Question

Which number should follow in this series: 64/64 9/12 6/12​

Answer 1

`\texttt{The number following is }(1)/(4)`

Explanation:

Series is

`(64)/(64),(9)/(12),(6)/(12).....`

Let us simplify

`(64)/(64),(9)/(12),(6)/(12).....=1,(3)/(4),(1)/(2).....`

So this is arithmetic progression with 1 as first term and
`-(1)/(4)` as common difference.

Next term of AP will be
`(1)/(2)-(1)/(4)=(1)/(4)`

`\texttt{The number following is }(1)/(4)`

Answer 2

Answer:
`(1)/(4)`

Explanation:

You can reduce the fractions, then:

`(64)/(64)=1`

`(9)/(12)=(3)/(4)`

`(6)/(12)=(3)/(6)=(1)/(2)`

Rewrite them as following:

`1,(3)/(4),(1)/(2)`

If you subtract the first number and the second number, you obtain:

`1-(3)/(4)=(1)/(4)`

If you subtract the second number and the second number, you obtain:

`(3)/(4)-(1)/(2)=(1)/(4)`

Therefore, you must subtract
`(1)/(2)` and
`(1)/(4)` to obtain the number asked. Then, this is:

`(1)/(2)-(1)/(4)=(1)/(4)`