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Mathematics · Fractions and decimals

The fraction model and unit fractions

What happens when you split a whole into equal parts? Explore what the numerator and denominator mean, what unit fractions are, and why 1/8 is smaller than 1/4, using pizza and chocolate.

  • 15 min
  • 1 simulation
  • Mini quiz

Updated:

Preview

The question

On Saturday evening Elif is making pizza at home with her mum and her two siblings. When the pizza comes out of the oven, her little brother Can objects: "Let's cut it into 8 slices, then I'll get to eat more!" Do you think he's right? If you cut a pizza into 8 equal slices instead of 4, does each slice get bigger or smaller? And if Can takes 2 of the 8 slices, has he eaten more than Elif, who takes 1 of the 4 slices?

In this lesson you'll learn to write the answer to these questions as a single number: a fraction.

Try it yourself

No account needed: change the values and check your answer. Some simulations ask for a prediction before they start; it doesn't matter whether it's right or wrong.

Fraction model

3/8 of a pizza

First set the number of parts with the slider, then tap slices to select them. When you're ready, press Check.

Prediction

Predict first

If you cut the same pizza into 8 equal slices instead of 4, what happens to each slice?

It doesn’t matter whether you’re right; the simulation opens once you choose.

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Frequently asked

5 questions

What is a unit fraction?

A unit fraction has a numerator of 1, such as 1/2, 1/3 or 1/8. It shows just one of the equal parts of a whole. You can think of any fraction in unit fractions: 3/5 means three pieces of 1/5.

What do the numerator and the denominator tell you?

The denominator tells you how many equal parts the whole is split into; the numerator tells you how many of those parts you take. In 3/8 the whole is split into 8 equal parts and 3 parts are taken.

Why is a unit fraction with a bigger denominator smaller?

The more parts you split the whole into, the smaller each part gets. That is why 1/8 is smaller than 1/4: one eighth of a pizza is less food than one quarter of the same pizza.

If the parts are not equal, can I write a fraction by counting the parts?

No. The denominator tells you how many EQUAL parts the whole is split into, and a unit fraction is one of those equal parts. If you cut a cake into three unequal pieces, you cannot call one slice "a third of the cake" just because there are three pieces. That slice can still be a fraction of the whole (for example 1/2 if it is exactly half), but you find it by comparing the slice with equal parts, not by counting pieces.

Is half of a large pizza the same as half of a small pizza?

No. When you compare fractions, the wholes have to be the same. Half of the large pizza is more pizza than half of the small one: the fractions match, but the wholes do not.