1. ## Find X

Hey y'all this is my first post here and for forewarning I am horrible at math. Anyway here's the problem I'm having trouble with:

5 1/6 + x = 7 1/1

The book says the answer is 1 5/6 and I can tell that's right the problem I'm having is figuring out where the extra whole number disappeared to. Here's how I worked it out:

5 1/6 - 5 1/6 + x = 7 1/1 - 5 1/6
x = 7 1/1 - 5 1/6
7 1/1 * 6/6 - 5 1/6 * 1/1
7 6/6 - 5 1/6
x = 7 6/6 - 5 1/6 = 2 5/6

So my question is how did the book get rid of the extra 1 in the solution? Also if I've done anything else horribly bad please let me know.

Thanks!

-El Cid

2. Writing $5\frac{1}{6}$ as $5 + \frac{1}{6}$ will make it easier (same goes for $7\frac{1}{1}$)

$5\frac{1}{6} + x = 7\frac{1}{1}$

$5 + \frac{1}{6} + x = 7 + \frac{1}{1}$

$5 + \frac{1}{6} + x = 7 + 1$

$5 + \frac{1}{6} + x = 8$

Leave x alone;

$x = 8 - 5 - \frac{1}{6}$

$x = 3 - \frac{1}{6}$

$x = \frac{18}{6} - \frac{1}{6}$

$x = \frac{17}{6}$

$x = 2\frac{5}{6}$

But.. Are you sure that it is $7\frac{1}{1}$ rather than $7\cdot\frac{1}{1}$ ? I ask this because if it's $7\cdot\frac{1}{1}$, the answer of the book is true.