Fraction Calculator guide
How to Simplify a Fraction to Lowest Terms
To simplify a fraction, divide the numerator and denominator by their greatest common divisor. For 18/24, the greatest common divisor is 6, so dividing both gives 3/4. A fraction is in lowest terms when the only number dividing both parts is 1.
What simplifying does, and does not, change
Simplifying a fraction does not change its value at all. 18/24 and 3/4 are the same amount, written two ways.
It works because dividing the top and the bottom by the same number keeps their relationship intact. You are describing the same portion using fewer, larger pieces.
Most courses expect answers in lowest terms, so it is usually the last step of any fraction question.
The method
Find the largest number that divides both the numerator and the denominator — the greatest common divisor, or GCD — and divide both by it.
For 18/24: the numbers dividing 18 are 1, 2, 3, 6, 9, 18. Those dividing 24 are 1, 2, 3, 4, 6, 8, 12, 24. The largest in both lists is 6.
18 ÷ 6 = 3 and 24 ÷ 6 = 4, so 18/24 = 3/4.
If you cannot spot the GCD
You do not have to find it in one go. Divide by any common factor you notice, then look again.
For 18/24: both are even, so divide by 2 to get 9/12. Both divide by 3, giving 3/4. Two easy steps instead of one harder one, and the same destination.
This is often faster in practice, since spotting that two numbers are both even takes no thought at all.
Divisibility shortcuts
These make common factors much easier to spot:
- By 2 — the number ends in an even digit.
- By 3 — the digits add up to a multiple of 3. For 24: 2 + 4 = 6, so yes.
- By 5 — it ends in 0 or 5.
- By 9 — the digits add up to a multiple of 9.
- By 10 — it ends in 0.
Knowing when to stop
A fraction is fully simplified when the only number dividing both top and bottom is 1. That is what "lowest terms" means.
3/4 is done: 3 divides only by 1 and 3, and 4 is not divisible by 3.
A useful shortcut: if the numerator is a prime number and does not divide the denominator exactly, you are finished. 5/12 is in lowest terms because 5 is prime and 12 is not a multiple of 5.
Simplifying before you calculate
Simplifying is usually taught as a final step, but doing it early often saves considerable work.
When multiplying, cancel common factors before multiplying out. When adding, simplify each fraction first so the common denominator you need is smaller.
The calculator on this page shows the greatest common divisor it used in the working, so you can check your own factor against it when a simplification does not come out as you expected.
