Q. 4 Solve the following:

1. 4 2/3 + 3 1/2

Solution: First Convert 4 2/3 into improper fraction we get:   ( 4 x3 + 2)/3 = 14/3

Convert 3 1/2 into improper fraction we get:  (2 x 3 + 1) / 2 = 7/2

Now we have to add 14/3 + 7/2

These fractions are unlike fraction where denominator and numerator are different numbers. So we have to convert

to like fractions where denominator of both the fractions are same and then we can simply add the two fractions.

To convert to like fraction we have to first find LCM of denominator 3 and 2

2 |   3 ,    2

3 |   3 ,    1

   |    1,     1 

Hence LCM is 2 x 3 = 6

Now take fraction 14 / 3, divide 6(LCM)  by 3 (Denominator)  we get 2

So multiply by 2 in denominator and numerator :   14 x 2 / 3 x 2 = 48/6

Similarly for the fraction 7/2 , divide 6 (LCM) by 2 we get 3

So multiply by 3 in denominator and numerator :   7 x 3 / 2 x 3 = 14/ 6

Now two fractions have become 48/6 + 14 / 6 we get (48 + 14) / 6 = 62/6 This is the answer.

2.  8 1/4 - 2 5/6

Solution: Here also we have convert mixed fraction to improper fraction we get

(8 x 4 + 1) /4 = 33/4

(2 x 6 + 5) / 6 = 17/6

Now convert both the improper fraction to like fraction and we get

LCM of 4 and 6 is 12

Now converting to like fraction we get :   33 x 3 / 4 x 3 = 99/12

Now converting 17 / 6 to like fraction we get :  17 x 2 / 6 x 2 = 34 / 12

99 / 12 - 34 / 12 = (99 - 34) / 12 =  65/12 is the answer

3. 0.007 + 8.5 + 30.08

Solution: We have to convert all the three numbers into equal digits ( before decimal and after decimal), therefore

0.007 becomes 00.007

8.5 becomes 08.500

30.08 becomes 35.080

Now we can add

           00.007

+         08.500

+         35.080

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            43.587      

4. 21.05 - 15.27

Solution:                                   21.05

                                         -       15.27

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                                                  5. 78   Answer