Finding Equivalent Fractions

We will discuss about finding equivalent fractions.

Equivalent fractions can be obtained by multiplying the numerator and the denominator of a fraction by the same non-zero number.

For example, look at the following rectangles.

(i)

Finding Equivalent Fractions

(ii)

Building Equivalent Fractions

(iii)

Equivalent Fraction

The shaded part of 1st rectangle can be denoted as ½. In the same way, 2nd and 3rd can be denoted as 2/4 and 3/6. Because all are showing same part of rectangle i.e., half of rectangle so they are equivalent fractions.

i.e., ½ = 2/4 = 3/6                or, ½ = 1 X 2/2 x 2 = 1 X 3/2 X 3

½ = 1 X 2/2 x 2 = 2/4    (We can get 2/4 from ½ by multiplying the numerator and the denominator of ½ by 2.)

½ = 1 X 3/2 X 3 = 3/6          (We can get 3/6 from ½ by multiplying the numerator and the denominator of ½ by 3.)

So, we can get equivalent fractions by multiplying the numerator and the denominator of a fraction by a non-zero number.

For example, 3/5 = 3 x 3/5 x 3 = 9/15

Or, 3/5 = 3 x 6/5 x 6 = 18/30

Or, 3/5 = 3 x 8/5 x 8 = 24/40

Here, 3/5, 9/15, 18/30 and 24/40 are equivalent fractions.

We can also obtain an equivalent fraction of a fraction by dividing the numerator and the denominator both by the same non-zero number.

For example, observe the shaded parts of these rectangles.

(i)

Understanding Equivalent Fractions

(ii)

Equivalent Fractions Calculator

(iii)

Equivalent Fractions Examples

The shaded parts in the 1st rectangle can be denoted as 8/16 in the same way, 2nd and 3rd can be denoted as 4/8 and 2/4. Because, all are shown same part i.e., half of the rectangle, so they are equivalent fractions.

i.e., 8/16 = 4/8 = 2/4

or

8/16 = 8 ÷ 2/16 ÷ 2 = 8 ÷ 4/16 ÷ 4

(We can obtain 4/8 and 2/4 from 8/16 by dividing their numerator and denominator from non-zero numbers 2 and 4 respectively.)

But it is easier to obtain an equivalent fraction by multiplying its numerator and denominator by the same non-zero number.

Related Concept

Fraction of a Whole Numbers

Representation of a Fraction

Equivalent Fractions

Properties of Equivalent Fractions

Like and Unlike Fractions

Comparison of Like Fractions

Comparison of Fractions having the same Numerator

Types of Fractions

Changing Fractions

Conversion of Fractions into Fractions having Same Denominator

Conversion of a Fraction into its Smallest and Simplest Form

Addition of Fractions having the Same Denominator

Subtraction of Fractions having the Same Denominator

Addition and Subtraction of Fractions on the Fraction Number Line



4th Grade Math Activities

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