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Subtract Fractions with Different Denominators

Fractions are denoted by $\frac{a}{b}$ where a and b are whole numbers and b not equals to 0. For comparing and ordering of unlike fractions, first convert them into like fractions and then compare or rearrange them in the order as desired. When the numerator and denominator of fraction which are multiplied or divided by same number, we get its own equivalent fractions. 

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Like and Unlike Fractions

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Fractions can be classified on the basis of the denominators. Two fractions may have same or different denominators.

  • Like fractions
  • Unlike fractions


Like Fractions: The number a is called Fractions having the same denominators are called like fractions

Example: $\frac{4}{11}$ , $\frac{6}{11}$ are all like fractions.

Unlike Fractions: The fractions which contains different denominator numbers are called unlike fractions.

Example: $\frac{3}{5}$ , $\frac{4}{7}$ are all unlike fractions. Let us see how to subtract fractions with unlike denominators in this article.

How to Subtract Fractions with Unlike Denominators

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Below are the steps for how to subtract fractions with different denominators -

Step 1. Find out Lowest Common Denominator(LCD) of the fractions.

Step 2. Rename fractions to have LCD.

Step 3. Now subtract the numerators of the given fractions.

Step 4. The difference will be the numerator and the LCD will be the denominator of the answer.

Step 5. Simplify the Fraction if needed.


Examples

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Below are the solved examples on subtracting fractions with different denominators -

Solved Examples

Question 1: Subtract $\frac{5}{12}$ from $\frac{13}{24}$
Solution:
Here we have unlike fractions, so we have to take LCM for 12 and 24 is 24

$\frac{5}{12}$
 = $\frac{5\times2}{12\times2}$ = $\frac{10}{24}$

$\frac{13}{24}$ - $\frac{5}{12}$
 = $\frac{13}{24}$ - $\frac{10}{24}$

= $\frac{3}{24}$ 


Correct answer is $\frac{1}{8}$
Question 2: $\frac{7}{10}$ - $\frac{8}{15}$
Solution:
Here we have unlike fractions, so we have to take LCM for 10 and 15 = 30.


$\frac{7}{10}$ - $\frac{8}{15}$
 = $\frac{7\times3}{10\times3}$ - $\frac{8\times2}{15\times2}$


= $\frac{21}{30}$ - $\frac{16}{30}$


= $\frac{21-16}{30}$ = $\frac{5}{30}$



Correct answer is $\frac{1}{6}$
Question 3: Subtract 3$\frac{2}{5}$ - 2$\frac{3}{8}$
Solution:
Given fraction is unlike mixed fractions take LCM, LCM for 5 and 8 is 40

3$\frac{2}{5}$ - 2$\frac{3}{8}$ = $\frac{17}{5}$ - $\frac{19}{8}$

= $\frac{17\times8}{5\times8}$ - $\frac{19\times5}{8\times5}$

= $\frac{136}{40}$ - $\frac{95}{40}$

= $\frac{41}{40}$


Correct answer is 1$\frac{1}{40}$

Practice Problems

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Problem 1: Subtract $\frac{2}{3}$ from $\frac{6}{11}$.

Problem 2:
Find the difference between $3\frac{1}{2}$ and $6\frac{1}{3}$.
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