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 nonzero number.
For example, look at the following rectangles.
(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 nonzero 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 nonzero number.
For example, observe the shaded parts of these rectangles.
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 nonzero numbers 2 and 4 respectively.)
But it is easier to obtain an equivalent fraction by multiplying its numerator and denominator by the same nonzero number.
Related Concept
● Representation of a Fraction
● Properties of Equivalent Fractions
● Comparison of Like Fractions
● Comparison of Fractions having the same Numerator
● 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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