simplify the ratio: 14/25:7:10show all your working out and explain how you got the answer.

The given ratio is 
14/15:7:10.

The given ratio is  ordered triple number or in
simple language 3 numbers (terms) in an order.

A ratio does
not change in value by multiplying (or dividing) each its terms by equal number (but
never by zero).

A ratio is in simplest form when all the
terms are in the minimum posinble intgers.

In the given
ratio 14/25 can be 14 in the ratio if we multiply each of the 3 terms by
14:

(14/25)*25 : 7*25 :
10*25

14 : 175 : 250

Now the
three terms  i 14 : 175 : 25 together do not have any common (in fact HCF) factor other
than 1. 

Therefore,  14 : 175 : 250 is the simple form of
the given ratio.