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← Level 3 – Fraction kid

28 / 30 ⏱ 17 minutes

Word problems with fractions

A method for word problems: find the whole, find the part, answer in a sentence.

Fractions in action

“There are 28 children in the class and 3/4 of them went on a trip. The bus has 24 seats. Is that enough?” This is no longer fraction practice — this is life. And word problems are training for it.

Good news: everything you need, you already know. A fraction of a whole (lesson six), adding fractions (nine and ten), conversions (eleven). Today it joins into a four-step method that can handle every word problem with fractions:

1. Find the whole. What is 100%, that “whole pizza”? (A class, pocket money, a book, a tank…)

2. Find the fraction and the question. What part is counted — and do they ask for a part, for the rest, or for a comparison?

3. Count. Split and take, or add fractions.

4. Answer in a full sentence and check the sense. “21 children went on the trip.” Is 21 less than 28? Is it more than a half? It sits.

Most mistakes in word problems do not come from counting — they come from reading. So never skip steps 1 and 2.

Ema reads the question: “Jonáš spent 2/5 of his pocket money on a comic and 1/5 on ice cream. He had 60 Kč left. How much did he get?” Filip multiplies at once: “Two fifths of sixty…” Ema stops him: “Stop. Sixty is not the whole! Sixty is the REST.” She draws a strip and splits it into 5 parts: two parts comic, one ice cream — 2 parts left. “Two parts = 60 Kč, so one part = 30 Kč. And the whole is five parts: 150 Kč.” Filip stares at the picture: “I counted from the wrong number…” That is exactly why a problem is first read and drawn, then counted.

💡

Draw a strip (a rectangle), split it into parts by the denominator and label what is what. The picture will tell you whether you count from the whole, or from the rest.

Four steps and three types of problem

Type 1: I know the whole, I look for a part. “3/4 of 28 children went on a trip.” That is pure lesson six: 28 : 4 = 7, then 3 × 7 = 21 children.

Type 2: I look for the rest. “I read 2/3 of a book of 240 pages. How much is left?” Two paths: work out what is read (160) and subtract from the whole (240 − 160 = 80), OR first with a fraction: 1 − 2/3 = 1/3 is left, and a third of 240 is 80. The second path is often faster — the whole is always 1 (so 3/3, 4/4, 5/5…).

Type 3: I know a part, I look for the whole. The trickiest! “A third of a tank is 15 litres. How much is a full tank?” Now you go backwards: I know one part (15 l = 1/3), the whole is three parts: 15 × 3 = 45 litres. A tell: the number in the question belongs to a part, not to the whole.

How to tell the type? Ask: which piece of the strip does the number from the question belong to? To the whole strip → type 1 or 2. To a coloured part → type 3. That is why we draw.

And always at the end a sense check: a part must be smaller than the whole, rest + part = the whole, counts of children come out whole. If 21.5 children come out, there is a mistake somewhere.

Type 1 and 2: a trip and a bus

There are 28 children in the class, 3/4 went on a trip. The bus has 24 seats — is that enough?

Whole: 28 children. Part: 3/4 of 28 → 28 : 4 = 7, then 3 × 7 = 21 children went.

Rest: 28 − 21 = 7 children stayed (that is exactly 1/4 ✓).

Answer with a check: 21 children went, a bus with 24 seats is enough and 3 empty seats are left.

Type 3: I know a part, I look for the whole

Sofie saved 2/5 of the amount for a bike. She has 800 Kč saved. How much does the bike cost?

Watch: 800 Kč is not the whole — it is the size of the part 2/5!

One part (1/5): 800 : 2 = 400 Kč.

The whole (5/5): 5 × 400 = 2 000 Kč.

Check: 2/5 of 2 000 → 2 000 : 5 = 400, times 2 = 800 ✓. The bike costs 2 000 Kč and Sofie still needs to save 1 200.

A mix: two fractions and the rest

Jonáš’s pocket money from the story: 2/5 on a comic, 1/5 on ice cream, 60 Kč left.

Spent as a fraction: 2/5 + 1/5 = 3/5 (lesson nine — same denominators).

Rest as a fraction: 1 − 3/5 = 5/5 − 3/5 = 2/5.

Part → whole (type 3): 2/5 = 60 Kč → 1/5 = 30 Kč → the whole 5 × 30 = 150 Kč.

Check: comic 60, ice cream 30, rest 60 — together 150 ✓.

⚠️

Do not count from the first number you see in the question. The number may belong to a part, to the rest, or to the whole — and for each case there is a different method. First a strip, labels, and only then counting. A minute of drawing saves the whole problem.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. Bắt đầu with ten. When it goes well, add more.

Train the base of all word problems: a fraction of a whole. Split by the denominator, take by the numerator. The answer is a number.

Practise the questions

On paper

For every problem a strip with labels. No picture, no go.

  1. A book has 180 pages. Adam read 4/9. How many pages did he read and how many are left? Solve the rest both ways (by subtracting and with the fraction 5/9).

  2. A quarter of a car tank is 12 litres. How many litres does a full tank have and how much is in it when it is 3/4 full?

  3. Tereza spent 1/2 of her pocket money at the cinema and 1/6 on a drink. What fraction is left? (Different denominators — lesson ten!) And how many korunas is that, if she got 120 Kč?

  4. Invent your own word problem of the type “I know a part, I look for the whole” about your favourite food and solve it including a check.

Now you 💪

  1. I can find the whole in a problem and tell which piece the given number belongs to.
  2. I can solve the rest through a fraction: 1 minus the spent part.
  3. I can handle a reverse problem: from a part I work out the whole through one part.
✅

Done when: You solve word problems with fractions with a four-step method and a strip picture, and you tell problems about a part, the rest and the whole.

What to take from this lesson

© 2026 Ing. Martin Polak / AlgoRhino · Điều khoản sử dụng nội dung