What is an Equivalent Fraction

What is an Equivalent Fraction

Equivalent Fraction

To understand the concept of equivalent fractions, let us take an example – Rama gave four cakes to his four children. The first child cut his cake into two equal halves and ate the first half. The second child cut his cake into four equal parts and ate two pieces out of four. The third child cut his cake into six equal parts and ate three of them, and the fourth child cut the cake into eight equal pieces and ate four of them.
What is an Equivalent Fraction 1
Do you think, they have eaten equal parts of the cake? Yes.
What is an Equivalent Fraction 2
This means they all ate \(\frac{1}{2}\) of the cake. Thus, fractions \(\frac{1}{2}\), \(\frac{2}{4}\), \(\frac{3}{6}\), \(\frac{4}{8}\) represent the same fraction \(\frac{1}{2}\). These are called equivalent fractions. So, two or more fractions representing the same part (value) of the whole are called equivalent fractions.
To check if the fractions are equivalent or not, we do cross-multiplication.
What is an Equivalent Fraction 3
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Note:
We can get as many equivalent fractions as we want, by multiplying/dividing the numerator and denominator of the given fraction by the same number.

Example 1: Write five equivalent fractions of \(\frac{3}{5}\)
Solution:
What is an Equivalent Fraction 5
Hence, the five equivalent fractions of \(\frac{3}{5}\) are
What is an Equivalent Fraction 6

Example 2: Which ofthefollowing pairs of fractions are equivalent:
What is an Equivalent Fraction 7
Solution:
(i) By cross-multiplying the terms of the fractions,
What is an Equivalent Fraction 8
5 × 72 = 12 × 30
360 = 360
∴   \(\frac{5}{12}\) is equivalent to \(\frac{30}{72}\)
(ii) By cross-multiplying the terms of the fractions,
What is an Equivalent Fraction 9
∴   \(\frac{6}{7}\) is equivalent to \(\frac{12}{14}\)

Simplest Form of a Fraction

A fraction is said to be in the lowest term or the simplest form, if its numerator and denominator do not have any common factor other than 1.

Methods to reduce a fraction into the simplest form:
(i) Find the HCF of the numerator and the yg denominator of the given fraction.
(ii) Divide its numerator and denominator by their HCF.
What is an Equivalent Fraction 10
Example: \(\frac{162}{90}\)
HCF of 162 and 90 = 18
Dividing the numerator and denominator of the fraction by their HCF,
So, \(\frac{9}{5}\) is the lowest form of the given fraction because common factor of 9 and 5 is only 1.

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