Question

Which is larger `3/7` or `13/40` ?

Answer 1

3/7

Explanation:

Rearrange so that they have the same denominator, then you can easily see which one is bigger.

7 isn't a factor of 40, so you will have to find their lowest common multiple.

The easiest way to do this is to multiply 7 by 40.

This gives 280.
Now multiply the top line by whatever you multiplied the bottom line:

`(3times40)/280` and `(7 times 13)/280`

=`120/280` and `91/280`

Now you can see that `120/280` is bigger.

Answer 2

`3/7`

Explanation:

If `a, b, c, d` are all positive then note that:

`a/b < c/d" "` if and only if `" "ad < bc`

So in our example, we find:

`3*40 = 120`

`7*13 = 91`

So:

`7 * 13 < 3 * 40`

and

`13/40 < 3/7`