I want." Said every time for a week, it stops being a sentence and becomes a habit.

Circle what the question wants. Before any working, circle the last few words: "left", "spent", "altogether", "in total". Slip 3 disappears when the child knows, before they start, which number the question is asking for. The same habit helps with word problems where the sums are fine but the story is not.

Write the whole beside each step. For two-step questions, write "of $48" or "of $36" next to the fraction. That tiny label is what keeps the wrong whole out.

What does not help

A check any child can do for themselves

The answer to "3/4 of 24" has to be smaller than 24 but bigger than half of 24, which is 12. The answer 18 passes. The answer 6 fails (too small for three quarters) and the answer 32 fails (bigger than the whole). Teaching a child to ask "is it bigger or smaller than half?" catches most of these slips before the page is handed in.

Which level is this?

Fractions of a quantity are set by the school's scheme of work and the MOE syllabus, which you can check at moe.gov.sg. It is the fractions-of-a-remainder questions at upper primary, like Ben's lunch above, that make the wrong-whole slip common. The jump between levels is covered in what changes between P4 and P5.

The short version

Related reading: ratio and percentage: the three slips, which uses the same "of what?" question one step further on. For adding and subtracting fractions with different bottom numbers, see why 1/2 + 1/3 is not 2/5.

Try the free maths practice →

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