What will come in place of question mark (?) in the following equation? 12 – [3 – {6 – (15 – 7)}] = ?
7
Solving the Nested Brackets Equation
This question asks us to find the value represented by the question mark (?) in the given mathematical equation involving nested brackets. To solve this accurately, we must follow the standard order of operations, often remembered by the acronym BODMAS or PEMDAS.
BODMAS stands for:
- Brackets (or Parentheses)
- Orders (or Exponents/Indices)
- Division
- Multiplication
- Addition
- Subtraction
We will solve the equation step-by-step, starting from the innermost brackets.
The equation is: 12 – [3 – {6 – (15 – 7)}] = ?
-
Innermost Bracket: First, calculate the expression inside the innermost parentheses: $(15 - 7)$.
Calculation: $15 - 7 = 8$
The equation becomes:
12 – [3 – {6 – 8}] = ? -
Next Level Bracket: Next, solve the expression within the curly braces: $\{6 - 8\}$.
Calculation: $6 - 8 = -2$
The equation now is:
12 – [3 – (-2)] = ? -
Outer Bracket: Now, calculate the expression inside the square brackets: $[3 - (-2)]$. Remember that subtracting a negative number is the same as adding the positive number.
Calculation: $3 - (-2) = 3 + 2 = 5$
The equation simplifies to:
12 – 5 = ? -
Final Calculation: Perform the final subtraction.
Calculation: $12 - 5 = 7$
Final Result
Therefore, the value that comes in place of the question mark (?) is 7.
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Important Questions from Simplification
Simplify
6 × {28 ÷ 84 × {36 × 49 ÷ (6 × 7)}}.
Simplify.
- A bag contains ₹5, 2 and 1 coins in the ratio of 3 : 4 : 5. The total value of all the coins is ₹2,100. How many coins of ₹5 are there in the bag?
- \(\frac{6}{2}\times\frac{10}{2}\div\frac{6}{2}\times6^2+5\times4=?\)
- Find the value of 2.\(\overline {36} \) + 3.\(\overline {21} \) - 1.\(\overline {05} \)
