Question

find the three rational number between -3/7 and - 1/7​

Answer 1

Answer:

Solution :

A rational number -1 and 7 is

R1=12(−1+7)=3

∴ −1<3<7

Again, a rational number between -1 and 3 is

R2=12(−1+3)=1

∴ −1<1<3

and, a rational number between 3 and 7 is

R3=12(3+7)=5

∴ 3<5<7

Thus, −1<1<3<5<7.

∴ Three rational number between -1 and 7 are 1,3,5.

Alternate Methode to Find 'n' Rational Numbers between Two Rational Numbers :

Let a and are two rational number such that a<b.

Let a1,a2,a3,....,an be n rational numbers between a nad b,

such that a<a1<2<a3<...<an<b

The difference of a and b = b - a

Divide this difference by (n+1) and obtain b−an+1.

Multiply it by the numbers 1,2,3, . . . n and add a in each to find the values of a1,a2,a3,...an respectively.

∴ a1=a+b−an+aa2=a+2(b−a)n+1a3=a+3(b−a)n+1⋮ ⋮an=a+n(b−a)n+1⎫⎭⎬⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪n rational number between a and b