In this post we will methods to **subtract two or more fractions**.

To understand the methods, you should have basic understanding of the concept of fractions and LCM.

**How to subtract fractions?**

There are two types of subtraction methods:

(a) Subtraction when fractions have same denominator.

(b) Subtraction when fractions have different denominator.

We will learn both the methods, step by step.

**Subtracting Fractions with same denominator**

In this case, **simply subtract the numerator and retain the same denominator**.

In the above image; A/C & B/C are the fractions with same denominator.

Note that in the subtraction, we simply subtracted the numerator (A – B) and maintained the same denominator C.

**Subtracting Fractions with different denominator**

In this case, we have to** manipulate the fractions so that all of them have common denominator**.

Follow the below steps:

(a) **Find LCM of the denominators**.

(b) **Multiply the fractions** such that **denominator becomes equal to LCM valu**e.

(c) Now all denominator have same value.**Simply subtract the numerator and retain the denominator**.

**Why its important to have same denominator in fraction subtraction?**

Because with different denominator it becomes difficult to subtract fraction.

For example, consider the fraction 1/2 and 2/3.

**Fraction 1/2** mean that the **object is divided into two equal part and 1 part is shaded**.

**Fraction 2/3** mean that **object is divided into three equal part and 2 part is shaded**.

Since the objects are divided into different parts it is very difficult to do subtraction.

Now consider the fraction 2/4 and 1/4.**Fraction 2/4** mean that the **object is divided into 4 parts and 1 part is shaded**.

Similarly **fraction 1/4** signifies that the** object is divided into 4 equal part and 1 part is shaded**.

Since the object is divided into same parts (i.e. same denominator), the subtraction process gets straightforward.

Notice the above image, here we have simply subtracted the numerator and left the denominator as it is.

**Subtraction of Fraction examples**

**Example 01**

Subtract the fractions; \mathtt{\ \frac{6}{3} \ \ \&\ \ \frac{2}{3}}

**Solution**

The fractions have same denominator.

So, simply subtract the numerator and retain denominator.

\mathtt{\Longrightarrow \ \frac{6}{3} \ -\ \frac{2}{3} \ \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{6\ -\ 2\ }{3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{4}{3}}

**Hence, 4/3 is the solution.**

**Example 02**

Subtract the fractions \mathtt{\frac{2}{9} \ \ \&\ \ \frac{1}{18}}

**Solution**

Here the fractions have different denominator.

Follow the below steps:

**(a) Find LCM of denominator**

LCM (9, 18) = 18

**(b) Multiply the fractions to make denominator 18**

**Fraction 2/9**

Multiply numerator and denominator by 2

\mathtt{\Longrightarrow \frac{2\ \times \ 2}{9\ \times \ 2} \ =\ \frac{4}{18}}

**Fraction 1/18**

Here denominator is already 18, so no need to multiply anything.

(c) Now both the fractions have same denominator.**Subtract the numerator and retain the denominator**.

\mathtt{\Longrightarrow \ \frac{4}{18} \ -\ \frac{1}{18} \ \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{4\ -\ 1}{18}}\\\ \\ \mathtt{\Longrightarrow \ \frac{3}{18}}

The fraction can be further simplified.

Divide numerator and denominator by 3

\mathtt{\Longrightarrow \ \frac{3\div 3}{18\div 3}}\\\ \\ \mathtt{\Longrightarrow \frac{1}{6}}

**Hence, 1/6 is the solution.**

**Example 03**

Subtract the fractions, \mathtt{\frac{3}{2} \ \ \&\ \ \frac{1}{5}}

**Solution**

The fractions have different denominator.

Follow the below steps:

**(a) Find LCM of denominator**

LCM (2, 5) = 10

**(b) Multiply fractions to make denominator 10**

**Fraction 3/2**

Multiply numerator and denominator by 5

\mathtt{\Longrightarrow \frac{3\ \times \ 5}{2\ \times \ 5} \ =\ \frac{15}{10}}

**Fraction 1/5**

Multiply numerator and denominator by 2

\mathtt{\Longrightarrow \frac{1\ \times \ 2}{5\ \times \ 2} \ =\ \frac{2}{10}}

(c) Now both the fractions have same denominator.

Simply **subtract the numerator and leave the denominator as it is**.

\mathtt{\Longrightarrow \ \frac{15}{10} \ -\ \frac{2}{10} \ \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{15\ -\ 2}{10}}\\\ \\ \mathtt{\Longrightarrow \ \frac{13}{10}}

**Hence, 13/10 is the solution.**

**Example 04 **

Subtract the fractions, \mathtt{\frac{19}{11} \ \ \&\ \ \frac{3}{7}}

Follow the below steps:

**(a) Find LCM of denominators**

LCM (11, 7) = 77

**(b) Multiply the fractions to make denominator 77**

**Fraction 19/11**

Multiply numerator and denominator by 7

\mathtt{\Longrightarrow \frac{19\ \times \ 7}{11\times \ 7} \ =\ \frac{133}{77}}

**Fraction 3/7**

Multiply numerator and denominator by 11

\mathtt{\Longrightarrow \frac{3\ \times \ 11}{7\times \ 11} \ =\ \frac{33}{77}}

(c) Both the fraction now have same denominator.**Subtract the numerator and retain the denominator**.

\mathtt{\Longrightarrow \ \frac{133}{77} \ -\ \frac{33}{77} \ \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{133\ -\ 33}{77}}\\\ \\ \mathtt{\Longrightarrow \ \frac{100}{77}}

**Hence, 100/77 is the solution**.

**Example 05**

Subtract the fraction, \mathtt{\frac{17}{20} \ \ \&\ \ \frac{11}{20}}

**Solution**

Both the subtraction have same denominator.

So, subtract the numerator and retain the denominator.

\mathtt{\Longrightarrow \ \frac{17}{20} \ -\ \frac{11}{20} \ \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{17\ -\ 11}{20}}\\\ \\ \mathtt{\Longrightarrow \ \frac{6}{20}}

The fraction can be simplified further.

Divide numerator and denominator by 2.

\mathtt{\Longrightarrow \ \frac{6\div 2}{20\div 2}}\\\ \\ \mathtt{\Longrightarrow \frac{3}{10}}

**Hence, 3/10 is the right answer.**

**Fraction Subtraction -Solved Problems**

(01) Subtract the fractions; \mathtt{\ \frac{4}{3} \ \ \&\ \ \frac{2}{3}}

(a) 4/3

(b) 2/3

(c) 5/3

**Option (b) is correct **

**Solution**

The fractions have same denominator.

Simply subtract the numerator and retain the denominator.

\mathtt{\Longrightarrow \ \frac{4}{3} \ -\ \frac{2}{3} \ \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{4\ -\ 2}{3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{2}{3}}

**Hence, 2/3 is the solution**.

(02) Subtract the fraction; \mathtt{\frac{7}{4} \ -\ 1}

(a) 3/4

(b) 5/4

(c) 1/4

**Option (a) is correct**

**Solution**

The given numbers are 7/4 and 1.

1 can be written as 4/4.

Now we have same denominator fractions 7/4 and 4/4.

Subtract the numerator and retain the denominator.

\mathtt{\Longrightarrow \ \frac{7}{4} \ -\ \frac{4}{4} \ \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{7\ -\ 4}{4}}\\\ \\ \mathtt{\Longrightarrow \ \frac{3}{4}}

**Hence, 3/4 is the solution.**

(03) Subtract the fractions, \mathtt{\frac{6}{10} \ \ \&\ \ \frac{2}{5}}

(a) 2/5

(b) 1/5

(c) 6/10

(d) 8/10

**Option (b) is correct**

**Solution**

Here the fractions have different denominator.

Follow the below steps:

**(a) Find LCM of the denominators**

LCM (10, 5) = 10

**(b) Multiply the fractions to get denominator 10.**

Fraction 6/10

The denominator is already 10.

No need to do anything.

Fraction 2/5

Multiply numerator and denominator by 2

\mathtt{\Longrightarrow \frac{2\ \times \ 2}{5\times \ 2} \ =\ \frac{4}{10}}

**(c) Now we have fractions with same denominator.**

Subtract the numerator and leave the denominator as it is.

\mathtt{\Longrightarrow \ \frac{6}{10} \ -\ \frac{4}{10} \ \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{6\ -\ 4}{10}}\\\ \\ \mathtt{\Longrightarrow \ \frac{2}{10}}

The fraction can be simplified further.

Divide numerator and denominator by 2.

\mathtt{\Longrightarrow \ \frac{2\div 2}{10\div 2}}\\\ \\ \mathtt{\Longrightarrow \frac{1}{5}}

**Hence, 1/5 is the solution.**

(04) Subtract the fraction, \mathtt{\frac{7}{25} \ \ \&\ \ \frac{9}{50}}

(a) 2/10

(b) 5/10

(c) 1/10

(d) 3/10

**Option (c) is correct**

**Solution**

The fractions have different denominator.

Follow the below steps.

**(a) LCM of denominator**

LCM (25, 50) = 50

**(b) Multiply the fraction to make denominator 50**

Fraction 7/25

Multiply numerator and denominator by 2

\mathtt{\Longrightarrow \frac{7\ \times \ 2}{25\times \ 2} \ =\ \frac{14}{50}}

Fraction 9/50

Denominator is already 50.

No need to do anything.

**(c) Now we have fraction with same denominator.**

Subtract the numerator and retain the denominator.

\mathtt{\Longrightarrow \ \frac{14}{50} \ -\ \frac{9}{50} \ \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{14\ -\ 9}{50}}\\\ \\ \mathtt{\Longrightarrow \ \frac{5}{50}}

The fraction can be simplified further.

Divide numerator and denominator by 5.

\mathtt{\Longrightarrow \ \frac{5\div 5}{50\div 5}}\\\ \\ \mathtt{\Longrightarrow \frac{1}{10}}

**Hence, 1/10 is the solution.**

(05) Subtract the fraction; \mathtt{\frac{9}{20} \ \ \&\ \ \frac{4}{20}}

(a) 1/5

(b) 1/3

(c) 1/7

(d) 1/4

**Option (d) is correct**

Both the fractions have same denominator.

Subtract the fraction and leave the denominator as it is.

\mathtt{\Longrightarrow \ \frac{9}{20} \ -\ \frac{4}{20} \ \ \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{9\ -\ 4}{20}}\\\ \\ \mathtt{\Longrightarrow \ \frac{5}{20}}

The fraction can be further simplified.

Divide numerator and denominator by 5.

\mathtt{\Longrightarrow \ \frac{5\div 5}{20\div 5}}\\\ \\ \mathtt{\Longrightarrow \frac{1}{4}}

**Hence, 1/4 is right answer**