Question

Find the compound ratios of the following

a) 3 : 4 and 2 : 3 

b) 4 : 5 and 4 : 5 

c) 5 : 7 and 2 : 9

Answer 1

Compound ratio of a : b and c : d is ac : bd.

     Given ratio                    Compound ratio

a) 3 : 4 and 2 : 3   \(\rightarrow\) \(\frac34\,\times\,\frac23\) = \(\frac{3\,\times\,2}{4\,\times\,\,3}\) = \(\frac12\)  =  1:2

b) 4 : 5 and 4 : 5  \(\rightarrow\) \(\frac45\,\times\,\frac45\)  = \(\frac{16}{25}\)  = 16:25

c) 5 : 7 and 2 : 9  \(\rightarrow\) \(\frac57\,\times\,\frac29\) = \(\frac{10}{63}\) = 10:63