Concept 4 of 7
Simplest Clothes: Lowest Form
Today's big idea
Divide top and bottom by the same number until only 1 will go into both.
Simplifying regroups the pieces; it never takes any of the amount away.
How it works
👀 What's going on?
Nobody says they ate four-eighths of a cake. They say half. Both are true, but one is easier to picture and quicker to check. Every fraction has a simplest version, and finding it is a habit worth building early.
💡 Here's the trick
Look at the three bars above. The shaded length never changes, but the pieces get bigger and fewer as 8/12 becomes 4/6 and then 2/3. Dividing the top and the bottom by the same number regroups the pieces without taking any of the amount away. A fraction is in lowest form when nothing but 1 divides both parts.
🪄 How to do it
- 1.Find a number that divides the top and the bottom exactly, as the bars above are divided by 2.
- 2.Divide them both by it.
- 3.Ask again whether anything still divides both, and stop only when the answer is no.
✍️ Try it
Write 6/8 in its lowest form. Then write 20/24 in its lowest form.
For 6/8, both parts divide by 2, giving 3/4, and 3 and 4 share nothing else, so it is 3/4. For 20/24, dividing by 2 gives 10/12 and dividing by 2 again gives 5/6. You could also have divided by 4 in one go and landed in the same place.
⚠️ Watch out
You might be thinking one round of dividing is always enough. Take 8/24: dividing by 2 gives 4/12, and again gives 2/6, and again gives 1/3. Stop at 2/6 and the fraction is smaller but still not lowest, which usually loses the mark.
🌟 Why this matters
Simplest form is how people actually talk about parts, saying half the class rather than fifteen-thirtieths of it. Smaller numbers are also far easier to compare and check.
Exam tip: Papers almost always want the answer in lowest form, even when the question does not say so.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Reduce 9/12 to its lowest form.”
- 1
Find a number that divides BOTH
9 ÷ 3 = 3 ✓. 12 ÷ 3 = 4 ✓. 3 works. 🧼
- 2
Divide both
Now we have 3/4. Can we go smaller?
- 3
Check again
3 and 4 share no common factor → STOP.
- 4
Lowest form ✓
9/12 = 3/4
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Tap a number that divides both the top and bottom. Keep going until nothing divides evenly — that is lowest form.
LOWEST FORM · ROUND 1 OF 3
6/8
Quick check
✅ VERIFICATION
What is 9/15 in its lowest form?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Same Bottom
Bigger numerator wins when denominators match.