Use Their Knowledge of the Order of Operations to Carry Out Calculations Involving the Four Operations 5 - Reasoning

Esin has attempted to solve the mathematical expression 3 + 33 ÷ 3 – 3 x 3 and arrived at an answer of 3. However, her method does not adhere to the correct order of operations, commonly known as BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) in British English. Esin first added 3 to 33, giving 36, then divided by 3 to get 12, and finally subtracted the product of 3 x 3, which is 9, to conclude with an answer of 3. This approach is incorrect because it overlooks the priority of division and multiplication over addition and subtraction.

The accurate sequence to solve the expression is to first perform the division and multiplication before the addition and subtraction. This means dividing 33 by 3 to get 11, and multiplying 3 by 3 to get 9, and then adding and subtracting these results to and from the initial 3. The correct calculation should therefore be 3 + (33 ÷ 3) – (3 x 3), which simplifies to 3 + 11 – 9, resulting in a final answer of 5. Hence, Esin's conclusion that the answer is 3 is incorrect due to her mishandling of the order of operations.