How to Simplify Fractions: A Grade 6 Guide

To simplify a fraction means to write it with smaller numbers that mean the same amount, like 6/8 written as 3/4. I divide the top and the bottom by the same number, again and again, until no number except 1 divides both. The value never changes, only the numbers get smaller.

What Does It Mean to Simplify a Fraction?

To simplify a fraction means to write the same amount with smaller numbers, like 6/8 written as 3/4. The top and the bottom both shrink, but the amount stays exactly the same, because you divide both by the same number. A simplified fraction is the shortest way to write that amount.

I show it with a pizza, because a child can see it. Six slices out of eight is the same amount of pizza as three slices out of four, so 6/8 and 3/4 are the same fraction in different clothes.

The top number is the numerator, and the bottom number is the denominator. Simplifying never changes the amount, so it never changes the answer to a real question.

How Do You Simplify a Fraction Step by Step?

To simplify a fraction, find the greatest common factor of the top and the bottom, then divide both by it. For 12/18, the greatest common factor is 6, so 12 ÷ 6 is 2 and 18 ÷ 6 is 3, which gives 2/3. That is the whole method, in one move.

If the greatest common factor is hard to spot, divide by a small common factor first, then look again. For 12/18, divide by 2 to get 6/9, then divide by 3 to get 2/3. Two small steps land in the same place as one big step.

I explain the greatest common factor in full in my Factors and Multiples guide, where listing factors in pairs finds it fast.

How Do You Know When a Fraction Is Fully Simplified?

A fraction is fully simplified when no number except 1 divides both the top and the bottom. For 2/3, no number except 1 divides both 2 and 3, so 2/3 is in simplest form, while 6/9 is not, because 3 divides both 6 and 9.

I call it the “nothing left in common” test. Look at the top and the bottom together and ask: does any number divide both? If the answer is no, the fraction is done. If the answer is yes, divide again.

One is the only number that divides everything, and it does not count. Dividing by 1 changes nothing, so the test is always “anything bigger than 1?”

What Mistakes Do Children Make Most When Simplifying?

The commonest mistake is dividing only the top number and leaving the bottom alone, which changes the amount. Children also stop too early, leaving a fraction like 6/9 unsimplified, and divide the top and bottom by different numbers, which also changes the amount.

The fix is one rule, said out loud before every sum: whatever you do to the top, you do to the bottom. I make children write the divisor beside both numbers, so the eye catches it if one side is missed.

Stopping too early is the quietest mistake, because the answer looks finished. After every step, ask the “nothing left in common” test again, and only stop when the answer is no.

A Real-Life Case: Sharing a Pizza

Here is one case, worked in full, the way I do it in class.

Step 1: A pizza is cut into 8 equal slices, and you eat 6 of them. You ate 6/8 of the pizza, which is a correct fraction, but it is not the simplest way to say it.

Step 2: Find the greatest common factor of 6 and 8, which is 2. Divide the top by 2 to get 3, and divide the bottom by 2 to get 4. You ate 3/4 of the pizza.

Step 3: Check it: 6/8 and 3/4 are the same amount, because 3 slices out of 4 is the same share as 6 slices out of 8. The numbers got smaller, and the pizza did not change.

Fractions run daily life, and I show how in my Why Do We Learn Fractions guide, where pizza, recipes and money all split into parts.

Try It Yourself: 3 Practice Questions

Cover the answers, try all three, then check.

1. Simplify 6/8.
2. Simplify 12/18.
3. Simplify 15/25.

Answers

1. 3/4. The greatest common factor of 6 and 8 is 2, so 6 ÷ 2 is 3 and 8 ÷ 2 is 4.
2. 2/3. The greatest common factor of 12 and 18 is 6, so 12 ÷ 6 is 2 and 18 ÷ 6 is 3.
3. 3/5. The greatest common factor of 15 and 25 is 5, so 15 ÷ 5 is 3 and 25 ÷ 5 is 5.

Key Takeaways

• Simplify: divide top and bottom by the same number.
• Use the GCF: the greatest common factor finishes it in one step.
• Test for done: nothing bigger than 1 divides both numbers.
• Same to both sides: whatever you do to the top, do to the bottom.
• Amount never changes: 6/8 and 3/4 are the same pizza.

If your child answered all three questions, she is ready for a longer page. For more free practice at this level, browse our Grade 6 math worksheets page. Every sheet is free to print.