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Adding Fractions with Different Denominators

A fraction consists of a numerator and a denominator. For adding fractions with different denominators, all you have to do is take a common denominator by finding the lowest common denominator. The easiest way to find the common denominator is to multiply the denominators.
A part of a whole numbers called fraction.

Fractions can be created by having two numbers minimum. Upper number of the fraction called numerator. Lower number of the fraction called as denominator. i.e, $\frac{Numerator}{Denominator}$

A mathematical problems are relating numbers or two quantities, one divided by the other called as fraction.

For example, $\frac{1}{4}$ is a fraction.

Fractions could be used to solve addition of fractions, subtraction of fractions, multiplication of fractions, and division of fractions. In this article, we shall discuss about adding fractions with different denominators.

The method of adding like fraction (same denominator) and unlike fraction (different denominator) is different. Here we are going learn about addition of fraction with different denominator. Let us learn how to do it.

Adding Fractions with Different Denominators


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How to Add Fractions with Unlike Denominators

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Below are the steps for how to add fractions with unlike denominators-

Step 1 : Find the Least Common Denominator (LCD) of the fractions.

Step 2 : Rename the fractions to have the LCD.

Step 3 : Add the numerators of the fractions.

Step 4 : Simplify the fraction.

Now see the solved examples on how to add fractions with different denominators -

Solved Examples

Question 1: Add $\frac{50}{9}$ and $\frac{30}{10}$
Solution:
The given two fractions $\frac{50}{9}$ and $\frac{30}{10}$ are unlike fractions

Step 1: LCD of 9 and 10 => 90

Step 2: So, $\frac{50\times10}{9\times10}$ + $\frac{30\times9}{10\times9}$

= $\frac{500}{90}$ + $\frac{270}{90}$

Step 3: Since the denominators are same so, add the fractions together

= $\frac{500 + 270}{90}$

The sum of 500 and 270 is 770

= $\frac{770}{90}$


Correct answer is $\frac{77}{9}$
Question 2: Add $\frac{280}{2}$ and $\frac{270}{3}$
Solution:
The given two fractions $\frac{280}{2}$ and $\frac{270}{3}$ are unlike fractions

Step1: LCD of 2 and 3 = 6

Step 2: So, $\frac{280\times3}{2\times3}$ + $\frac{2\times270}{2\times3}$

= $\frac{840}{6}$ + $\frac{540}{6}$

Step 3: Since the denominators are same so, add the fractions together 

= $\frac{840+540}{6}$

The sum of 840 and 540 is 1380

= $\frac{1380}{6}$


Correct answer is 230
Question 3: Add $\frac{320}{10}$ and $\frac{330}{11}$
Solution:
The given two fractions $\frac{320}{10}$ and $\frac{330}{11}$ are unlike fractions

Step 1: LCD of 10 and 11 = 110

Step 2: So, $\frac{320\times11}{10\times11}$ + $\frac{10\times330}{10\times11}$

= $\frac{3520}{110}$ + $\frac{3300}{110}$

Step 3: Since the denominators are same so, add the fractions together

= $\frac{3520+3300}{110}$

The sum of 3520 and 3300 is 6820

= $\frac{6820}{110}$


Correct answer is 62
Question 4: Add $\frac{340}{12}$ and $\frac{350}{13}$
Solution:
The given two fractions $\frac{340}{12}$ and $\frac{350}{13}$ are unlike fractions

Step 1: LCD of 12 and 13 = 156

Step 2: So, $\frac{340\times13}{12\times13}$ + $\frac{12\times350}{12\times13}$

= $\frac{4420}{156}$ + $\frac{4200}{156}$

Step 3: Since the denominators are same so, add the fractions together

= $\frac{4420 + 4200}{156}$

The sum of 4420 and 4200 is 8620

= $\frac{8620}{156}$


Correct answer is $\frac{2155}{39}$
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