Adding and Subtracting Fractions with Like Denominators

Preview

Adding and subtracting fractions with like denominators is probably the easiest type of math you could do with fractions because all you have to do is add/subtract the numerators because the denominator is brought in the answer as it is. So let's take the two fractions 2/7+4/7 and put it in vertical form like this:

2      4

7  +  7

And now all you have to do is add the two numerators 2+4 and we know the answer is 6 and so all we have to do is write the numerator and bring the denominator as it is like this:

2      4       6

7  +  7  =   7

So now we have our answer to our problem 2/7+4/7 which is 6/7.

Now let's take the problem 5/8-3/8 and let's subtract and you should know that subtracting is the same as adding except you only subtract the numerators like this:

5      3      2

8  -   8  =  8

So now we know that the answer is 2/8 of the problem 5/8-3/8 and if you want you can simplify it and make it 1/4.
 Now try some of these and make sure to watch the video on YouTube.

Sheet 1 Adding and Subtracting Fractions with Like Denominators

Common Denominators

Preview

Common denominators can be very useful when you are doing addition and subtraction with fractions. So what are common denominators and how do you find them? Common denominators are two denominators of two fractions that are common. So let's take the two fractions 3/4 and 3/5 and to find the common denominators for the two fractions we will have to write the fractions out in vertical form like this:

3

4

    

5

6

So now that we have the two fractions we have to take the denominators and find the LCM of the two numbers like this:

3

4                            4, 8, 12, 16, 20

    =  4 and 6 =                                  LCM=12

5                            6, 12, 18, 24, 30

6

We know that the LCM of the two denominators is 12 so now we have to rename the fractions like this:

3     = ?            

4        12

5     = ?   

6        12

So now we have to rename the numerators by multiplying them by the same we multiplied each denominator by to get 12 like this:

3          9    

4         12

=4 x 3=12

5         10

6         12

=6 x 2=12

We now know that the common denominators for the two fractions 3/4 and 5/6 is 12. And so our fractions with common denominators are 9/12 and 10/12.
Now try some of these and make sure to watch the video on YouTube.

Sheet 1 How to find Common Denominators

Sheet 2 How to find Common Denominators

How to Find Common Denominators

Introduction

Finding common denominators is the main thing when adding and/or subtracting fractions. Therefore, this topic is very important, too! 

The key to finding a common denominator is common multiples. All you have to do is find a common multiple of both denominators and you should be on you way!

Find Common Denominators!

Let's say that we have 6/9-3/5.

Remember, all you do is find a common multiple of the denominators.

9= 9,18,27,36,45

5= 5,10,15,20,25,30,35,40,45

As you can see, the LCM is 45. Therefore our new denominators are 45. Now all we do is multiply the numerator by the number we multiplied the denominator by to get 45:

6/9= 30/45 because you multiply by 5 to get 45.

3/5= 27/45 because you multiply by 9 to get 45.

Therefore, we now have 30/45-27/45.

The last step is simple: subtract the numerators. (Remember that the denominators stay the same.)

30-27=3.

The difference of 6/9-3/5= 3/45

 Sheet 1 Practice Problems on Finding Common Denominators