Which of the following operations should be interchanged to make the following equation correct? 12 + 12 − 4 × 4 ÷ 2 = 22

Correct — C. Rule: make the swap in writing, then evaluate by BODMAS — division and multiplication before addition and subtraction, each pair worked left to right.

Swapping ÷ and − turns 12 + 12 − 4 × 4 ÷ 2 into 12 + 12 ÷ 4 × 4 − 2.

12 ÷ 4 = 3
3 × 4 = 12
12 + 12 = 24
24 − 2 = 22

That matches the right-hand side, so the pair to interchange is ÷ and − — option (c).

Why the others are wrong

• (a)
  − and + — Swapping these gives 12 − 12 + 4 × 4 ÷ 2, and the two 12s cancel before 8 is added, leaving 8.
• (b)
  + and ÷ — Swapping these gives 12 ÷ 12 − 4 × 4 + 2 = 1 − 16 + 2 = −13, a long way below 22.
• (d)
  × and − — Swapping these gives 12 + 12 × 4 − 4 ÷ 2 = 12 + 48 − 2 = 58, far above 22.

Sign-interchange questions are BODMAS drill with one extra step in front. Rewrite the whole expression with the swap already made before touching any arithmetic — holding the swap in your head is where the marks go.

Then evaluate strictly in order: brackets, orders, division and multiplication left to right, then addition and subtraction left to right.

With four options and short arithmetic inside each, working through all of them is a legitimate strategy when no swap suggests itself on sight.

Key facts

• As printed, the left-hand side evaluates to 16 rather than 22.
• After swapping ÷ and −, the expression reads 12 + 12 ÷ 4 × 4 − 2.
• Division and multiplication are worked left to right, so 12 ÷ 4 × 4 is 12 and not 12 ÷ 16.

Common traps

• Working 12 ÷ 4 × 4 as 12 ÷ 16 by taking the multiplication first
• Swapping the signs only at their first appearance instead of everywhere they occur
• Evaluating the expression as printed and comparing it to 22 without making the swap at all

No directly related past PYQ was found.