Final answer:
The reciprocal of a number added to 2/3 gives us 8/3. By isolating the reciprocal and simplifying, we find that the number is 1/2.
Step-by-step explanation:
To solve the problem where 2/3 is added to the reciprocal of a number to get 8/3, we can set up the equation as follows: 2/3 + 1/x = 8/3. To find the number, let's solve for x.
Step 1: Subtract 2/3 from both sides of the equation to isolate the reciprocal on one side.
2/3 + 1/x = 8/3
1/x = 8/3 - 2/3
1/x = 6/3
Step 2: Since 6/3 simplifies to 2, our equation now is:
1/x = 2
Step 3: The reciprocal of x is 2, so x must be the reciprocal of 2, which is 1/2.
Therefore, the number we were looking for is 1/2.