Question

Use the method of average to write 2 rational numbers between `14/5` and `16/3`

Answer 1

The average of a and b is `1/2("a" + "b")`

The average of `14/5` and `16/3` is C₁ = `1/2(14/5 + 16/3)`

C₁ = `1/2((42 + 80)/15)`

C₁ = `122/30`

C₁ = `61/15`

`14/5 < 61/15 < 16/3`  ....(1)

The average of `14/5` and `61/15` is C₂ = `1/2(14/5 + 61/15)`

C₂ = `1/2 xx ((42 + 61)/15)`

C₂ = `1/2 xx 103/15 = 103/30`

∴ `14/5 < 103/30 < 61/15`  ....(2)

From (1), (2) we get, `14/5 < 103/30 < 61/15 < 16/3`