How to Simplify Fractions

Is 12/18 the same as 2/3? Yes, and here is how to see it. To simplify a fraction, you divide the top number and the bottom number by the same value until they share no common factor. The fastest way is to divide both by their greatest common factor, or GCF. The fraction still means the same amount, just written with smaller, cleaner numbers.

What “Simplify” Means

Simplifying a fraction means rewriting it with the smallest possible whole numbers on top and bottom. The value stays exactly the same. You are changing the look, not the size.

A fraction is in lowest terms (also called simplest form) when the top and bottom share no common factor except 1. For example, 2/3 is already simplest, because 2 and 3 have nothing in common but 1.

Why bother? Smaller numbers are easier to read, compare, and use in later math. Both 12/18 and 2/3 point to the same spot on a number line, but 2/3 is much easier to picture.

Teachers usually expect a final answer in lowest terms. It also makes fractions simpler to add, compare, or turn into a decimal or percentage later on.

Think of a pizza cut into 18 slices. Taking 12 of them is the same as taking 2 out of 3 equal shares. Nothing about the amount of pizza changes; you just describe it with tidier numbers. That is the whole idea behind simplifying.

The Method: Divide by the GCF

The cleanest way to simplify is to divide the top and bottom by their greatest common factor. The GCF is the largest number that divides both evenly. Do it once and you land in lowest terms in a single step.

Take 12/18. First find the GCF of 12 and 18, which is 6 (the largest number that divides both). If you need to see how to find a GCF, our guide on LCM and GCF explained walks through it. Now divide both parts by 6:

12/18 = (12/6)/(18/6) = 2/3

Check the result: 2 and 3 share no common factor except 1, so 2/3 is in lowest terms. You are done. The whole method is just “find the GCF, then divide both numbers by it.”

More Fractions Reduced by the GCF

The same three moves work on any fraction. Here are a few more, each divided by its GCF in one step:

Every row uses the exact same rule. Find the biggest shared factor, divide it out of the top and bottom, and read off the simplest form.

The Step-by-Step Way

Not sure of the GCF? You do not need it. You can divide by any common factor you spot, then repeat until nothing divides both numbers. You reach the same answer, just in more steps.

1. Look at the top and bottom and find any number that divides both. For 12/18, both are even, so divide by 2: 12/18 = 6/9.
2. Look again at the new fraction. For 6/9, both split by 3, so divide by 3: 6/9 = 2/3.
3. Repeat until the top and bottom share no common factor except 1. Here, 2 and 3 share nothing, so stop.
4. The fraction you are left with, 2/3, is in lowest terms.

Notice both roads end at 2/3. Dividing by the GCF is the shortcut; dividing by small factors again and again is the safe, no-guessing path.

This method is handy when the numbers are large and the GCF is hard to spot. Start with an easy factor you can see. If both numbers are even, divide by 2. If both end in 0 or 5, divide by 5. If the digits of each add up to a multiple of 3, divide by 3. Keep chipping away, and you will land in lowest terms without ever needing the GCF up front.

Simplify an Improper Fraction to a Mixed Number

An improper fraction has a top number that is larger than its bottom, like 7/2. You can rewrite it as a mixed number: a whole number plus a proper fraction.

Divide the top by the bottom. The whole-number part is how many times the bottom fits, and the remainder becomes the new top over the same bottom. Keep the bottom number the same the whole time.

Take 7/2. How many times does 2 go into 7? It goes in 3 times (3 x 2 = 6), with a remainder of 1. So:

7/2 = 3 and 1/2

Always simplify the leftover fraction too. Here 1/2 is already in lowest terms, so the mixed number 3 and 1/2 is your final answer. If the fraction part could reduce, you would divide by its GCF first.

Try another: 8/3. How many times does 3 go into 8? Twice (2 x 3 = 6), with 2 left over. So 8/3 = 2 and 2/3. The remainder 2 sits over the same bottom, 3, and 2/3 is already in lowest terms.

Mixed numbers are easier to read in everyday life, like measuring 3 and 1/2 cups. Once a fraction is in lowest terms, it is also simpler to convert into decimals and percentages when you need a different form.

Common Fraction Mistakes

A few slips trip people up again and again. Watch for these when you simplify:

• Dividing only one part. You must divide the top and the bottom by the same number. Changing just one changes the value.
• Subtracting instead of dividing. Simplifying uses division, not subtraction. Taking 6 away from both 12 and 18 does not give an equal fraction.
• Stopping too early. 6/9 is smaller than 12/18 but not finished. Keep going until nothing divides both numbers.
• Forgetting the mixed-number fraction. After splitting an improper fraction, reduce the leftover part if it can shrink.
• Assuming odd tops cannot reduce. 9/12 looks stuck, but both share 3, so it becomes 3/4.

One more check: 8/12 reduces the same way as 12/18. The GCF of 8 and 12 is 4, so 8/12 = (8/4)/(12/4) = 2/3. Different starting numbers, same simplest form.

When in doubt, slow down and do one factor at a time. A steady step-by-step reduction beats a rushed guess, and it always brings you to the correct lowest terms.

Frequently Asked Questions About Simplifying Fractions

Sources

This article is for general education only. Always double-check the formulas and math for your own problem before you rely on the result. Reviewed for accuracy by Prof. Dr. Khalil Mudassar, PhD. Last updated September 11, 2026.