If ‘A’ stands for ‘÷’, ‘B’ stands for ‘×’, ‘C’ stands for ‘+’ and ‘D’ stands…

Concept

In letter-for-symbol substitution problems, each letter is first replaced by the arithmetic operator it stands for. The resulting numerical expression is then evaluated by the standard order of operations (BODMAS): division and multiplication are settled before addition and subtraction, and operators of equal precedence are applied from left to right. Renaming the operators as letters changes only how they are written, never their precedence.

Application

1. Substitute each letter with the operator it stands for, turning "99 D 144 A 6 B 3 C 11" into 99 − 144 ÷ 6 × 3 + 11.

2. Division and multiplication share the same precedence, so they are taken from left to right. The division stands first: 144 ÷ 6 = 24.

3. The multiplication then acts on that result: 24 × 3 = 72.

4. With the higher-precedence block resolved, the expression reduces to 99 − 72 + 11.

5. Subtraction and addition also share the same precedence, so they too are taken from left to right: 99 − 72 = 27.

6. Finally, 27 + 11 = 38.

Cross-check

Re-order the last stage as 99 + 11 − 72 = 110 − 72 = 38, an independent route to the same value, and reverse the division to confirm it: 24 × 6 = 144. It also helps to see what the precedence rule rules out. Multiplying before dividing would read the middle block as 144 ÷ (6 × 3) = 144 ÷ 18 = 8 and give 99 − 8 + 11 = 102, while ignoring precedence altogether and working straight from the left would give (99 − 144) ÷ 6 × 3 + 11 = −11.5. Neither is a legitimate reading of the expression.

So the expression evaluates to 38.