Concept 3 of 7
Same Value, Different Look: Equivalent Fractions
Today's big idea
Multiply top and bottom by the same number and the amount stays the same.
More pieces, each smaller, adding up to exactly what you started with.
How it works
👀 What's going on?
Half a pizza and two quarters of a pizza look nothing alike on the plate. One is a single big piece, the other is two smaller ones. Eat either and you have eaten the same amount, which is a strange thing for two different-looking fractions to do.
💡 Here's the trick
Look at the bars above. Cutting each piece into more pieces makes every piece smaller, but it makes more of them, and those two changes cancel out exactly. So 1/2, 2/4 and 4/8 are all the same amount. Multiply the top and the bottom by the same number and the value does not budge.
🪄 How to do it
- 1.Pick any number you like, the way the bars above each cut the one before them further.
- 2.Multiply both the top and the bottom by that number. The fraction you get is worth the same as the one you started with.
✍️ Try it
Find a fraction equal to 2/5 by multiplying by 3. Then find the fraction equal to 3/4 that has 20 on the bottom.
For the first, 2 × 3 = 6 and 5 × 3 = 15, so 2/5 = 6/15. For the second, going from 4 to 20 is × 5, so do the same on top: 3 × 5 = 15, giving 15/20.
⚠️ Watch out
You might be thinking you can add the same number to both instead of multiplying. Add 1 to each part of 1/2 and you get 2/3, which is more than a half. Only multiplying keeps the value, because only multiplying cuts every piece the same way.
🌟 Why this matters
Doubling a recipe, or swapping 50 paise for two 25-paise coins, is this same move. So is reading half a litre off a jug marked in quarters.
Exam tip: Equivalents are how you compare fractions with different bottoms, which is the next thing you will be asked to do.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Find an equivalent fraction for 2/3.”
- 1
The Golden Rule
Multiply BOTH top and bottom by the same number → equivalent. 👯
- 2
Pick a number, say 2
Multiply top × 2: 2 × 2 = 4. Multiply bottom × 2: 3 × 2 = 6.
- 3
Write it
2/3 = 4/6
- 4
Equivalent twin ✓
2/3 = 4/6 (also 6/9, 8/12 …)
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Cut each piece into more pieces so the bottom becomes 6. Watch the shaded amount stay the same!
EQUIVALENT · ROUND 1 OF 3
Start: 1/2 · Make the bottom 6
1/2
Quick check
✅ VERIFICATION
Which fraction is equivalent to 1/3?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Simplest Clothes
Divide top and bottom by the same number.