Question

Find 4 rational numbers between the following
given
two rational numbers -3/5,-1/7 ​

Answer 1

To insert four rational number between -3/5 and -1/7

We find the mean of -3/5 and -1/7

i. e., 1/2 ( -3/5 + -1/7 ) = 1/2 × -26/35 = -13/35

We find that -3/5<-13/35<-1/7

We now find another rational number between -3/5 and -13/35. For this ,we again find the mean of -3/5 and -13/35

i. e. 1/2(-3/5 + -13/35) = 1/2 × -34/35 = -17/35

We find that -3/5<-17/35<-13/35<-1/7

Now we find the mean of -13/35 and -1/7

i. e. 1/2(-13/35+-1/7) = 1/2 × -18/35 = -9/35

We get -3/5<-17/35<-13/35<-9/35<-1/7

Now we find the mean of -3/5 and -17/35

i. e. 1/2(-3/5+-17/35) = 1/2 × -38/35 = -19/35

Thus, we get -3/5<-19/35<-17/35<-13/35<-9/35<-1/7

Hence, 4 rational numbers between -3/5 and -1/7 are -19/35,-17/35,-13/35,-9/35

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