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

Question

Accepted Answer

Step 1: Evaluate the original expression 12 + 12 − 4 × 4 ÷ 2 using BODMAS:
- Multiplication and division first:
  4 × 4 = 16
  16 ÷ 2 = 8
- Now the expression becomes 12 + 12 − 8
- Perform addition and subtraction from left to right:
  12 + 12 = 24
  24 − 8 = 16
So, original expression equals 16, not 22.

Step 2: Check each option by interchanging the operations and evaluate:

Option 1: Interchange − and +
Expression becomes: 12 − 12 + 4 × 4 ÷ 2
Calculate multiplication and division:
  4 × 4 = 16
  16 ÷ 2 = 8
Expression: 12 − 12 + 8
Calculate left to right:
  12 − 12 = 0
  0 + 8 = 8
Result is 8, not 22.

Option 2: Interchange + and ÷
Expression becomes: 12 ÷ 12 − 4 × 4 + 2
Calculate multiplication and division:
  12 ÷ 12 = 1
  4 × 4 = 16
Expression: 1 − 16 + 2
Calculate left to right:
  1 − 16 = -15
  -15 + 2 = -13
Result is -13, not 22.

Option 3: Interchange ÷ and −
Expression becomes: 12 + 12 ÷ 4 × 4 − 2
Calculate multiplication and division from left to right:
  12 ÷ 4 = 3
  3 × 4 = 12
Expression: 12 + 12 − 2
Calculate left to right:
  12 + 12 = 24
  24 − 2 = 22
Result is 22, which matches the right side.

Option 4: Interchange × and −
Expression becomes: 12 + 12 × 4 − 4 ÷ 2
Calculate multiplication and division:
  12 × 4 = 48
  4 ÷ 2 = 2
Expression: 12 + 48 − 2
Calculate left to right:
  12 + 48 = 60
  60 − 2 = 58
Result is 58, not 22.

Therefore, interchanging ÷ and − makes the equation correct.

Answer

Answer

Answer