The value of e:g is 2:7.
A ratio indicates how many times one number contains another.
Given:
e:f=3:7
f:g=2:3
Now take LCM of 2 and 7 i.e., 14.
e/f= 3/7= 3*2/7*2= 6/14
and, f/g= 2/3= 2*7/3*7= 14/21
So,
e/g= e/f *f /g
= 6/14*14/21
= 6/21
e:g = 2:7
Hence, the value of e:g is 2:7.
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