Equivalent fractions are different fractions having a same value. A fraction is part of whole. i.e.

**Fraction = Part/Whole = numerator/denominator**

Therefore, if both of part and whole (i.e. numerator and denominator) grow equally, then the value of fraction can continue to remain same.Hence, fractions with different numerators and denominators but having a same value are called equivalent fractions. The following figure illustrates the concept of equivalent fractions. In the above figure, ABCD is a rectangle and PQRS is a circle.

**{In ABCD, AC is diagonal, and in PQRS, O is center}**

The area of the rectangle shaded is ½, and the area of the circle shaded is 2/4. Though ½ and 2/4 are two different fractions, still they have a same value i.e. in the respective figures a same fraction of the area is shaded. A few examples of equivalent fractions are 1/2 and 3/6, 3/4 and 6/8.

**How to find equivalent fractions of given fraction? **Fractions continue to have same value even when both of their numerators and denominators grow equally. Therefore, to find equivalent fractions of a given fraction: multiply or divide numerators and denominators with a same value.

## 1. Equivalent fractions of 3/5 thru multiplying are

In the equivalent fractions for 3/5, the numerator and denominator are multiplied by a same value.

*6/10 = (3 × 2)/ (5 × 2)*

*9/15 = (3 × 3)/ (5 × 3)*

*12/20 = (3 × 4)/ (5 × 4)*

*All of the fractions 6/10, 9/15 and 12/20 have a same value as 3/5 does.*

Therefore, a few equivalent fractions of 3/5 are *6/10, 9/15 and 12/20.*

## 2. Equivalent fractions of 32/40 thru dividing are:

(*32÷ 2)/ (40 ÷ 2) = 16/20,*

*(32÷ 4)/ (40 ÷ 4) = 8/10,*

*(32÷ 8)/ (40 ÷ 8) = 4/5*

All of the fractions 16/20, 8/10 and 4/5 have a same value as 32/40 does. Therefore, a few equivalent fractions of 32/40 are 16/20, 8/10 and 4/5.

**Note:**

1. Addition of a same number to numerator and denominator will change the value of the fraction. *3/5 ≠ (3 + 2)/ (5 + 2), i.e. 3/5 ≠ 5/7*

2. Subtraction of a same number from both numerator and denominator will also not yield equivalent fractions. 5/ 7 ≠ (5 – 2)/ (7 – 2) ≠ 3/5

**How to determine if two fractions are equivalent fractions:**

Consider the two fractions a/b and c/d. Cross multiply the two fractions a/b and c/d, to find if they are equivalent fractions as below.

If a/b and c/d are equivalent fractions, then *a × d = b × c*

**Example:**

Find whether the two fractions 5/9 and 30/54 are equivalent fractions.

**Solution:**

**Cross multiply the two fractions 5/9 and 30/54 as below:**

*5 × 54 = 9 × 30*

*i.e. 270 = 270.*

Therefore, 5/9 and 30/54 are equivalent fractions.