Final answer:
The numbers that are a distance of 2/3 unit from 1/2 on a number line are 7/6 and 1/6. To find these, we add and subtract 2/3, converted to sixths (4/6), to 1/2, also converted to sixths (3/6).
Step-by-step explanation:
To find the numbers that are a distance of 2/3 unit from 1/2 on a number line, we need to add and subtract 2/3 from 1/2. When dealing with fractions, it's often helpful to find a common denominator. In this case, the common denominator of 2 and 3 is 6.
First, we convert 1/2 into sixths, which is equivalent to 3/6. Now we can clearly see the math: add 2/3 (which is the same as 4/6) to 3/6 and subtract 2/3 from 3/6.
Adding 4/6 to 3/6 gives us 7/6, while subtracting 4/6 from 3/6 gives us -1/6, which is the same as 1/6 when considering distances on a number line (since distance is always positive).
Therefore, the numbers a distance of 2/3 unit from 1/2 on a number line are 7/6 and 1/6.