basic algebra question

Question

-5X + 4Y where X = 1/2 and Y = -1

 

-5 (1/2) + 4(-1) 

 

- 11/2 + -4 =

 

-11/2 + - 8/2 =

 

-19/2 = -9 1/2

 

HOWEVER

 

the textbook reads the answer should be -6 1/2

 

Where am I going wrong?????

 

Answer 1

-5(1/2) = -5/2, not -11/2.  Think of it this way - it's 1/2 of -5 , which is -2 1/2 = -5/2:

 

-5      1      -5*1      -5

--- * --- =  -----  =   ----

 1      2       1*2        2

 

Hence

 

(-5)(1/2) + 4(-1) = -5/2 - 4 = -5/2 -8/2 = -13/2 = -6 1/2

Answer 2

First of all you have (-5)(1/2) + 4(-1), which gives you (-5/2) +  -4. Then you have to get a common denominator. 2 is the common denominator. So, -4 changes to -8/2... which means you are now adding (-5/2) and (-8/2), getting (-13/2). This changes to -6 1/2