3.8 Equations with Fractions

The first, and only, rule about fractions is get rid of them. Fast.

This is so that your equation is a ‘one liner’, i.e. all written on one line, because it is then more easily dealt with.

Let’s go back to a numerical example

Although this means ‘5 equals 20 divided by 4’ it can also mean ‘a fraction equivalent of 5 is 20 over 4’.

Since the 20 and the 4 are glued together by division, we can unglue them by using the inverse operation of division. We can multiply both sides by the denominator of the fraction (the number on the bottom).

On the right-hand side of this the 4s cancel out top and bottom, and we are left with

which I’m sure you knew anyway (as far back as page 5/77). But it’s the technique that’s important.