Given Equation: 65 ÷ 13 × 8 + 39 - 105 = 106
CONCEPT:
Follow BODMAS rule to solve this question by putting combination of signs given in each option, as per the order given below,
Step - 1 - Parts of an equation enclosed in 'Brackets' must be solved first,
Step - 2 - Any mathematical 'Of' or 'Exponent' should be solved next,
Step - 3 - Then, the parts of the equation containing 'Division' and 'Multiplication' operations are solved,
Step - 4 - And lastly, the parts of the equation that contains 'Addition' and 'Subtraction' should be calculated.
So, on using BODMAS and solving each option,
Option 1: + and -
On interchanging these signs, the given equation becomes: 65 ÷ 13 × 8 - 39 + 105 = 106
Solving LHS of the equation,
65 ÷ 13 × 8 - 39 + 105
= 5 × 8 - 39 + 105
= 40 - 39 + 105
= 145 - 39
= 106 = RHS = 106, This satisfies the equation.
Option 2. ÷ and -
On interchanging these signs, the given equation becomes: 65 - 13 × 8 + 39 ÷ 105 = 106
Solving LHS of the equation,
65 - 13 × 8 + 39 ÷ 105
= 65 - 13 × 8 + 0.37
= 65 - 104 + 0.37
= 65.37 - 104
= - 38.63 ≠ 106 , This does not satisfy the equation.
Option 3. + and ×
On interchanging these signs, the given equation becomes: 65 ÷ 13 + 8 × 39 - 105 = 106
Solving LHS of the equation,
65 ÷ 13 + 8 × 39 - 105
= 5 + 8 × 39 - 105
= 5 + 312 - 105
= 317 - 105
= 212 ≠ 106, This does not satisfy the equation.
Option 4. × and ÷
On interchanging these signs, the given equation becomes- 65 × 13 ÷ 8 + 39 - 105 = 106
Solving LHS of the equation,
65 × 13 ÷ 8 + 39 - 105
= 65 × 1.625 + 39 - 105
= 105.625 + 39 - 105
= 144.625 - 105
= 39.625 ≠ 106, This does not satisfy the equation.
Hence, (+ and -) should be interchanged to make the given equation correct.