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)
 (ii)
 (iii)

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)
 (ii)
 (iii)

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

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Recent Articles

1. Intersecting Lines | What Are Intersecting Lines? | Definition

Jun 14, 24 11:00 AM

Two lines that cross each other at a particular point are called intersecting lines. The point where two lines cross is called the point of intersection. In the given figure AB and CD intersect each o…

2. Line-Segment, Ray and Line | Definition of in Line-segment | Symbol

Jun 14, 24 10:41 AM

Definition of in Line-segment, ray and line geometry: A line segment is a fixed part of a line. It has two end points. It is named by the end points. In the figure given below end points are A and B…

3. Definition of Points, Lines and Shapes in Geometry | Types & Examples

Jun 14, 24 09:45 AM

Definition of points, lines and shapes in geometry: Point: A point is the fundamental element of geometry. If we put the tip of a pencil on a paper and press it lightly,

4. Subtracting Integers | Subtraction of Integers |Fundamental Operations

Jun 13, 24 04:32 PM

Subtracting integers is the second operations on integers, among the four fundamental operations on integers. Change the sign of the integer to be subtracted and then add.