Equivalent Fractions

Let’s observe these fractions.

If we place the above pictorial representation one over the other, they are found to be equal. These fractions are called equivalent fractions.

Equivalent fractions are fractions that look different but have the same value.

Example:

Let’s understand how are they the same?

They are the same because when we multiply or divide both the top and bottom by the same number, the fraction keeps its value.

Or

Note: Choose the number you divide by carefully, so that it divides the numerator and denominator without leaving any remainder.

How to find equivalent fractions?

To find an equivalent fraction of a given fraction, we can multiply or divide both the numerator and the denominator of the given fraction by the same number.

Example 1: Find two equivalent fractions of 1/3

Solution:

Here the given fraction is in the simplest form, so we will multiply both the numerator and the denominator of the given fraction by the same number.

Example 2: Find two equivalent fractions of 18/36

Solution:

Here the given fraction is not in the simplest form, so we can multiply or divide both the numerator and the denominator of the given fraction by the same number.

 Or

Example 3: Find the equivalent fraction of 2/7 with numerator 8.

Solution: We know 2 × 4 = 8. This means we need to multiply both the numerator and the denominator by 4 to get the equivalent fraction.

Hence, 8/28 is the required equivalent fraction.

Example 4: Find the equivalent fraction of 15/35 with denominator 7.

Solution: We know that 35 ÷ 5 = 7. We, therefore, divide both the numerator and the denominator of by 5.

How do you know if a fraction is equivalent?

A simple way to look at how to check for equivalent fractions is to do what is called “cross-multiplication”, which means multiply the numerator of one fraction by the denominator of the other fraction and numerator of second fraction by the denominator of the first fraction. Now compare the two cross products to see if they are equal. If the products are equal, then fractions are equivalent.

Example 5: Check whether the given fractions are equivalent:

 

Solution:

5 x 54 = 9 x 30

270 = 270

Here, the products are equal, so the fractions are equivalent.

Key Points

     •     We can make equivalent fractions by multiplying or dividing both top and bottom by the same amount.

     •     We only multiply or divide, never add or subtract, to get an equivalent fraction.

     •     Only divide when the top and bottom stay as whole numbers.

     •     A simple way to look at how to check for equivalent fractions is to do what is called “cross-multiplication”.