To simplify fractions means to reduce those fractions to their lowest term in such a way that they can’t be reduced further. Canceling common fractions to their lowest term is also called simplifying fractions.
A simpler form of the fraction is often found by dividing the top number (numerator) and bottom number (denominator) by the same number.
Now let’s go straight to looking at how to simplify fractions.
How to simplify fractions (Steps)
To simplify a given fraction to its lowest term follow the steps below.
Step 1: write down the factors of the numerator and the denominator
Step 2: pick out common factors from the factors of the numerator and the denominator.
Step 3: Take the numerator and denominator and divide each of them by the highest common factor. The fraction so obtained is the simplest form of the given fraction.
Let’s look at some examples below.
\text{Example 1:} \space\text{simplify\space the fraction}\space \frac{24}{36} \space\text{to it's lowest term}.\\\space
Answer: \text{write down the factors of 24 and 36}\space\\
Factors of 24 = { 1,2,3,4,6,8,12,24}
factors of 36={1,2,3,4,6,9,12,18,36}
common factors of 24 and 36 ={1,2,3,4,6,12}
Now the highest common factor of 24 and 36 is 12. Then divide the numerator “24” and denominator “36” by 12.
\frac{24÷12}{36÷12}=\frac{2}{3}This is the quickers way to simplify fractions
Click here to see how to find the highest common factor of numbers
Another way to simplify fractions is by dividing the numerator and denominator by same number. And that number should be a factor of the numerator and denominator. Let’s look at example to this.
\begin{aligned}&\text{Example 1:}\space\text{Simplify } \space\frac{24}{36}\\\space
&Answer: \text{ Divide}\space \frac{24}{36} \space\text{by} \space2=\space\frac{24÷2}{36÷2}=\frac{12}{18}\\&\text{Divide}\space\frac{12}{18}\space \text{by}\space2=\frac{12÷2}{18÷2}=\frac{6}{9}\\&\text{Then, divide}\space\frac{6}{9}\space\text{by}\space3=\frac{6÷3}{9÷3}=\frac{2}{3}\end{aligned}