Final Answer:
The fraction 8/₁₀ is greater than 3/₄ when rounded to the nearest half.
Step-by-step explanation:
To compare the fractions 3/₄ and 8/₁₀ using rounding to the nearest half, we need to find a common denominator. In this case, the least common denominator is 4.
For 3/₄, there is no rounding needed as it is already in its simplest form. For 8/₁₀, when expressed with a denominator of 4, it becomes 4/₅. Now, comparing 3/₄ to 4/₅, we can see that 4/₅ is greater when rounded to the nearest half.
Rounding to the nearest half is equivalent to rounding to the nearest multiple of 0.5. In this context, 4/₅ is closer to 0.5 than 3/₄. Therefore, 8/₁₀ is greater than 3/₄ when considering rounding to the nearest half.
In summary, the comparison is facilitated by finding a common denominator, and in this case, 8/₁₀ (or 4/₅ in simplified form) is greater than 3/₄ when rounded to the nearest half.