**Subtraction of Mixed Fractions:** The operation of subtracting mixed fractions is similar to the addition of mixed fractions. So, the students who have knowledge of the addition of mixed fractions can easily solve the subtraction of mixed fractions. There are different methods to find the subtraction of mixed fractions.

We will discuss how to subtract the mixed fractions with brief explanations here. So, the students are suggested to read the steps and know how to subtract mixed fractions with whole numbers, unlike denominators, and like denominators.

**Do Refer:**

### Subtraction of Mixed Fractions with Different Denominators | Subtracting Mixed Fractions with Unlike Denominators

If the denominators of the given fractions are different then convert the unlike denominators to the like denominators. And then convert into the improper fraction and subtract the numerators.

**Example: **

Subtract the mixed fractions 7 \(\frac{1}{5}\) and 3 \(\frac{1}{4}\)

**Solution:
**Given the fractions 7 \(\frac{1}{5}\) and 3 \(\frac{1}{4}\)

Here the denominators of the fractions are different.

You need to find the common denominator of the given fractions.

Multiples of 5: 5, 10, 15, 20,..

Multiples of 4: 4, 8, 12, 16, 20,…

20 is the LCM of 4 and 5.

Now rewrite the given fractions with common denominator.

\(\frac{1}{5}\) . \(\frac{1}{4}\) = \(\frac{4}{20}\)

\(\frac{1}{4}\) . \(\frac{5}{5}\) = \(\frac{5}{20}\)

Write the expression using the mixed fractions with same denominator

7 \(\frac{4}{20}\) – 3 \(\frac{5}{20}\)

6 \(\frac{24}{20}\) – 3 \(\frac{5}{20}\)

6 – 3 = 3

\(\frac{24}{20}\) – \(\frac{5}{20}\) = \(\frac{19}{20}\)

Now combine the whole number and the fraction

6 \(\frac{19}{20}\)

Thus the subtraction of the mixed fractions 7 \(\frac{1}{5}\) and 3 \(\frac{1}{4}\) is 6 \(\frac{19}{20}\)

### Subtraction of Mixed Fractions with Same Denominators | Mixed Fractions Subtraction with Like Denominators

The subtracting fraction problems are those that have two proper fractions with a common denominator. If the denominators are the same you can subtract the numerators and write the fractions. The process is the same for subtracting mixed fractions with the same denominators.

**Example: **

Subtract 6 \(\frac{1}{3}\) and 2 \(\frac{1}{3}\)

**Solution:
**Given the mixed fractions 6 \(\frac{1}{3}\) and 2 \(\frac{1}{3}\)

Here the denominators of the fractions are the same.

First, subtract the whole numbers and then subtract the like fractions.

6 – 2 = 4

\(\frac{1}{3}\) – \(\frac{1}{3}\) = 0

Thus the subtraction of the mixed fractions 6 \(\frac{1}{3}\) and 2 \(\frac{1}{3}\) is 4.

### How to Subtract Mixed Fractions with Whole Numbers?

In subtracting mixed fractions with whole numbers you have to make the whole number as a mixed number to perform the subtraction operation. For better understanding let us see some examples regarding subtracting mixed fractions with whole numbers.

**Example:** Subtract the fractions 6 and 4\(\frac{2}{3}\).

**Solution:
**Given the fractions 6 and 4\(\frac{2}{3}\)

6 – 4\(\frac{2}{3}\)

Let us write the equivalent fraction that has the same denominator.

5\(\frac{3}{3}\) – 4\(\frac{2}{3}\)

First subtract the whole numbers.

5 – 4 = 1

\(\frac{3}{3}\) – \(\frac{2}{3}\) = \(\frac{1}{3}\)

Now combine the results

1\(\frac{1}{3}\)

Thus the subtraction of the mixed fractions 6 and 4\(\frac{2}{3}\) is 1\(\frac{1}{3}\)

### How to Solve Subtraction of Mixed Fractions?

There are some steps to subtract the mixed fractions with whole numbers, unlike denominators, and like denominators. Follow the below-given steps and try to solve the problems related to the subtraction of mixed fractions.

1. In the case of whole numbers first convert the whole number into the mixed number with the same denominator and then subtract the mixed fractions.

2. In the case of like or same denominators convert the mixed fractions into the improper fractions and then perform subtraction operations.

[or]

Subtract the whole number first and then subtract the fractions and then combine the result.

3. In the case of subtraction of mixed fractions with different or unlike denominators find the lcm of the denominators and then subtract the mixed fractions.

### Examples of Subtraction of Mixed Fractions

**Example 1.**

Subtract the fractions 3 \(\frac{1}{100}\) and 2 \(\frac{1}{100}\).

**Solution:
**Given the mixed fractions 3 \(\frac{1}{100}\) and 2 \(\frac{1}{100}\).

Here the denominators of the fractions are the same.

First, subtract the whole numbers and then subtract the like fractions.

3 \(\frac{1}{100}\) – 2 \(\frac{1}{100}\)

3 – 2 = 1

Now subtract the fractions with the same denominator.

\(\frac{1}{100}\) – \(\frac{1}{100}\) = 0

Thus the difference of 3 \(\frac{1}{100}\) and 2 \(\frac{1}{100}\) is 1

**Example 2.**

Subtract the fractions 7 \(\frac{1}{12}\) and 7 \(\frac{1}{12}\).

**Solution:**

Given the fractions 7 \(\frac{1}{12}\) and 7 \(\frac{1}{12}\).

Here the denominators of the fractions are the same.

First, subtract the whole numbers and then subtract the like fractions.

7 \(\frac{1}{12}\) – 7 \(\frac{1}{12}\)

7 – 7 = 0

Now subtract the fractions with the same denominator.

\(\frac{1}{12}\) – \(\frac{1}{12}\) = 0

Therefore the subtraction of the mixed fractions 7 \(\frac{1}{12}\) and 7 \(\frac{1}{12}\) is 0.

**Example 3.**

Subtract the fractions 5 and 2 \(\frac{1}{5}\).

**Solution:**

Given the fractions 5 and 2 \(\frac{1}{5}\).

5 – 2\(\frac{1}{5}\)

Let us write the equivalent fraction that has the same denominator.

4\(\frac{5}{5}\) – 2\(\frac{1}{5}\)

First subtract the whole numbers.

4 – 2 = 2

\(\frac{5}{5}\) – \(\frac{1}{5}\) = \(\frac{4}{5}\)

Now combine the results

2\(\frac{4}{5}\)

Therefore the subtraction of the mixed fractions with whole number 5 and 2 \(\frac{1}{5}\) is 2\(\frac{4}{5}\)

**Example 4.**

Subtract the fractions 6 \(\frac{1}{4}\) and 2 \(\frac{3}{4}\).

**Solution:**

Given the fractions 6 \(\frac{1}{4}\) and 2 \(\frac{3}{4}\).

Here the denominators of the fractions are the same.

Write the equivalent fraction of the fraction.

6 \(\frac{1}{4}\) – 2 \(\frac{3}{4}\)

6 \(\frac{1}{4}\) can be written as 5 \(\frac{5}{4}\)

5 \(\frac{5}{4}\) – 2 \(\frac{3}{4}\)

First, subtract the whole numbers and then subtract the like fractions.

5 – 2 = 3

Now subtract the fractions with the same denominator.

\(\frac{5}{4}\) – \(\frac{3}{4}\) = \(\frac{2}{4}\)

Now combine the results

3\(\frac{2}{4}\)

Therefore the subtraction of the mixed fractions 6 \(\frac{1}{4}\) and 2 \(\frac{3}{4}\) is 3\(\frac{2}{4}\)

**Example 5.**

Subtract the fractions 9 \(\frac{1}{6}\) and 6 \(\frac{1}{3}\).

Solution:

Given the fractions 9 \(\frac{1}{6}\) and 6 \(\frac{1}{3}\).

Here the denominators of the fractions are the same.

Write the equivalent fraction of the fraction.

Find the LCM of 3 and 6.

Multiples of 3 is 3, 6, 9,…

Multiples of 6 is 6, 12, 18,..

Thus the LCM of 3 and 6 is 6.

9 \(\frac{1}{6}\) – 6 \(\frac{1}{3}\)

9 \(\frac{1}{6}\) Ã— \(\frac{1}{1}\)– 6 \(\frac{1}{3}\) Ã— \(\frac{2}{2}\)

9 \(\frac{1}{6}\) – 6 \(\frac{2}{6}\)

Now the denominators of the fractions are the same.

8 \(\frac{7}{6}\) – 6 \(\frac{2}{6}\)

First, subtract the whole numbers and then subtract the like fractions.

8 – 6 = 2

Now subtract the fractions with the same denominator.

\(\frac{7}{6}\) – \(\frac{2}{6}\) = \(\frac{5}{6}\)

Now combine the results

2\(\frac{5}{6}\)

Therefore the subtraction of the mixed fractions 9 \(\frac{1}{6}\) and 6 \(\frac{1}{3}\) is 2\(\frac{5}{6}\)

### FAQs on Subtraction of Mixed Fractions

**1. What is meant by a mixed fraction?**

A fraction represented with its quotient and the remainder is a mixed fraction. For example, 1 1/2 is a mixed fraction where 1 is the quotient, 1 is the remainder.

**2. What is the formula of the mixed fractions?**

(i) Divide the Fraction’s numerator with the denominator, i.e. 4/3.

(ii) The integer part of the answer will be the integer part for a mixed fraction, i.e. 1 is an integer.

(iii) The Denominator will be the same as the original, i.e 3.

**3. How to subtract mixed fractions?**

Subtraction of mixed fractions is the same as the addition of mixed fractions. We have to convert mixed fractions into improper fractions then subtract them.