Concept 7 of 9
The Block Smasher: Decomposing Fractions
Today's big idea
Any fraction breaks into smaller pieces that all keep the very same bottom number.
4/6 comes apart into 1/6 + 1/6 + 1/6 + 1/6, every piece still a sixth.
How it works
👀 What's going on?
Every fraction is made of smaller pieces glued together. Pulling one apart is called decomposing, and it turns a single awkward fraction into a handful of easy ones.
💡 Here's the trick
Look at the blocks above. 4/6 comes apart into 1/6 + 1/6 + 1/6 + 1/6, four pieces each one sixth in size. The bottom number never changes, because every piece is still a sixth. Only the top number gets split up.
🪄 How to do it
- 1.Keep the bottom number exactly as it stands in the picture above.
- 2.Split the top into smaller numbers that add back up to it.
✍️ Try it
Break 5/8 into single pieces. Then find a way to break it into only two pieces.
Single pieces give 1/8 + 1/8 + 1/8 + 1/8 + 1/8, five of them. Two pieces could be 2/8 + 3/8, or 1/8 + 4/8. More than one answer is right, as long as the tops add to 5 and every bottom stays 8.
⚠️ Watch out
You might be thinking the bottom splits as well, so 5/8 could become 1/4 + 1/4. Those are quarter-sized pieces and two of them make a half, which is not 5/8. The bottom is the size of a piece, and decomposing never changes a size.
🌟 Why this matters
Breaking an amount into pieces you can handle is how people pay in instalments or spread a job across several days. In maths it turns one hard fraction sum into several easy ones.
Exam tip: Decomposing is often the quickest way to see that two fractions are secretly the same.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Decompose 3/5 into unit fractions.”
- 1
Keep the bottom the same
The bottom (5) tells us each piece is a fifth. Don't change it.
- 2
Break the top into 1s
The top is 3 → split into 1 + 1 + 1.
- 3
Stick each 1 over a 5
1/5 + 1/5 + 1/5
- 4
Decomposed ✓
3/5 = 1/5 + 1/5 + 1/5
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Every fraction is built from UNIT fractions (1/4). Drop 1/4 tiles into the tray until it equals the target.
Target: 3/4
Tray total: 0/4
Quick check
✅ VERIFICATION
Which of these does NOT equal 6/8?
⚡ Finish the activity above first to answer.
Keep going!
Up next: The Bridge Builder
Multiply a whole number by a fraction.