Question

Lesson name:- number system

1) find 5 ration number between (-1) and 1

method;- by arthimatic mean

Answer 1

For first rational number

let the a=(-1),b=1

1. now arthimatic mean formula=a+b/2
2. a+b/2=-1+1/2
3. -1+1/2=0

For second rational number

let a=(-1),b=0

1. a+b/2=-1+0/2
2. -1+0/2=-1/2

For third rational number

let a=(-1),b=-1/2

1. a+b/2=-1+(1/2)/2
2. -1+(-1/2)/2=-3/4

For fourth rational number

let a=(-1),b=-3/4

1. a+b/2=-1+(-3/4)/2
2. -1+(+3/4)/2=-7/8

For fifth rational number

let a=(-1),b=-7/8

1. a+b/2=-1+(-7/8)/2
2. -1+(-7/8)/2=-15/16

so the five rational numbers are -1<-15/16<-7/8<-3/4<-1/2<0<1