Math

# Subtracting Fractions With Like And Unlike Denominators & Examples

A fraction is a part of a whole number with a numerator and denominator. To subtract two or more fractions, there are techniques that you must follow.

Firstly, there are types of fractions, and knowing this will let you know the approach to use when subtracting fractions.  We have the unit, improper, proper, and mixed fractions. An example of a unit fraction is ½, improper is 5/2, proper is 2/5, and mixed is 2 1/3.

There are fractions with like denominators and some with unlike denominators. So, the approach to use for each of them will be a bit different, as I show you some examples.

## Subtracting Fractions with Unlike Denominators

Unlike denominators means the numbers aren’t the same. For example, subtracting 1/4 from 2/3. The first fraction has a denominator of 4, while the second one has a denominator of 3.

So, to solve this fraction, you will find the L.C.M (lowest common multiple) of 4 and 3. The LCM is 12.

2/3 – 1/4

The next step is to divide the LCM, which is 12 divided by the first denominator 3 (= 4), and also divide 12 by the second denominator 4 (=3)

After that, I will multiply the numerator of the first fraction by 4 (2*4 =8) and the numerator of the second fraction by 3 (1*3 = 3).

Now, subtract the result

2/3 – 1/4  = (2*4) – (1*3) / 12 = 8 – 3/12 = 5/12

In conclusion, subtracting 1/4 from 2/3 will give 5/12.

The example I give above is for a proper fraction.

### Subtracting mixed fractions with unlike denominators

The easiest way to go about this type of question is to convert mixed fractions into proper ones.

For example, subtract 2 3/4 from 5 1/3. Like I said, we change to a proper fraction before subtracting.

2 ¾ to proper fraction is [(2*4 +3) /4 = 11/4]

5 1/3 = [(5*3 + 1)/3 = 16/3]

16/3 – 11/4, the LCM is 12

Using the same approach as the one above, (12 /3 *16 = 4*16 = 64) and (12/4 *11 = 3*11 = 33)

16/3 – 11/4 = (12 /3 *16) – (12/4 *11) / 12 =( 64 – 33) / 12 = 31/12

The answer is 31/12, which is an improper fraction because the denominator is less than the numerator. So, we can change it to a mixed fraction

31/12  to a mixed fraction (how many times can 12 go in 31 = 2 times, and it will remain 6). This will now be 2 whole number 7 over 12 ( 2 7/12)

So, 5 1/3 – 2 ¾ = 2 7/12

## Subtracting Fractions with Like Denominators

This is the simplest of it. Examples of fractions with like denominators are 1/9, 5/9, 2/9, etc. To subtract a fraction of this type, you only need to subtract the numerators.

Example

Subtract ¼ from ¾

¾ – ¼ = the LCM is 4 = (3-1)/4 = 2/4 (these can be expressed in the lowest fraction, and that will be 2/4)

### Bolarinwa Olajire

A tutor with a demonstrated history of working in the education industry. Skilled in analytical skills. Strong education professional with a M. SC focused in condensed matter. You can follow me on Twitter by clicking on the icon below to ask questions.