Subtraction of Unlike Fractions

Steps to Subtract Unlike Fractions

Step 1: Use LCM method to convert the unlike fractions into like fractions.

Step 2: Find out new numerators of the given fractions.

Step 3: Find difference of new numerators.

Step 4: Write the resulting numerator after subtraction over the LCM as denominator.

Step 5: If resultant fraction is an improper fraction then convert it into mixed fraction.

Example 1:

Here denominators are different. So, we will first make denominators of the given fractions equal, using LCM method.

LCM OF 3 and 4

= 3x4

= 12

Now we have to find out new numerators of the both fractions.

New Numerator of the first fraction =

LCM ÷ Denominator of the first fraction x Numerator of the first fraction

= 12 ÷ 3 = 4 (LCM ÷ Denominator of the first fraction)

= 4x2 =8 (Resultant answer x Numerator of the first fraction)

New numerator of first fraction is 8

New Numerator of the second fraction =

LCM ÷ Denominator of the second fraction x Numerator of the second fraction

= 12 ÷ 4 = 3 (LCM ÷ Denominator of the second fraction)

= 3x1 =3 (Resultant answer x Numerator of the second fraction)

New numerator of second fraction is 3

Now subtract new numerators

= 8 - 3

= 5

Then write the resulting numerator after subtraction over the LCM as denominator.

Example 2:

Here denominators are different. So, we will first make denominators of the given fractions equal, using LCM method.

LCM OF 7 and 14

= 7 x 2

= 14

Now we have to find out new numerators of the fractions.

New Numerator of the first fraction =

LCM ÷ Denominator of the first fraction x Numerator of the first fraction

= 14 ÷ 7 = 2 (LCM ÷ Denominator of the first fraction)

= 2x4 = 8 (Resultant answer x Numerator of the first fraction)

New numerator of first fraction is 8

New Numerator of the second fraction =

LCM ÷ Denominator of the second fraction x Numerator of the second fraction

= 14 ÷ 14 = 1 (LCM ÷ Denominator of the second fraction)

= 1x1 =1 (Resultant answer x Numerator of the second fraction)

New numerator of second fraction is 1

Now subtract the new numerators

= 8 - 1

= 7

Then write the resulting numerator after subtraction over the LCM as denominator.

Note:

       1.   In subtraction of a whole number and a fractional number, we assume denominator of whole number as 1 for calculation.

       2.   In subtraction of mixed fractions, convert mixed fraction into improper fraction before starting to subtract.