$91\frac{3}{7}+83\frac{5}{7}+81\frac{6}{7}$

The correct answer is:

$257$

Step-by-Step Explanation:

To find the sum of the mixed numbers, we can separate each mixed number into its integer (whole number) component and its fractional component.

We are given the expression:

$91\frac{3}{7}+83\frac{5}{7}+81\frac{6}{7}$

Step 1: Group the whole numbers and fractions separately.

By using the associative and commutative properties of addition, we can rewrite the expression as:

$(91+83+81)+(\frac{3}{7}+\frac{5}{7}+\frac{6}{7})$

Step 2: Add the whole numbers together.

$91+83+81=255$

Step 3: Add the fractional parts together.

Since all the fractions have the same common denominator of 7, we simply add their numerators:

$\frac{3}{7}+\frac{5}{7}+\frac{6}{7}=\frac{3+5+6}{7}=\frac{14}{7}=2$

Step 4: Combine the whole number sum and the fractional sum.

Now, add the sum of the whole numbers to the simplified sum of the fractions:

$255+2=257$

Therefore, the final value of the given expression is 257.