Question

The reciprocal of a number plus the reciprocal of three times the number equals`1/3`. What is the number?

Answer 1

The number is 4.

Explanation:

Calling the number `n`, we need to first step up an equation, which should look something like this:

`1/n+1/(3n)=1/3`

Now, it's just a matter of rearranging to get n as the subject.

To add the fractions, we need to have the same denominator, so let's start there

`(1*3)/(n*3) +1/(3n)=1/3`

which simplifies to
`(3+1)/(3n)=1/3`

adding the 3 and 1
`4/(3n)=1/3`

Multiply both sides by `3n` and you should get
`4=(3n)/3`

Now, the 3s on the right side cancel out- which gives the answer:

`4=n`