Concept 1 of 9
The Pizza Slice: What IS a Fraction?
Today's big idea
The bottom counts the equal pieces the whole was cut into; the top counts how many you have.
Pizza cut into 4 equal slices with 1 eaten, which is 1/4.
How it works
👀 What's going on?
You and three friends order a pizza. The shop cuts it into 4 equal slices and you eat one. You did not eat a whole pizza, and you did not eat nothing either. Maths needs a name for the amount in between.
💡 Here's the trick
Look at the pizza above. It was cut into 4 equal pieces and 1 of them is gone, which we write as 1/4. The bottom number counts how many equal pieces the whole was cut into. The top number counts how many of those you have. The word equal is doing a lot of work in that sentence.
🪄 How to do it
- 1.Count the equal pieces the whole was cut into, as the picture above counts 4.
- 2.Count how many of those pieces you have, and write that number on top.
✍️ Try it
A chocolate bar splits into 8 equal pieces and you eat 3. What fraction did you eat, and what fraction is left in the wrapper?
You ate 3 of the 8 pieces, so that is 3/8. The 5 still in the wrapper are 5/8. The two tops add up to 8, which is the whole bar, and both fractions keep the same bottom.
⚠️ Watch out
You might be thinking any cut-up thing gives you a fraction. It only works when the pieces are equal. A pizza cut into one huge piece and three slivers is not quarters, however many pieces you can count.
🌟 Why this matters
Half an hour, a quarter of a cake, two-thirds of a bottle. Fractions are how people talk about amounts that are not whole numbers, and most amounts in a day are not.
Exam tip: Check the pieces really are equal before naming a fraction, because papers hide unequal cuts inside the picture.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A cake is cut into 6 equal pieces. You eat 2. What fraction did you eat?”
- 1
Count total equal pieces
The cake has 6 equal slices. That's the denominator.
- 2
Count pieces eaten
You ate 2. That's the numerator.
- 3
Stack them — top / bottom
2 / 6
- 4
Fraction eaten ✓
You ate 2/6 of the cake
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Cut the pizza into equal slices, then tap slices to “eat” them. Watch the fraction update!
0 / 4
You ate 0 out of 4 equal pieces = 0/4
Quick check
✅ VERIFICATION
A ribbon is cut into 5 equal parts and 4 of them are used. What fraction is left?
⚡ Finish the activity above first to answer.
Keep going!
Up next: The Golden Rule
Why 1/2 = 2/4 = 4/8 and how to make them.