# ADDING MIXED NUMBERS WITH REGROUPING

## About "Adding mixed numbers with regrouping"

"Adding mixed numbers with regrouping" is sometimes a difficult job for the children who study math in primary level.

Actually it is not a difficult one, once we have understood the concept.

Here, we explain two methods to add mixed numbers with unlike denominators. Here students may have a question.

That is, "When do we have to use the appropriate method in adding mixed numbers with regrouping"?

Answer for the above question is given with detailed explanation.

## Cross-multiplication method If the denominators of the fraction parts are co-prime or relatively prime, we have to apply this method.

Fro example, let us consider the two mixed numbers

218  and  513

In the above two mixed numbers, denominators of the fraction 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 fraction parts 1/8 and 1/3 using cross multiplication as given below. Step 3 :

Now, write step1 value and step 2 together as given below.

7114

## 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 consider the two mixed numbers

2512  and  7120

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 x 3

20 = 2² x 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 = 2² x 3 x 5

= 4 x 3 x 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 given below. Step 4 :

Now write step1 value and step 2 together as given below.

9715

After having gone through the stuff and examples, we hope that the students would have understood "How to add mixed numbers with unlike denominators" 