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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

#### 1 comment:

1. The two fractions can be reduced to simplest form by fractions to decimals cross canceling out each other's numerator and denominator. The numerator of the first fraction (15) and the denominator of the second fraction (30) are both divisible by 15.