# Simplifying fractions

Simplifying fractions (also known as reducing fractions) involves finding the greatest common factor - this is the largest number that divides exactly into both the numerator and the denominator of a fraction.

In other words, by dividing by the greatest common factor, you end up with an equivalent fraction made up of the smallest possible numerator and denominator.

## Let's look at an example

In the fraction

5/25

- five twenty-fifths, the greatest common factor is 5.

If you divide numerator and denominator by this factor, you can see that you're left with the fraction 1/5 (one fifth)

Often, such as in this example, the greatest common factor is the same as the numerator of the fraction being simplified - the denominator can be divided by the numerator exactly. In this case, 25 divides by 5 to give 5.

## But what if this isn't the case?

For instance, consider the fraction

9/15

The denominator cannot be divided by the numerator exactly – 15 divided by 9 gives one and two thirds (i.e. not a whole number).

The greatest common factor here is 3 - dividing 9 and 15 by this factor gives the smallest possible numerator (3) and denominator (5), the fraction 3/5 or three fifths

## What if the greatest common factor isn't obvious?

If you come across a fraction for which the greatest common factor isn’t obvious, simply pick any factor by which both numerator and denominator divide.

For example, the fraction 16/44 appears quite daunting but if you divide numerator and denominator by 2 and then by 2 again you're left with a much simpler looking fraction

- four elevenths. There is no further factor by which numerator and denominator can be divided to give a more simple fraction.

In this case, you have divided numerator and denominator by a factor of 2 twice. Multiplying these factors together, 2 x 2, gives you the greatest common factor, 4. You can check this as shown below

Now let’s simplify the fraction 36/84 – don’t worry, it’s easier than it looks!

Both 18 and 42 will also divide by a factor of 2

Finally, both 9 and 21 will divide by a factor of 3 to give the smallest possible numerator and denominator

- three sevenths – much better!

The greatest common factor here is 2 x 2 x 3 = 12 (in other words, it’s the result or product of multiplying together each of the dividing factors you’ve used to reach the simplest possible fraction)

## Have a go at simplifying fractions yourself

With time, you’ll learn to spot the greatest common factor with fewer steps or even straight away! Don’t be frightened by fractions with large numerators and denominators. Simplifying fractions becomes easier with practice – try writing down a few of your own fractions and simplifying them.

For more on fractions click:

Math fractions

Equivalent fractions

How to subtract fractions

Multiplying fractions

How to divide fractions

Improper fractions

Mixed fractions (mixed numbers)

Comparing fractions

Ordering fractions

Fraction to decimal

Fraction to decimal chart

Decimal to fraction

Fraction to percent