Addition and Subtraction of Fractions
2026-02-28 21:32 Diff
https://brightchamps.com/en-us/math/numbers/addition-and-subtraction-of-fractions

When adding and subtracting fractions with different denominators, we must convert the unlike fractions into like fractions. First, we change the different denominators to a common denominator. Adding or subtracting the numerators, while keeping the denominator the same, are as follows -  

For instance, add  and  \( \frac{1}{3},\quad \frac{3}{4} \)

First, we must change the unlike denominators to a common denominator. For that, we need to find the least common multiple of 3 and 4. 

Multiples of 3 include 3, 6, 9, 12, 15, 18, ...


Multiples of 4 include 4, 8, 12, 16, 20, …

Here, the smallest common multiple that appears in both lists is 12. Hence, 12 is the LCD of 3 and 4. 

Next, we can convert the fractions to get a denominator of 12.

Convert : (1 × 4) / (3 × 4) = \(\frac{4}{12} \)


Convert: (3 × 3) / (4 × 3) = \(\frac{9}{12} \)

Now the denominators are the same. Next, add the numerators together.

    \(\frac{4}{12} + \frac{9}{12} \)+  = (4 + 9) / 12 = \(\frac{13}{12} \)

is an improper fraction, so convert it into a mixed fraction.

Divide 13 by 12: 13 ÷ 12


Quotient = 1


Remainder = 1


Fraction can be expressed as a mixed fraction in the following way: Q


Here, Q is the quotient, R is the remainder, and D is the denominator. 


 So \(\frac{13}{12} \) can be written as 1 \(\frac{1}{12} \)

Subtracting fractions with unlike denominators


The rules to add unlike fractions can also be applied to subtract unlike fractions. For a better understanding, take a look at this example. 


Subtract- \(\frac{4}{5} - \frac{1}{4} \)


Find the LCD of 5 and 4. 

20 is the least common multiple of both 5 and 4. So, we can convert the unlike fractions into like fractions. 

Convert :\( \frac{4 \times 4}{5 \times 4} \) = \(\frac{16}{12} \)


Convert : \(\frac{1 \times 5}{4 \times 5} \)  = \(\frac{5}{20} \)

Next, subtract the numerators.

   \(\frac{16}{20} - \frac{5}{20} \)  - = \(\frac{16 - 5}{20} \) = \( \frac{11}{20} \)

Thus,  -  = \(\frac{16}{20} - \frac{5}{20} = \frac{11}{20} \)