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Simplest Form of a Fraction

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Simplest Form of a Fraction: A fraction is said to be in the simplest (or lowest) form if its numerator and denominator have no common factor except 1. `4/3, 2/5` etc. are examples of the simplest form of a fraction.

notes

Simplest Form of a Fraction:

A fraction is said to be in the simplest (or lowest) form if its numerator and the denominator have no common factor except 1.

For Example: `4/3, 2/5` etc.

Given the fraction `36/54`,

Let us try to get an equivalent fraction in which the numerator and the denominator have no common factor except 1.

We see that both 36 and 54 are divisible by 2.

`36/54 = (36 ÷ 2)/(54 ÷ 2) = 18/27`.

But 18 and 27 also have common factors other than one. The common factors are 1, 3, 9; the highest is 9. Therefore,

`18/27 = (18 ÷ 9)/(27 ÷ 9) = 2/3`.

Now 2 and 3 have no common factor except 1; we say that the fraction `2/3` is in the simplest form.

The shortest way:

To find the equivalent fraction which is the simplest form we have to find the HCF of numerator and denominator and then divide them both by that HCF.

Consider another example `(36)/(24)`

The HCF of 36 and 24 is 12.

Therefore, `(36)/(24) = (36 ÷ 12)/(24 ÷ 12) = 3/2`

The fraction `3/2` is in the lowest form.

Thus, HCF helps us to reduce a fraction to its lowest form.

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