A fraction: a part of a whole

Three quarters of a pizza, half a chocolate bar

“Will you give me half?” “You ate three quarters!” You have used fractions for ever — now you will learn to write them and count with them.

A fraction is a part of a whole. It is written with two numbers one above the other (in text we write them with a slash, for example 3/4): at the bottom the denominator, at the top the numerator.

• The denominator (bottom) says into how many equal parts the whole was split. A four at the bottom = a pizza cut into 4 pieces.
• The numerator (top) says how many parts I take. A three at the top = I take 3 pieces.

So 3/4 of a pizza = a pizza into 4 parts, I have 3 of them.

How to remember it: the denominator gives the parts a name (quarters, thirds, eighths) — that is why it is the denominator. The numerator is a counter — it counts how many parts you have.

Important: the parts must be the same size. A chocolate bar broken into a big piece and a small piece are not halves, even if there are two pieces.

Sofie brought chocolate to school — a bar with 12 squares. “I’ll give you a third,” she says to Adam. Adam wants to take 3 squares, because “a third = three”. Sofie stops him: “A third means the whole bar is split into THREE equal parts. Twelve squares into three parts — that is four each.” She breaks off 4 squares for him. Adam counts: 12 : 3 = 4. “Ah. The denominator says into how many parts I split. Not how many I get.” Exactly — and from that moment Adam never mixes a third with three squares again.

How to work out a fraction of a whole

A fraction of a whole you count exactly by that command — in two steps:

Step 1: Divide the whole by the denominator. That tells you how big one part is.

Step 2: Multiply one part by the numerator. That tells you how many of your parts there are together.

Example: 3/4 of 20 sweets.

1. Split: 20 : 4 = 5 sweets in one part (one quarter = 5).
2. Take: 3 × 5 = 15 sweets.

Remember the middle step: first find one part. Who knows one quarter can easily find three quarters, two quarters or five quarters.

A few special fractions you will meet all the time:

• 1/2 — a half. You divide by two.
• 1/4 — a quarter. You divide by four. (Half of a half!)
• 3/4 — three quarters. Almost the whole, one quarter is missing.
• 4/4 — four quarters = the whole whole. When the numerator is the same as the denominator, you have everything.

And watch the language: “a third” is not 3, “an eighth” is not 8. The bigger the denominator, the smaller the part — a pizza for 8 people means smaller pieces than a pizza for 4.

How much is 2/5 of 30 Kč?

The command is: split 30 into 5 parts, take 2.

Step 1: 30 : 5 = 6. One fifth of 30 Kč is 6 Kč.

Step 2: 2 × 6 = 12 Kč.

A common-sense check: 2/5 is less than a half (a half would be 2.5/5). Half of 30 is 15 — and 12 really is a bit less. It fits.

What part of the bar is left?

The chocolate has 12 squares. Filip ate 5. What fraction of the bar is left?

The whole = 12 squares, so the denominator is 12. 12 − 5 = 7 squares left, so the numerator is 7.

7/12 of the bar is left. And 5/12 is eaten. Together 5/12 + 7/12 = 12/12 = the whole bar — nothing got lost.

Notice: the denominator does not change as long as we talk about the same bar. Only the number of parts we talk about changes.

A PE lesson: 3/4 of an hour

Training lasts 3/4 of an hour. How many minutes is that?

The whole is 1 hour = 60 minutes.

Step 1: 60 : 4 = 15 minutes. A quarter of an hour is 15 minutes — you know that from the clock!

Step 2: 3 × 15 = 45 minutes.

You have used fractions of time for a long time: a quarter of an hour, half an hour, three quarters. Now you know that “three quarters” is the fraction 3/4 and why it is exactly 45 minutes.

Play it

Before you go to the sheet, feel it with your eyes. This is not a test — it is a game. Tap until you see it.

Practice: now you do it 🎲

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

Tap which fraction of the pizza is coloured.

Practise the questions

On paper

Draw. Fractions are understood best through pictures you draw yourself.

1. Draw three identical rectangles (chocolate bars). Colour 1/2 in the first, 1/4 in the second, 3/4 in the third. Under each write the fraction.

2. Work out with the two-step method: 2/3 of 18, 3/5 of 25, 5/6 of 30. By each one write the middle step “one part = …”.

3. There are 28 children in the class and 1/4 of them went to a tournament. How many children went and how many stayed at school?

4. Write as a fraction: how much is one square of a twelve-square chocolate bar? And how much is 6 squares? What fraction comes out and what does it remind you of?

Now you 💪

1. I can show in the fraction 3/8 which number is the numerator and which is the denominator — and what each means.
2. I can work out 3/4 of 20 with the two-step method: split, take.
3. I know why 1/8 is smaller than 1/4, even though 8 is a bigger number than 4.

What to take from this lesson

• Denominator (bottom) = into how many equal parts the whole is split. It gives the parts a name.
• Numerator (top) = how many parts I take. It counts.
• A fraction of a whole: divide by the denominator, multiply by the numerator. 3/4 of 20 → 20 : 4 = 5, then 3 × 5 = 15.
• The bigger the denominator, the smaller the part: 1/8 < 1/4.
• Numerator = denominator means the whole whole: 4/4 = 1.

© 2026 Ing. Martin Polak / AlgoRhino · 内容使用条款