Simplify: \(110 - [125 \div (5 \times 5) + 6 + 12 \div \overline{7-3} + 10]\)

Concept

When simplifying a numerical expression, follow the order of operations: first evaluate grouping symbols such as parentheses and a vinculum, then multiplication or division from left to right, and finally addition or subtraction from left to right.

A vinculum groups the terms beneath it, so the subtraction under the bar is completed before the surrounding division.

Application

1. Evaluate the product in the denominator: 5 × 5 = 25.

2. Divide: 125 ÷ 25 = 5.

3. Evaluate the vinculum: 7 − 3 = 4.

4. Divide: 12 ÷ 4 = 3.

5. Add the terms inside the square brackets: 5 + 6 + 3 + 10 = 24.

6. Subtract the bracket value from 110: 110 − 24 = 86.

Cross-check

The inner total and the result recombine as 24 + 86 = 110, confirming the subtraction.

Therefore, the simplified value is 86.