Before we get into the how of simplifying fractions, let’s talk about the why. Imagine a giant pizza that’s cut into 32 pieces. Someone comes by and eats 16 of the pieces… They were hungry! If you asked them how much of the pizza they ate, would it be easier for you to understand that they ate 16/32 or 1/2 of the pizza? 1/2 for sure! That’s why we simplify fractions – because they’re easier to understand when they’re in their simplified form.

How do you simplify fractions?

In order to have a fraction in its simplest form, the numerator (top number) and denominator (bottom number) can have no common factors except 1. That means that the two numbers that make up the fraction can’t both be divided by anything except 1.

Example: Simplify 15/45.

Step 1 – Find the factors of 15 and 45.

• • 15: 1, 3, 5, 15
  • 45: 1, 3, 5, 9, 15, 45
  • 3, 5, and 15 are all common factors, but 15 is the greatest. That’s the number we’re looking for – the biggest.

Step 2 – Divide the numerator and denominator by the greatest common factor (GCF).

• • 15 ÷ 15 = 1
  • 45 ÷ 15 = 3

Step 3 –  Substitute.

• • 15/45 = 1/3
  • 1/3 is your answer.

What is the easiest way to simplify fractions?

If you know your multiplication tables really well then you’ll be able to simplify smaller fractions in your head, or with very little work. Sometimes, though, fractions are so big that you won’t know how to simplify them quickly, and writing out all the factors would be time-consuming. Here are some simplifying fractions tips:

1. If the numerator and denominator end in a 0 or a 5 you can immediately know that 5 is a factor. Divide both parts of your fraction by 5 to get a more manageable fraction.
2. If the numerator and denominator end in an even number, then 2 is a factor. Divide both parts by 2 to get a more manageable fraction.
3. If the numerator and denominator end in a 0, then 10 is a factor. Divide both parts by 10 to get a more manageable fraction.
4. There are other tricks like this. Below you can see how to tell if a number is divisible by:

• • 3: if the sum of the digits is divisible by 3.
  • 4: if the number formed by the last 2 digits is divisible by 4 (or if the last 2 digits are zeros).
  • 6: if the number is divisible by 2 AND 3.
  • 8: if the number formed by the last 3 digits is divisible by 8 (or if the last 3 digits are zeros).
  • 9: if the sum of the digits is divisible by 9.

For all of the tricks listed above, make sure you check the numerator and denominator for divisibility.

Can fractions always be simplified?

No. Fractions can only be simplified if they have a common factor, other than 1. The fraction 7/11 is already in its simplest form, so it can’t be simplified any further. To show you:

• The factors of 7 are 1 and 7.
• The factors of 11 are 1 and 11.
• The only common factor they have is 1.
• If we try to simplify 7/11 using their common factor we would end up with the same fraction
• 7 ÷ 1 = 7, 11 ÷ 1 = 11
• So 7/11 = 7/11