Question 266885
5 1/2 - 2 7/10 

First convert each mixed fraction to an improper fraction:

1.) 5 1/2 = 10/2 + 1/2 = 11/2

2.) 2 7/10 = 20/10 + 7/10 = 27/10

In order to add 11/2 and 27/10 together we need for each to be expressed with the same denominator.  To find the lowest common denominator find the factors of each: 2 = 1*2 and 10 = 1*2*5. To get our LCD choose all the unigue factors appearing in either number and then multiply these together. In this case the factors are 1,2 and 5 (if one of the numbers has the same factor more than once use the highest number of times the factor appears). In this case then the LCD = 1*2*5 = 10. 

Now we need to alter each number to make 10 the denominator. There is nothing to do in the second case (i.e. 27/10). For the first number 11/2 we can multiply both numerator and denominator by 5. Then we will have;

11/2 = (5*11)/(5*2) = 55/10

Now we can add 55/10 and 27/10 giving 82/10 (remember (a/b + c/b = (a+b)/b).

82/10 = 8 2/10 = 8 1/5