Fraction Question

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Interceptor

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Nov 13, 2010
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There are two fraction problems I'm struggling to understand. I am in a college level pre-algebra class, and the book provides the answers to both of these problems, but I'm not getting the same answer, and I don't know what I'm doing wrong.
Here's the first problem:

x/5-x=1/5

The book says the answer is -1/4, and I keep getting 1. The book says to multiply both sides by the LCD, which in this case is 5, right? So, 5(x/5) gives me x. and 5(x/1)= 5x. So I'm left with 5x-x, right? Then I multiply the other side by 5, like so:
1/5(5)= 1, right? So shouldn't my problem look like this now: 5x-x=1 ? Now what? I'm very confused by this!

Here's the second problem. I finally got the right answer, but I don't understand why we don't reduce further. The problem is: x/3+2/1
5/1+1/3

So, I solved the numerator first, getting x+6/3. For the denominator of 5/1+1/3 I got 16/3. I then solved this complex fraction by using the reciprocal of 16/3 to multiply 3/16(x+6/3). I finally got x+6/16, which is the answer the book gave. However, my question is, why can't you reduce x+6/16 to x+3/8 ? I know you can't do operations on constants and variables, but isn't x alone, allowing us to reduce 6/16 to 3/8. By the way...I hate fractions!
 
Interceptor & my edit said:
x/5 - x = 1/5

The book says the answer is -1/4, and I keep getting 1. The book says to multiply both sides by the LCD, which in this case is 5, right? So, 5(x/5) gives me x. and 5(x/1)= 5x. So I'm left with 5x-x, right?

\(\displaystyle No, \ you \ have \ the \ order \ reversed. \ \ It \ is \ x - 5x.\)

Then I multiply the other side by 5, like so:
1/5(5)= 1, right? So shouldn't my problem look like this now: 5x-x=1 ?

\(\displaystyle No, \ from \ the \ above, \ it \ becomes \ x - 5x \ = \ 1.\)

Now what? I'm very confused by this!

Here's the second problem. I finally got the right answer, but I don't understand why we don't reduce further. The problem is: x/3+2/1
5/1+1/3 . . . . . This problem must be: \(\displaystyle Simplify \ \ \frac{ \frac{x}{3} + \frac{2}{1}}{ \frac{5}{1} + \frac{1}{3}}. . . . . . **\)

So, I solved \(\displaystyle [you're \ not \ solving \ it, \ but \ you \ are \ combining \ them\ into \ one \ fraction]\) the numerator first, getting x+6/3. \(\displaystyle No, \ it \ is \ to \ be \ (x + 6)/3. \ \ You \ must \ have\ grouping \ symbols.\)

For the denominator of 5/1+1/3 I got 16/3. I then solved \(\displaystyle [no, \ you \ attempted \ to \ simplifly]\) this complex fraction by using the reciprocal of 16/3 to multiply 3/16(x+6/3). I finally got x+6/16, \(\displaystyle [No, \ this \ is \ to \ be \ (x + 6)/16],\) which is the answer the book gave.

However, my question is, why can't you reduce x+6/16 to \ x+3/8 ?

\(\displaystyle It's \ not \ those \ fractions; \ you \ are \ supposed \ to \ have \ (x \ + \ 6)/16 \ for \ the \ first \ fraction.\)
I know you can't do operations on constants and variables, but isn't x alone, \(\displaystyle [No, \ x\ is \ being \ added \ to \ 6]\)
allowing us to reduce 6/16 to 3/8.
Click to expand...

\(\displaystyle **\) \(\displaystyle Multiply \ each \ separate \ fraction \ by \ \frac{3}{1}, a \ form \ of \ the \ least \ common \ denominator:\)

\(\displaystyle \frac{ (\frac{3}{1})\frac{x}{3} + (\frac{3}{1})\frac{2}{1}}{ (\frac{3}{1})\frac{5}{1} + (\frac{3}{1})\frac{1}{3}} =\)

\(\displaystyle \frac{x + 6}{15 + 1} =\)

\(\displaystyle \frac{x + 6}{16} \ [which \ does \ not \ reduce],\ and\)

\(\displaystyle this \ is \ not \ equal \ to \ x \ + \ \frac{6}{16}\ .\)

\(\displaystyle And \ this \ last \ fraction \ is \ not \ equal \ to \ x \ + \ \frac{3}{8}, \ anyway.\)
 
Interceptor said:
x/5-x=1/5
The book says the answer is -1/4, and I keep getting 1. The book says to multiply both sides by the LCD, which in this case is 5, right? So, 5(x/5) gives me x. and 5(x/1)= 5x. So I'm left with 5x-x, right? Then I multiply the other side by 5, like so:
1/5(5)= 1, right? So shouldn't my problem look like this now: 5x-x=1 ? Now what? I'm very confused by this!
Click to expand...
5(x/5) = x : correct
5(-x) = -5x : not +5x
5(1/5) = 1 : correct
So:
x - 5x = 1
-4x = 1
x = -1/4
 
Interceptor said:
Here's the second problem.......I finally got x+6/16, which is the answer the book gave. However, my question is, why can't you reduce x+6/16 to x+3/8 ? I know you can't do operations on constants and variables, but isn't x alone, allowing us to reduce 6/16 to 3/8.
Click to expand...
You finally got (x+6) / 16, NOT x + 6/16 : see that?
 
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