Solve Mixed Number Equation: 98 6/7 - (8/10 - 6/5)

To solve this problem, we'll follow these steps:

• Step 1: Convert the mixed number to an improper fraction.
• Step 2: Simplify the expression inside the parentheses.
• Step 3: Perform the arithmetic operations to find the final result.

Let's work through each step:

Step 1: Convert $98\frac{6}{7}$ to an improper fraction. This mixed number can be expressed as $\frac{689}{7}$ since $98 \times 7 + 6 = 686 + 6 = 692$.

Step 2: Simplify the expression $\frac{8}{10} - \frac{6}{5}$. To do this, find a common denominator:

• The common denominator of 10 and 5 is 10.
• Thus, $\frac{8}{10}$ remains $\frac{8}{10}$, and $\frac{6}{5}$ can be written as $\frac{12}{10}$.
• Subtract the fractions: $\frac{8}{10} - \frac{12}{10} = \frac{8 - 12}{10} = \frac{-4}{10}$.
• Simplify $\frac{-4}{10}$ to $\frac{-2}{5}$.

Step 3: Perform the subtraction: $98\frac{6}{7} - \left(\frac{8}{10} - \frac{6}{5}\right)$ becomes $\frac{689}{7} - \left(\frac{-2}{5}\right)$.

• Convert the subtraction to addition: $\frac{689}{7} + \frac{2}{5}$.
• Find a common denominator for 7 and 5, which is 35.
• Convert: $\frac{689}{7} = \frac{689 \times 5}{35} = \frac{3445}{35}$ and $\frac{2}{5} = \frac{2 \times 7}{35} = \frac{14}{35}$.
• Add the fractions: $\frac{3445}{35} + \frac{14}{35} = \frac{3445 + 14}{35} = \frac{3459}{35}$.

Convert the improper fraction back to a mixed number. Divide $3459$ by $35$:

• 3459 divided by 35 gives a quotient of 99 with a remainder of 9, thus $99\frac{9}{35}$.

Therefore, the solution to the problem is $99\frac{9}{35}$.