ADDING MIXED NUMBERS WITH UNLIKE DENOMINATORS

We can use one of the following methods to add fractions with unlike denominators. 

1. Cross-Multiplication method

2. LCM Method.

Cross-Multiplication Method

If the denominators of the fractional parts are co-prime or relatively prime, we have to apply this method.

Fro example, let us add the two mixed numbers given below.

5 1/3 and 2 1/8

In the above two mixed numbers, denominators of the fractional parts are 8 and 3.

For 8 and 3, there is no common divisor other than 1. So 8 and 3 are co-prime.

Here we have to apply cross-multiplication method to add the two mixed numbers using the steps given below.

Step 1:

First we have to add the integer parts 2 and 5.

2 + 5 = 7

Step 2 :

Now, we have to add the fractional parts 1/8 and 1/3 using cross multiplication as given below.

Step 3 :

Now, write step 1 value and step 2 together as shown below.

L.C.M method

If the denominators of the fraction parts  are not co-prime (there is a common divisor other than 1), we have to apply this method.

Fro example, let us add two mixed numbers given below.

2 5/13 and 7 1/20

In the above two mixed numbers, denominators of the fraction parts are 12 and 20.

For 12 and 20, if there is at least one common divisor other than 1, then 12 and 20 are not co-prime.

For 12 & 20, we have the following common divisors other than 1.

They are 2 & 4.

So 12 and 20 are not co-prime.

Here we have to apply L.C.M method to add the two mixed numbers using the steps given below.

Step 1 :

First we have to add the integer parts 2 and 7.

2 + 7  =  9

Step 2 :

Now, we have to add the fraction parts 5/12 and 1/20 using L.C.M method.

Let us find L.C.M of (Least common multiple) of 12 and 20. 

12  =  2² ⋅ 3

20  =  2² ⋅ 5

When we decompose 12 and 20 in to prime numbers, we find 2, 3 and 5 as prime factors for 12 and 20. 

To get L.C.M of 12 and 20, we have to take 2, 3 and 5 with maximum powers found above.

So, L.C.M of 12 and 20 is 

=  2² ⋅ 3 ⋅ 5

=  4 ⋅ 3 ⋅ 5

=  60

Step 3 :

Now we have to make the denominators of both the fractions to be 60 and add the two fractions 5/12 and 1/20 as shown below.

Step 4 :

Now, write step 1 value and step 3 together as shown below. 

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