next up previous
Next: Finding simpler forms by Up: Manipulation of fractions Previous: Manipulation of fractions

Addition, subtraction, multiplication, and division

Addition and subtraction of fractions requires a common denominator. Often the easiest one to find is the product of the denominators:

\begin{displaymath}\frac{a}{b}+\frac{c}{d}=\frac{ad}{bd}+\frac{cb}{bd}=\frac{ad + bc}{bd}\end{displaymath}

\begin{displaymath}\frac{a}{b}-\frac{c}{d}=\frac{ad}{bd}-\frac{cb}{bd}=\frac{ad - bc}{bd}\end{displaymath}

Multiplication and division are gotten somewhat more easily:




Use of parentheses in these situations is very helpful- put them in whenever you need them.

These operations will frequently be combined in one step:

\begin{displaymath}\frac{\frac{1}{x+h}-\frac{1}{x}}{h}=\frac{x-(x+h)}{h x  (x+h)}\end{displaymath}

Fill in any steps in your notes that you need to see how the algebra worked.

Another typical example:


Larry Stout 2003-01-09
buy snagit 11 buy autodesk autocad 2010 buy disk drill pro 1.8 mac buy autodesk autocad electrical 2015 buy adobe director 11.5 buy adobe audition cs5 buy adobe premiere pro cc buy microsoft office visio 2013 cheap microsoft office 2007