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.
(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.
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
● 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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