How to Find Equivalent Fractions?

For every fraction, we can determine an equivalent fraction either by multiplying or dividing both the numerator and the denominator with the same number. That’s why when all equivalent fractions are simplified, they are reduced to the same fraction. We have two ways of finding the equivalent fraction of any number,

• Multiplying Numerator and Denominator by Same Number
• Dividing Numerator and Denominator by Same Number

Now, let’s study these two cases in detail.

Case 1: Multiplying Numerator and Denominator by Same Number

For every fraction, we can determine an equivalent fraction by multiplying both the numerator and the denominator with the same number. For instance, to determine the equivalent fraction of 2/3, multiply both the numerator and the denominator with the same number, i.e., 2. Thus, the equivalent fraction of 2/3 is 4/6. Similarly, we can find some other equivalent fractions by repeating the same process.

Equivalent fractions of 2/3

• Multiplying Numerator and Denominator by 3, we get 2/3 × 3/3 = 6/9
• Multiplying Numerator and Denominator by 4, we get 2/3 × 4/4 = 8/12
• Multiplying Numerator and Denominator by 5, we get 2/3 × 5/5 = 10/15

Hence, we can conclude that equivalent fractions of 2/3 are 4/6, 8/12, and 10/15

Case 2: Dividing Numerator and Denominator by Same Number

For every fraction, we can determine an equivalent fraction by dividing both the numerator and the denominator by the same number. For instance, to find the equivalent fraction of 45/300, first, we have to find their common factors. Here, 3 is a common factor of both 45 and 300. So, the equivalent fraction of 45/300 can be found by dividing its numerator and denominator by 3. Thus, the equivalent fraction of  45/300 is 15/100. 

Let us simplify the fraction further.

5 is a common factor of 15 and 100. So, 15/100 = (15÷5)/(100÷5) = 3/20

Hence, the equivalent fractions of 45/300 are 15/100 and 3/20. As there are no common factors for 3 and 20 other than 1, 3/20 is the simplified form of 45/300.

Equivalent Fractions are the fractions that represent the same value and by simplifying the fraction in simplest form we always get the same fraction. We define the fraction as a way of representing a part of some quantity. Suppose we have one pizza with six equal sizes and Shiv takes two slices from it then the remaining pizza is represented as, 4/6 which is equivalent fraction to 2/3. The various other examples of equivalent fractions are 1/3, 2/6, 3/9, and others.

The simplest form of all the equivalent fractions is the same, i.e. if all the equivalent fraction is reduced to the simplest term then they all are the same. For example, the simplest form of 1/3, 2/6, and 3/9 is 1/3. Let’s learn more about equivalent fractions, its example, and others in detail in this article.