I am 29 and I enrolled in college to go to a math heavy degree, and so I decided to brush up on my math stuff. I ended highschool by barely retaining any knowledge from trig or pre-calc. My single largest issue throughout all of learning math was fractions. I remember I had always had a "different" method for doing problems. While watching a couple of videos on basic algebra review I am still running into that issue. I'll have the same final answer for everything. I'll pause the video, do the problem and watch him do it. It is so hard to learn when I approach problems different than seemingly every teacher I listen to / watch.

What I'm hoping to find is a universal way to deal with fractions from basic algebra to vector calculus. I don't care about "shortcuts". I'd rather do 4 more "steps" to ensure my answer is correct. I always seems to miss transposing a negative sign when I follow these "shortcuts".

http://imgur.com/a/MoyuU This image is my sheet of 3 problems. #1 and #2 are the same starting equation and #3 is a different one. #1 is my attempt at the problem with my work shown. #2 is the tutors attempt at the problem with his work shown. #3 is the next problem he covered and both of our methods are the same.

Because I drew all over the work, problem 1 and 2 is: (x 2) / 5 = 7/8

Can someone explain if there is a way to deal with fractions when resolving functions, every time, the same way?