Subtraction of Unlike Fraction(Different Denominators)

Subtracting Fractions With Different Denominators

We learned how to subtract like fractions(same denominators).

When denominators are different the fractions are called unlike fractions.

In this tutorial we will learn subtraction of fractions with different denominators.

When we subtract unlike fractions, first we convert them to like fractions by finding the LCM of the denominators, so the denominators becomes same and then subtract them.

Let us see the steps of subtraction of unlike fractions with the help of an example given below.

Example: Subtract 2/3 from 3/4

Solution: 3/4 – 2/3

Step 1: To subtract unlike fractions, First we convert them into like fractions.

So, to convert them into like fractions(common denominator), we find the LCM (least common multiple) of the different denominators of the given fractions.

In the given fraction denominators are different, as 4 and 3.

First we finding the LCM (least common multiple) of the denominators.

LCM of 4 and 3 is 12.

So we need to find fractions equivalent to, 3/4 and 2/3 which have 12 in the denominators.

Step 2: Multiply the numerator and denominator of 3/4 with 3

(3/4) x (3/3) = 9/12 and

multiply the numerator and denominator of 2/3 with 4

(2/3) x (4/4) = 8/12

Step 3: Now denominators of both fractions are same as 12.

We get two new fractions with common denominators are 9/12 and 8/12.

So we subtract the numerators and write the result over the common denominator.

So, the result is 9/12 – 8/12

= (9 – 8)/12

= 1/12

Step 3: Simplify the fraction to its lowest form, if needed.

Example: Subtract 1/4 from 2/3

2/3 – 1/4

Solution:

Step 1: In the given fraction denominators are different, as 4 and 3.

First we finding the LCM (least common multiple) of the denominators.

LCM of 4 and 3 is 12.

So we need to find fractions equivalent to 1/4 and 2/3 which have 12 in the denominators.

Step 2: Now multiply the numerator and denominator of 1/4 with 3

(1/4) x (3/3) = 3/12 and

multiply the numerator and denominator of 2/3 with 4

(2/3) x (4/4) = 8/12

Step 3: Now denominators of both fractions are same as 12.

We get two new fractions with common denominators are 3/12 and 8/12.

So we subtract the numerators and write the result over the common denominator.

So, the result is 8/12 – 3/12

= (8 – 3)/12

= 5/12

Example: Subtract 5/2 from 8/6

8/6 – 5/2

Example: Solve 7/4 – 3/5

In the given fraction denominators are 4 and 5.

LCM (least common multiple) of the denominators, 4 and 5 is 20.

Now multiply the numerator and denominator of 7/4 with 5

(7/4) x (5/5)

= 35/20 and

multiply the numerator and denominator of 3/5 with 4

(3/5) x (4/4)

= 12/20

Now denominators of both fractions are same as 20. So, we subtract the numerators and write the result over the common denominator.

So, the result is 35/20 – 12/20

= (35 – 12)/20

= 23/20