Subtraction of Unlike Fractions

Subtraction of Unlike Fractions | How to Subtract Fractions with Different Denominators?

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Subtraction of Unlike Fractions: Subtraction is one of the arithmetic operations which is used to take off the required number from the given number. To subtract the unlike fractions you have to make the denominators equal. Students feel that fractions are the difficult top among all. But if you understand the concept this will be the easiest topic.

In order to Subtract fractions having Unlike denominators, it is necessary for the students to learn the least common multiples and basics of fractions. Learn about Subtraction of Unlike Fractions from this page. This article helps you to know more about fractions, Steps to subtract fractions with Unlike Denominators with step by step explanation.

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How to Subtract Fractions with Different Denominators?

There are some steps to subtract the fractions with different denominators. They are given below,
1. First step is to check the denominators.
2. If the denominators are the same then you can directly subtract the fractions.
3. If the denominators are different then you have to change to the common denominator.
4. Cross multiply the fractions to get the common denominator.
5. Now, subtract the numerators without changing the bottom numbers.
6. Simplify the fraction if needed.

Subtracting Unlike Fractions Examples

Example 1.
Subtract the fractions \(\frac{2}{3}\) and \(\frac{1}{4}\) having different denominators.
Solution:
Given the fractions \(\frac{2}{3}\) and \(\frac{1}{4}\)
First, check whether the denominators are the same or not.
In this case, the fractions are unlike.
So make the denominators the same by finding the L.C.M of two denominators.
The multiples of 3 are 3, 6, 9, 12, 15,…
The multiples of 4 are 4, 8, 12, 20,….
Thus the L.C.M. of 3 and 4 is 12.
Now rewrite the fractions by cross multiplying the numerators and denominators.
\(\frac{2}{3}\) × \(\frac{4}{4}\) – \(\frac{1}{4}\) × \(\frac{3}{3}\)
\(\frac{8}{12}\) – \(\frac{3}{12}\)
\(\frac{8-3}{12}\) = \(\frac{5}{12}\)
Thus the subtraction of \(\frac{2}{3}\) and \(\frac{1}{4}\) with unlike fractions is \(\frac{5}{12}\)

Example 2.
Subtract the fractions \(\frac{4}{7}\) and \(\frac{14}{35}\) having different denominators.
Solution:
Given the fractions \(\frac{4}{7}\) and \(\frac{14}{35}\)
First, check whether the denominators are the same or not.
In this case, the fractions are unlike.
So make the denominators the same by finding the L.C.M of two denominators.
The multiples of 7 are 7, 14, 21, 28, 35,…
The multiples of 35 are 35, 70, 105,….
Thus the L.C.M. of 7 and 35 is 35.
Now rewrite the fractions by cross multiplying the numerators and denominators.
\(\frac{4}{7}\) × \(\frac{5}{5}\) – \(\frac{14}{35}\) × \(\frac{1}{1}\)
\(\frac{20}{35}\) – \(\frac{14}{35}\)
\(\frac{20-14}{35}\) = \(\frac{6}{35}\)
Thus the subtraction of \(\frac{4}{7}\) and \(\frac{14}{35}\) with unlike fractions is \(\frac{6}{35}\)

Example 3.
Subtract the fractions \(\frac{1}{6}\) and \(\frac{3}{4}\) having different denominators.
Solution:
Given the fractions \(\frac{1}{6}\) and \(\frac{3}{4}\)
First, check whether the denominators are the same or not.
In this case, the fractions are unlike.
So make the denominators the same by finding the L.C.M of two denominators.
The multiples of 6 are 6, 12, 18, 24,…
The multiples of 4 are 4, 8, 12,….
Thus the L.C.M. of 6 and 4 is 12.
Now rewrite the fractions by cross multiplying the numerators and denominators.
\(\frac{1}{6}\) × \(\frac{2}{2}\) – \(\frac{3}{4}\) × \(\frac{3}{3}\)
\(\frac{2}{12}\) – \(\frac{9}{12}\)
\(\frac{2-9}{12}\) = –\(\frac{7}{12}\)
Thus the subtraction of \(\frac{1}{6}\) and \(\frac{3}{4}\) with unlike fractions is –\(\frac{7}{12}\)

Example 4.
Subtract the fractions \(\frac{23}{35}\) and \(\frac{3}{5}\) having different denominators.
Solution:
Given the fractions \(\frac{23}{35}\) and \(\frac{3}{5}\)
First, check whether the denominators are the same or not.
In this case, the fractions are unlike.
So make the denominators the same by finding the L.C.M of two denominators.
The multiples of 7 are 7, 14, 21, 28, 35,…
The multiples of 5 are 5, 10, 15, 20, 25, 30, 35,….
Thus the L.C.M. of 35 and 5 is 35.
Now rewrite the fractions by cross multiplying the numerators and denominators.
\(\frac{23}{35}\) × \(\frac{1}{1}\) – \(\frac{3}{5}\) × \(\frac{7}{7}\)
\(\frac{23}{35}\) – \(\frac{21}{35}\)
\(\frac{23-21}{35}\) = \(\frac{2}{35}\)
Thus the subtraction of \(\frac{23}{35}\) and \(\frac{3}{5}\) with unlike fractions is \(\frac{2}{35}\)

Example 5.
Subtract the fractions \(\frac{5}{6}\) and \(\frac{1}{8}\) having different denominators.
Solution:
Given the fractions \(\frac{5}{6}\) and \(\frac{1}{8}\)
First, check whether the denominators are the same or not.
In this case, the fractions are unlike.
So make the denominators the same by finding the L.C.M of two denominators.
The multiples of 6 are 6, 12, 18, 24, 30,…
The multiples of 8 are 8, 16, 24, 32,….
Thus the L.C.M. of 6 and 8 is 24.
Now rewrite the fractions by cross multiplying the numerators and denominators.
\(\frac{5}{6}\) × \(\frac{4}{4}\) – \(\frac{1}{8}\) × \(\frac{3}{3}\)
\(\frac{20}{24}\) – \(\frac{3}{24}\)
\(\frac{20-3}{24}\) = \(\frac{17}{24}\)
Thus the subtraction of \(\frac{5}{6}\) and \(\frac{1}{8}\) with unlike fractions is \(\frac{17}{24}\)

FAQs on Subtraction of Unlike Fractions

1. How to Subtract Unlike Fractions?

You can subtract fractions with unlike denominators by finding the least common multiples (L.C.M). Make the common denominators and then subtract the fractions.

2. What are the three parts of subtraction?

The 3 parts of subtraction are as follows,
Minuend: The number from which we subtract the other number is known as the minuend.
Subtrahend: The number which is subtracted from the minuend is known as the subtrahend.
Difference: The final result obtained after performing subtraction is known as the difference.

3. Give one example for Subtraction of Unlike Fractions.

Subtract \(\frac{2}{5}\) and \(\frac{1}{10}\) having Unlike Fractions.
Solution:
First, check whether the denominators are the same or not.
In this case, the fractions are unlike.
So make the denominators the same by finding the L.C.M of two denominators.
The multiples of 10 are 10, 20, 30,…
The multiples of 5 are 5, 10, 15, 20,….
Thus the L.C.M. of 10 and 5 is 10.
Now rewrite the fractions by cross multiplying the numerators and denominators.
\(\frac{2}{5}\) × \(\frac{2}{2}\) – \(\frac{1}{10}\) × \(\frac{1}{1}\)
\(\frac{4}{10}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)

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