Simplifying Fractions

To simplify a fraction generally means to bring a fraction into its most reduced form and then can also be brought into the mixed fraction format if the fraction is improper.

An improper fraction is that whose numerator is greater than the denominator. For example, $16/7$, $25/16$, $182/5$, etc. These kinds of fractions are to be converted into mixed fraction format like $6 {6/7}$ etc.

A proper fraction is the one whose numerator is smaller than the denominator. For example, $3/16$, $1/2$, $5/8$ etc. It cannot be converted to a mixed fraction. It has to be reduced to its simplest form.

Steps to Simplify proper fractions:

Write in fraction form.

Now check every number starting from 2, 3, which divides both the numerator and the denominator.

Keep checking and reducing the fraction until it can no longer be divided by any number smaller than the numerator and denominator both.

You will obtain your result.

Example: Simplify $30/48$

Now we start making a check from the smallest digit i.e. 2. Both 30 and 48 are divisible by 2.

The first reduced form obtained will be $15/(24)$

Again checking with 2 both the numerator and denominator are not divisible by 2 any further. So we move on to 3. They are divisible by 3.

The next reduced form obtained is $5/8$

No other number now will be divisible by both the numerator and denominator. So the final result obtained is $5/8$

Steps to simplify improper fraction:

Write in fraction form.

Now check every number starting from 2, 3, ...... which divides both the numerator and the denominator.

Keep checking and reducing the fraction until it can no longer be divided by any number smaller than the numerator and denominator both.

Now since the numerator is greater than the denominator so we cannot leave it like that. We need to convert it into proper fraction so we convert it into a mixed fraction.

Steps to convert an improper fraction into a mixed fraction:

Divide the numerator by denominator.

The quotient and remainder are obtained where the remainder is not equal to zero.

The numerator becomes the remainder; denominator remains as it is and the quotient becomes the whole number.

Example: Simplify $32/6$

First, bring the fraction into its reduced form.

Now we start making a check from the smallest digit i.e. 2. Both 32 and 6 are divisible by 2.

The first reduced form obtained will be $16/(3)$

Now no further reduction is possible so we convert it into a mixed fraction.

$16 / 3$ gives quotient = 5 and remainder = 1

So the mixed fraction obtained is $51/3$ this is the final result.

So this is how simplification of fractions is performed.

Some other examples are:

Simplify $19/17$

Now, this is an improper fraction in its most reduced form so it is directly converted into mixed fraction as $19 / 17$ gives quotient = 1 and remainder = 2. So the mixed fraction obtained is $1 2/17$

There are various calculators available to perform such simplifications stepwise.