You want to place a towel bar that is 8 1⁄4 inches long in the center of a door that is 26 1⁄3 inches long. How far should you place the bar

Thanks Ninja,

I would have just said

$$\dfrac{26\frac{1}{3}-8\frac{1}{4}}{2}$$

$${\frac{\left(\left({\mathtt{26}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right){\mathtt{\,-\,}}\left({\mathtt{8}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right)\right)}{{\mathtt{2}}}} = {\frac{{\mathtt{217}}}{{\mathtt{24}}}} = {\mathtt{9.041\: \!666\: \!666\: \!666\: \!666\: \!7}}$$

$${\mathtt{217}} \,{mod}\, {\mathtt{24}} = {\mathtt{1}}$$   

 (I just wanted to try out the mod function on the calcuator - I haven't used it before  

Answer = 9 and 1/24 inches

We can set this up as an algebraic equation. X will equal the distance from the side of the door to the towel bar.

2x + 8 1/4 = 26 1/3

2x +33/4 = 79/3           ---Multiply the first fraction by 3/3 and the second by 4/4 to get a common denimiator.

2x + 99/12 = 316/12           ---Subtract 99/12 from both sides

2x = 217/12                      ---Divide both sides by 2

x = 217/12 ÷ 2             ---Dividing is the same as multiplying by the reciprocal

x = 217/12 * 1/2

x = 217/24

x = 9 and 1/24 inches

Here's a picture of this door:

To check this, let's add 8 1/4 +  9 1/24 + 9 1/24, and if they equal 26 1/3 inches then it works!

 8 1/4 +  9 1/24 + 9 1/24

8 1/4 + 18 2/24

26 + 1/4 + 2/24         ---Multiply 1/4 by 6/6 to get a common denominator

26 + 6/24 + 2/24

26 + 8/24                     ---Reduce the fraction by dividing the top and bottom by 8

26 + 1/3

It works!