SOLUTION: Hi, Need help with a fraction problem: x+2 over 2 = 14 over 16 Would you explain the steps the arrive at the answer? Thank you! Carrie

Question 596333: Hi,
Need help with a fraction problem:
x+2 over 2 = 14 over 16
Would you explain the steps the arrive at the answer?
Thank you!
Carrie
Found 2 solutions by unlockmath, bucky:
Answer by unlockmath(1688) (Show Source): You can put this solution on YOUR website!
Hello,
This x+2 over 2 = 14 over 16 can be rewritten as:
x+2/2 = 7/8
Multiply both sides by 8 ato get:
4(x+2)=7
Expand:
4x+8=7
Subtract 8 and divide by 4 to get"
x=-1/4
Make sense?
RJ
www.math-unlock.com
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Your problem is:
.

.
It's not necessary to do this now, but let's begin by simplifying the right side of the equation. The fraction of 14 over 16 can be reduced to 7 over 8 by dividing both the numerator and the denominator by 2 to reduce the equation to:
.

.
We can now get rid of all the denominators by multiplying both the left and right sides of this equation by 8, which is a common denominator because the denominator 2 on the left side is also a factor of 8. Multiplying both sides by 8 results in:
.

.
On the right side of the equal sign the 8 in the numerator cancels with the 8 in the denominator as follows:
.

.
and we are left with just 7 on the right side as follows:
.

.
Then on the left side we can divide the 2 in the denominator into the 8 in the numerator. The result of this division is 4 and the left side reduces as shown below:
.

.
Do the distributed multiplication on the left side by multiplying the 4 times each of the terms in the parentheses to get:
.

.
Get rid of the 8 on the left side by subtracting 8 from both sides as shown:
.

.
On the left side the +8 and the -8 cancel each other. And on the right side the 7 and the -8 combine to give -1. The result is:
.

.
Finally, we can solve for x by dividing both sides by 4. On the left side this results in the 4x becoming just 4 and on the right side we get the fraction as shown:
.

.
And that is the answer to this problem. I hope this helps you to understand the problem a little better and you can see a process by which it can be solved.
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