Understanding the Equation Problem
The question asks us to identify which pair of mathematical signs needs to be swapped in the given equation to make it mathematically correct. The equation is:
$$67 - 84 \div 12 \times 5 + 31 = 71$$
To solve this, we need to test the given options by interchanging the specified signs and then evaluate the equation using the standard order of operations (BODMAS/PEMDAS):
- Brackets / Parentheses
- Orders / Exponents
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Evaluating the Original Equation
First, let's check the value of the equation as it is given:
$$67 - 84 \div 12 \times 5 + 31$$
- Division: $84 \div 12 = 7$
- Multiplication: $7 \times 5 = 35$
- Subtraction: $67 - 35 = 32$
- Addition: $32 + 31 = 63$
The original equation evaluates to 63, not 71. So, we need to interchange signs.
Testing the Interchange of '+' and '-'
The correct answer suggests interchanging the addition (+) and subtraction (-) signs. Let's apply this change to the equation:
Original Equation: $67 - 84 \div 12 \times 5 + 31 = 71$
After swapping '-' and '+': $67 + 84 \div 12 \times 5 - 31 = 71$
Now, let's evaluate this new equation using BODMAS/PEMDAS:
- Division: $84 \div 12 = 7$
- Multiplication: $7 \times 5 = 35$
- Addition: $67 + 35 = 102$
- Subtraction: $102 - 31 = 71$
The equation now correctly evaluates to 71.
Conclusion
By interchanging the addition (+) sign and the subtraction (-) sign, the equation $67 - 84 \div 12 \times 5 + 31 = 71$ becomes correct. Therefore, the signs '+' and '-' should be interchanged.
Similar Questions
What will come in place of the question mark (?) in the following equation if '+' means 'x', 'x' means '-', '-' means '$\div$' and '$\div$' means '+'?
$18 \div 4 + 3 \times 2 - 2 = ?$Which two numbers (not individual digits) should be interchanged to make the given equation correct?
$56+ (11 \times 2) - (52 \div 4) + 16 = 76$What will come in the place of '?' in the following equation, if '+' and '-' are interchanged and also 'x' and '$\div$' are interchanged?
$13 \div 8-96 \times 6+17=?$Which two numbers (not digits of the numbers), from amongst the given options, should be interchanged to make the given equation correct?
$12 \times 9 + 27 \div 3 - 5 = 60$
- Which two signs should be interchanged to make the given equation correct?
$99 \div 33 - 6 + 48 \times 26 = 40$ If ‘A’ stands for ‘÷’, ‘B’ stands for ‘×’, ‘C’ stands for ‘+’ and ‘D’ stands for ‘−’, what will come in place of the question mark (?) in the following equation?
36 B 17 D 59 C 224 A 7 = ?What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘–’ are interchanged and ‘×’ and ‘÷’ are interchanged?
16 ÷ 6 + 12 × 3 – 6 = ?Which two signs should be interchanged to make the given equation correct?
$36+8 \times 184-23\div10 = 90$Which two signs should be interchanged to make the given equation correct?
$152 + 8 \times 16 \div 9 - 4 = 309$
What will come in the place of the question mark (?) in the following equation, if '+' and '-' are interchanged and 'x' and '÷' are interchanged?
(28 ÷ 4) - (15 x 3) + 48 = ?
Important Questions from Bodmas Rule
If 2945 ÷ 19 – 11 × 5 = 29 + a, find the value of a.
DIRECTIONS: What should come in place of the question mark (?) in the following question?
3800 - 22 × 1968 ÷ 48 = ? × 7
Solve: {7.88 × 2 + 2.4 × 5 - 242.4 ÷ 4 + [9.2 × 4 - 2.46 of 3 + (36.3 ÷ 3 - 1.42 × 2)]}
What will come in the place of question mark (?) in the given expression?
(420 ÷ 12 × 35 + 452- 152) = ?2
Evaluate: (13 × 8 - √81 × 6 + 1 ) ÷ (√49 + 72 - 18 × 2 + 19)
