To simplify a fraction, divide the numerator and denominator by the same number until they share no common factor. The fastest route is dividing both by their greatest common factor (GCF) in one step: for 6/8 the GCF is 2, so 6/8 = 3/4. The value doesn't change — 6/8 and 3/4 are the same amount written with smaller numbers.
Look for a number that divides both exactly. Quick checks: both even → divisible by 2; digit sums divisible by 3 → divisible by 3; both ending in 0 or 5 → divisible by 5.
Divide numerator and denominator by that factor. 18/45: both divide by 9, giving 2/5. Dividing top and bottom by the same number keeps the fraction's value — you're grouping the same amount into bigger pieces.
If you used a small factor, check again. 48/72 ÷ 2 = 24/36 ÷ 2 = 12/18 ÷ 2 = 6/9 ÷ 3 = 2/3. Using the GCF (here 24) gets there in one step, but repeated small steps reach the same place.
A fraction is in simplest form (lowest terms) when the only number dividing both top and bottom is 1. 2/3, 3/4 and 9/10 are done; 6/8 and 15/20 aren't.
One common factor
Simplify 6/8
Answer: 3/4
Using the GCF in one step
Simplify 18/45
Answer: 2/5
Repeated halving
Simplify 48/72
Answer: 2/3
You simplify by dividing top and bottom by the same number, never by subtracting the same number. 6/8 minus 2 from each gives 4/6 — a completely different value. 6/8 ÷ 2 gives 3/4, the same value.
If you halve the bottom you must halve the top too. 6/8 with only the 8 halved becomes 6/4 — that's 1 1/2, not 3/4. Every operation happens to both numbers.
12/18 ÷ 2 = 6/9 looks tidier, but 6 and 9 still share a factor of 3. Always run one final check: does anything bigger than 1 divide both? If yes, keep going.
Rewriting it with the smallest possible whole numbers while keeping the same value. 6/8 and 3/4 mark the same point on a number line — 3/4 just uses smaller numbers. It's also called reducing, cancelling or writing in lowest terms.
The largest number that divides both the numerator and denominator exactly. For 18 and 45 it's 9. Dividing both by the GCF simplifies the fraction fully in one step. It's also called the highest common factor (HCF).
When no whole number bigger than 1 divides both top and bottom. Quick screen: if both are even, or both divide by 3 or 5, it isn't done yet.
Small steps are fine and often easier: keep dividing by 2, 3 or 5 until nothing works. 48/72 halved three times then divided by 3 gives 2/3 — exactly what dividing by the GCF of 24 gives in one step.
No. Dividing top and bottom by the same number produces an equivalent fraction — the same amount described in bigger pieces. That's why simplified answers still count as correct answers.
The same way: 18/4 ÷ 2 = 9/2. Then convert to a mixed number if the question wants one: 9/2 = 4 1/2. Simplify first, convert second — the numbers stay smaller.
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