How to Simplify Fractions, Step by Step

A fraction is simplified (in lowest terms) when the top and bottom share no factor except 1. Simplifying doesn't change the value: 18/24 and 3/4 are the same amount, written with smaller numbers.

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The steps

Find the greatest common factor (GCF) of the top number (numerator) and the bottom number (denominator).
Divide the numerator by the GCF.
Divide the denominator by the same number.
Check that the new top and bottom have no common factor. If they do, repeat.
If the fraction is improper (the top is bigger), you can also write it as a mixed number.

A worked example

Simplify 18/24.

Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The GCF is 6.
Divide the top: 18 ÷ 6 = 3.
Divide the bottom: 24 ÷ 6 = 4.
3 and 4 share no factor except 1, so we are done.

18/24 = 3/4.

Why it works

Dividing the top and bottom by the same number is the same as multiplying the fraction by 1 (in this case 1/6 ÷ 1/6), so its value cannot change. Picture 18 of 24 equal slices of pizza. Group the slices in sixes and you have 3 groups out of 4. It is the same amount of pizza, with fewer pieces to count.

Try it with your own problem

Open the free The Fraction Bar with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: 18/24Opens The Fraction Bar with this example

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Common mistakes

Dividing only the top or only the bottom. Do the same to both, or the value changes.
Stopping early. Dividing 18/24 by 2 gives 9/12, which still simplifies. Dividing by the GCF finishes in one step.
Subtracting instead of dividing. 18/24 is not 12/18 (taking 6 off both). Use division.
Cancelling across a sum. In (2 + 3)/(2 + 5) you can't cancel the 2s. Only cancel factors.

Questions people ask

What if I can't find the GCF?

Divide by any common factor you can see (2, 3, 5, …) and repeat until nothing is left to divide by. It takes more steps but ends at the same answer.

Is 3/4 the same as 18/24?

Yes. Multiplying or dividing both parts by the same number gives an equivalent fraction.

How do I know a fraction is fully simplified?

When the GCF of the top and bottom is 1.

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