What will come in place of the question mark (?) in the following equation if '+' means 'x', 'x' means '-', '-' means '$\div$' and '$\div$' means '+'?
$18 \div 4 + 3 \times 2 - 2 = ?$
Understanding the Operator Substitution
The problem presents an equation with standard mathematical symbols, but requires us to interpret these symbols differently based on a given set of rules. We need to substitute the original operators with new ones before solving the equation.
Operator Substitution Rules:
- '+' symbol should be treated as 'x' (multiplication).
- 'x' symbol should be treated as '-' (subtraction).
- '-' symbol should be treated as '$\div$' (division).
- '$\div$' symbol should be treated as '+' (addition).
Applying the Substitution:
The original equation is: $18 \div 4 + 3 \times 2 - 2 = ?$
Let's substitute each operator according to the rules:
- The $\div$ sign between 18 and 4 becomes a + sign.
- The + sign between 4 and 3 becomes a x sign.
- The x sign between 3 and 2 becomes a - sign.
- The - sign between 2 and 2 becomes a $\div$ sign.
After substitution, the new equation becomes:
$18 + 4 \times 3 - 2 \div 2 = ?$
Solving the Modified Equation
Now, we need to solve the transformed equation $18 + 4 \times 3 - 2 \div 2$ using the standard order of operations (often remembered by the acronym BODMAS or PEMDAS).
BODMAS stands for:
- Brackets
- Orders (powers and square roots)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Step-by-Step Calculation:
- Division: First, perform the division operation: $2 \div 2 = 1$ The equation now looks like: $18 + 4 \times 3 - 1$
- Multiplication: Next, perform the multiplication operation: $4 \times 3 = 12$ The equation becomes: $18 + 12 - 1$
- Addition: Perform the addition operation: $18 + 12 = 30$ The equation simplifies to: $30 - 1$
- Subtraction: Finally, perform the subtraction operation: $30 - 1 = 29$
Therefore, the value that comes in place of the question mark (?) is 29.
Similar Questions
- Which two signs should be interchanged to make the given equation correct? $67 - 84 \div 12 \times 5 + 31 = 71$
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)
