SOLUTION: I am trying to help a student work his problems out but it has been a while for me. If you could show me the way to simplify it would be a big help. ___a___ a - a/2 Th

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: I am trying to help a student work his problems out but it has been a while for me. If you could show me the way to simplify it would be a big help. ___a___ a - a/2 Th      Log On


   

Question 70211: I am trying to help a student work his problems out but it has been a while for me. If you could show me the way to simplify it would be a big help.
___a___
a - a/2
This is for Algebra 1 -5 1101 through the School of Tomorrow. Christian Education

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
I interpret your problem as being asked to simplify:
a%2F%28a-%28a%2F2%29%29
Let's work on the denominator first. You may recognize is as "a" take away one-half "a".
The result is %281%2F2%29%2Aa
If you didn't recognize that, a more general approach would be to say that to combine
fractions you need to have them over a common denominator. How would you combine a with
a%2F2? One has a denominator and the other doesn't. What if you multiplied the a
by 2%2F2. [Since 2%2F2 is the same as 1, you are effectively multiplying
a by 1 so you are not really changing the a. You are just converting
the a to 2%2Aa%2F2.] In this form you now have a common form for the two terms in
the denominator of your problem. That denominator is:
%282%2Aa%2F2%29-%28a%2F2%29
Notice that these two terms have a common denominator of 2 so they can be combined.
%282a+-+a%29%2F2+=+a%2F2
Substituting this result into your problem results in your problem now being:
a%2F%28a%2F2%29
So you are dividing a by the fraction a%2F2}.
One way to look at this is to use the old arithmetic rule ... when you divide by a fraction,
you invert it and then multiply this inverted fraction times the number that you are dividing.
So, using that rule, we invert a%2F2 to get 2%2Fa. Then we multiply that by
the a that is the original numerator of your problem.
a+%2A+%282%2Fa%29
The a in the denominator of this product cancels with the a in the numerator
to leave just 2 as the simplification of your original problem.
A way that you could do a reality check of your answer is to return to the original
problem and assign a value to a. For example, you might say that a is 1.
This would make your original problem:
1%2F%281+-+%281%2F2%29%29
Using "real" numbers may make it a little easier for you to see that the denominator
%281+-+%281%2F2%29%29 simplifies to 1%2F2. Then ask yourself, "How many times does
1%2F2 go into 1?" A little thought will tell you that there are 2 halves in
1. So by using real numbers you have found that the problem reduces to 2. This helps
to confirm that our previous work was correct and that the original problem simplifies
to 2
Hope this helps.