The reciprocal of a number plus the reciprocal of three times the number equals1/3. What is the number?

1 Answer
Dec 2, 2017

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