Adding Fractions and Mixed Numbers

Preview

Adding a fraction is just as easy as adding a mixed number. It's just the difference of a whole number. So how do add fractions? Well first let's take the fraction problem 7/9+5/8 and the next thing we have to do is put the fractions in vertical form like this:

   7
   9
+
   5
   8

Next you have to find out the LCM of the two denominators 9 and 8 and then rename the fractions like this:
   7
   9      9,18,27,36,45,54,63,72
+     = 
   5      8,16,24,32,40,48,56,64,72
   8

    56
    72
+
    45
    72

So now that we have two fractions with like denominators all we have to do is add the numerators and keep the denominator as it is in the answer like this:
    56
    72            101            __1___
+              =   72   =  72/ 101        = 72x1=72
    45                                 72
    72                                 29
                                       
= 1 29
      72
So the answer to the problem 7/9+5/8=1 29/72 so the answer is a mixed number.

Now let's add mixed numbers by taking the two mixed numbers 4 2/4 + 5 3/5. Now the first thing we need to do is make the mixed numbers into improper fractions then add them vertical like this:
4 2        18
   4   =    4
4 x 4= 16
16+2= 18

5 3        28
   5   =    5
5 x 5= 25
25+3= 28

    18
     4
+
     28
      5

Now we have to find the LCM of the two denominators  and rename the fractions like this:

    18
     4        4,8,12,16,20
+         =  
    28       5,10,15,20,25

     5

     90
     20
+
    112
     20

So now all you have to do is add the numerators and keep the denominator as it is like this:
     90
     20      202           __10____
+          =  20  =  20/ 202          =    10    2
    112                       200                     20 
     20                            2

So the answer for the problem 4 2/4 + 5 3/5 is 10 2/20 or 10 1/10 and after all the answer is a mixed number.
Now try some of these and make sure to watch the video on YouTube:

 Sheet 1 Adding Fractions and Mixed Numbers