Concept 6 of 7
Comparing Unit Fractions
Today's big idea
With 1 on top, a bigger bottom cuts the whole into more pieces, so each is smaller.
Cutting a whole into more pieces has to make each piece smaller.
How it works
👀 What's going on?
You are offered a third of a cake or a sixth of the same cake. The number 6 is bigger than 3, so a sixth sounds like the better deal. It is not, and the reason is worth getting straight now, because it catches people for years.
💡 Here's the trick
Look at the stack of bars above. Each one has just 1 piece shaded. But the bar is chopped into more pieces as you go down, so that shaded piece keeps shrinking. With 1 on top, a bigger bottom number means the whole was cut into more pieces, so each piece is smaller.
🪄 How to do it
- 1.Check both fractions have 1 on top, the way the bars above each shade exactly one piece.
- 2.Look only at the bottom numbers.
- 3.The smaller bottom number is the bigger fraction.
✍️ Try it
Which is bigger, 1/9 or 1/14? Then order 1/8, 1/20 and 1/11 from biggest to smallest.
Nine pieces are bigger than fourteen pieces of the same thing, so 1/9 is bigger. For the second, put the smallest bottoms first: 1/8, 1/11, 1/20.
⚠️ Watch out
You might be thinking this backwards rule works for all fractions. It only works when both have 1 on top. Compare 2/3 with 1/2 and the smaller bottom belongs to 1/2, but 2/3 is the bigger fraction, because the tops are no longer both 1.
🌟 Why this matters
Splitting a bill between three friends or between eight settles this way. So does deciding whether a third of the pizza beats a quarter.
Exam tip: This reversal is a favourite trap, so read the tops before you trust the bottoms.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Which is bigger: 1/4 or 1/7?”
- 1
Both have 1 on top
So compare only the bottom numbers. 🍰
- 2
Bigger bottom = smaller piece
7 pieces are smaller than 4 pieces, so quarters are bigger.
- 3
Answer ✓
Bigger = 1/4
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Tap the biggest piece. Look how a bigger bottom makes a thinner slice.
UNIT FRACTIONS · ROUND 1 OF 3
Quick check
✅ VERIFICATION
Which is bigger: 1/6 or 1/10?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Fraction of a Group
3/4 of 24 → 24 ÷ 4 × 3 = 18.