Question 64856
<pre><font size = 5 color = "darkblue"><b>       13 - 2/5 = H + 6 - 4/15 

My daughter has just begun to take Pre-Alegbra
& we are seeking help in learning the proper to 
understand equations. Thanks!

The terms on the left are

13 and  -2/5

The terms on the right are

H, 6, and -4/15

The fraction terms are -2/5 and -4/15.

So we clear of fractions to make it easier:

We multiply every term on both sides by
their least common denominator, 15.  So we write
"<font color = "red">15ｷ</font>" just before every term.

      13 - 2/5 = H + 6 - 4/15

<font color = "red">15ｷ</font>13 - <font color = "red">15ｷ</font>2/5 = <font color = "red">15ｷ</font>H + <font color = "red">15ｷ</font>6 - <font color = "red">15ｷ</font>4/15

Now we multiply 
<font color = "red">15ｷ</font>13 and get 195
-<font color = "red">15ｷ</font>2/5 and get -6 
<font color = "red">15ｷ</font>H and get 15H
<font color = "red">15ｷ</font>6 and get 89
-<font color = "red">15ｷ</font>4/15 and get -4

So the equation is now

       195 - 6 = 15H + 90 - 4

Combine the 195 and -6 on the left and get 189
Combine 90 and -4 on the right and get 86

           189 = 15H + 86

Add -86 to both sides  to get rid of the 86 on the 
right, leaving only a term in H

           189 = 15H + 86
           -86        -86
          覧覧覧覧覧覧覧覧覧
           103 = 15H

Now th get rid if the 15 coefficient, we divide
both terms by 15:

        103/15 = 15H/15

        103/15 = H    

That's the solution, 103/15, which you can write
as 6 13/15. However in algebra, improper fractions
are quite proper!!!  :-)  

Edwin</pre>