I am one of the only seventh graders in an algebra 1 class she is basing her lessons on what the eighth graders learned last year in pre-algebra. My teacher calls the equations many different things and she is confusing me.
There are two ways for dealing with fractions in algebraic equations.
1. Multiply the whole equation with the LCM (lowest common denominator) of all fractions. This will then give you a whole number equation to work with.
Example: 1/2 x - 4 = 2/3 x + 5/6
Multiplying with the LCM of 6 gives
6*(1/2 x) - 6*4 = 6*(2/3 x) + 6*(5/6)
or 3x - 24 = 4x + 5
then solve as normal to get x = -29
2. Leave the equation as it is and work as you always do. Let's use the same example:
1/2 x - 4 = 2/3 x + 5/6
Work as always to collect the variables on one side and the non-variable terms on the other. I will do this here by subtracting 1/2 x from both sides and by subtracting 5/6 from both sides. That gives
-4 - 5/6 = 2/3 x - 1/2 x
or -4 - 5/6 = (2/3- 1/2) x
Now again, you will need to use the LCM (although here you just need to find the LCM of the fractions you actually want to add/subtract; coincidentally this is also 6, but you may, in other problems, find smaller LCMs)
with a common denominator you get
- 24/6 - 5/6 = (4/6 - 3/6)
or -29/6 = 1/6 x
Divide both sides by 1/6 and you get
-29 = x
Hope this helps!