Sometimes fractions are not written in the simplest way possible. This means that there is an equivalent fraction that uses simpler (in this case smaller) numbers.

Remember from our work in equivalent fractions, (see Is this the same as that? to refresh your memory), that some fractions have exactly the same value as another, like $\frac{1}{2}=\frac{2}{4}$12=24.

In reverse, we can could say that $\frac{2}{4}$24can be simplified to $\frac{1}{2}$12.

A simplified fraction is the equivalent fraction that has no common factors between the numerator and denominator.

We have already discussed common factors as well, if you would like a refresher go back to The Highs and Lows and Trees with Multiple Branches.

So lets look at some examples for simplifying fractions.

Example

Question 1

Simplify: $\frac{15}{25}$1525

Think: Identify common factors between 15 and 25. I can see that 15 and 25 both have a common factor of 5.

Do: I can rewrite $\frac{15}{25}$1525 as $\frac{3\times5}{5\times5}$3×55×5, and then I remove the common factor from the numerator and the denominator (top and bottom). This leaves $\frac{3}{5}$35. I check to make sure there are no more common factors, if not then this is the final answer.

Let's look at another.

Question 2

Simplify: $\frac{16}{40}$1640

Think: Identify common factors between 16 and 40.

Do: By using factor trees I could see that the common factors are $2\times2\times2=8$2×2×2=8.

So I can rewrite $\frac{16}{40}$1640 as $\frac{2\times8}{5\times8}$2×85×8, and then I can simplify the fraction to$\frac{2}{5}$25.

Question 3

Simplify $\frac{24}{42}$2442

Question 4

Simplify $\frac{40}{25}$4025 writing your answer as an improper fraction