## Introduction

In this topic, we will learn how to add and subtract mixed numbers with unlike denominators. Remember that unlike denominators are denominators that are not the same or they are different. Also, when it comes to addition or subtraction of mixed numbers, it is very important to convert them into improper fractions. This will work on both addition and subtraction of mixed numbers.

## Mixed Numbers with Unlike Denominators

Since the method is the same for both addition and subtraction, we can go ahead and do subtraction in this case.

4 2/5 - 2 5/8

Remember that we have to first convert these mixed numbers into improper fractions.
So we now have the two improper fractions of:

22/2 - 21/8

Next we have to get common denominators so that our unlike denominators are like denominators. Then we can go ahead and subtract:

In order to get common denominators, we have to list the common multiples of each and then find the LCM (least common multiples)

Multiples of 2: 2, 4, 6, 8
Multiples of 8: 8, 16

As you can see the LCM of 2 and 8 is the number 8!

So, we will rewrite our denominators as 8:

----- minus -----
8                8

Now look at the previous denominators for the first fraction: 2. Now what number multiplied by 2 gave us 8? 4!

So...

22      *4        88
----  equals   -----
2       *4         8

Since the second fraction already has 8 as the denominator, we don't need to change it:

88                  21                     67
----   minus  -----    equals  --------
8                     8                     8

So that means the difference is 67/8

Now the last thing we need to do to get our final answer is convert the improper fraction back into a mixed number. In order to do that just divide the numerator by the denominator:

67/8 equals 8 remainder 3.

Remember:

Quotient = Whole Number = 8
Remainder = Numerator = 3
Divisor = Denominator = 8

Put it all together and get 8 3/8.

That means the difference of 4 2/5 - 2 5/8 equals 8 3/8!

Sheet 1 Adding and Subtracting Mixed Numbers with Unlike Denominators

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