Final answer:
To find a fraction between 1/2 and 1/3, we can use a common denominator of 6 to express them as 3/6 and 2/6, respectively. Then, a fraction with a denominator of 6 and a numerator between 2 and 3, such as 5/12, fits between 1/2 (6/12) and 1/3 (4/12).
Step-by-step explanation:
Finding a Fraction Between 1/2 and 1/3
When considering fractions, it's sometimes useful to think about them in the context of something familiar, like slices of a pie or quarters in a dollar. The student asked for a fraction that lies between 1/2 and 1/3, which requires an understanding of how fractions work and how they can be compared. To compare or find a fraction between two others, we need to find a common denominator.
For instance, the denominators of 1/2 and 1/3 are 2 and 3 respectively. The smallest common denominator that both 2 and 3 divide into without a remainder is 6. Thus, we can express 1/2 as 3/6 and 1/3 as 2/6.
Now it's clearer to see that any fraction with a denominator of 6 and a numerator between 2 and 3 would lie between 1/2 and 1/3. A good example of such a fraction is 5/6, but since 5/6 is too large, we would look for a smaller numerator. The fraction 5/12 fits perfectly between 1/2 (6/12) and 1/3 (4/12), as its value is greater than 1/3 and less than 1/2.