Adding Fractions

Is ? (because it looks right?)

We know that the right hand side, , cannot be equal to the left hand side, , because we know that

The here is like the example above, with 1s in place of the n and m, so it equals

that is

which is nothing like !

We could deduce that cannot equal by thinking of what things mean. Start with

Changing this into

means increasing the divider, thus making the result smaller than ;

On the other hand,

is bigger than

so cannot be equal to .