Equivalent fractions
A set of fractions have a different numerator and denominator, but their values equal the same.
The fractions like 12,24,36,48 have a different numerator and different denominator but represent the same value. These are called equivalent fractions.
Obtaining the equivalent fractions:
To find the equivalent fraction of a given fraction, multiply/divide the numerator and denominator by the same number.
1. Equivalent fraction by multiplication:
\(1/5\) can be converted into its equivalent fraction as, 1×25×2=210;1×35×3=315
2. Equivalent fraction by division:
The equivalent fractions of \(frac{10}{20}\), 10÷220÷2=510;10÷520÷5=24;10÷1020÷10=12
Steps to find the equivalent fraction if denominator is given:
1. Observe the relation of the two given denominators.
2. Divide the \(1\)st denominator by the \(2\)nd denominator.
3. Divide this product with the given fraction.
Let us an example to understand this concept.
Find the equivalent fraction of \(\frac{54}{30}\) with denominator \(10\).
As per the above theory, divide the \(1\)st denominator by the \(2\)nd denominator.
That is, \(30 ÷ 10 = 3\).
No we divide this product with the given fraction.
Simplest Form of a Fraction
If the numerator and denominator of a fraction have no common factor other than \(1\), it is said to be in its simplest (or lowest) form of a fraction.
Steps to convert a fraction into the simplest form:
1. Find the HCF (Highest Common Factor) of the numerator and denominator of a fraction.
2. Then divide them by their HCF.
Write in the simplest form \(\frac{12}{8}\)
1. The HCF of numerator \(12\) and denominator \(8\) is \(4\).
2. Divide the numerator \((12)\) and the denominator \((8)\) by \(4\) which is equal to 32 that is 12÷48÷4=32.
[Note: Here we cannot reduce the fraction 32 further, since the common factor of numerator \((3)\) and the denominator \((2)\) is \(1\)].
Thus32 will be the simplest form of \(\frac{12}{8}\).