What should come in place of the question mark (?) in the following question? [((16 ÷ 4) × 4) ÷ 4] = ?
4
Understanding the Mathematical Problem
The question asks us to find the value of the expression given by [((16 \div 4) \times 4) \div 4]. This is a mathematical expression involving division and multiplication, with multiple levels of brackets. To solve this correctly, we need to follow the standard order of operations.
Applying the Order of Operations (BODMAS/PEMDAS)
When solving mathematical expressions with multiple operations, we must follow a specific order. A common mnemonic for this order is BODMAS or PEMDAS.
- B/P: Brackets or Parentheses first. Solve the operations inside the brackets, starting with the innermost ones.
- O/E: Orders or Exponents (powers, square roots, etc.) next.
- DM: Division and Multiplication. These are done from left to right.
- AS: Addition and Subtraction. These are done from left to right.
In this problem, we only have brackets, division, and multiplication. We will start with the operations inside the brackets.
Step-by-Step Calculation to Find the Value
Let's break down the given expression [((16 \div 4) \times 4) \div 4] step by step, following the BODMAS/PEMDAS rules.
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Solve the innermost bracket: The innermost operation is 16 \div 4.
16 \div 4 = 4
Now the expression inside the square brackets becomes [(4 \times 4) \div 4].
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Solve the next bracket: The operation within the remaining brackets is 4 \times 4.
4 \times 4 = 16
The expression simplifies to [16 \div 4].
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Perform the final operation: The remaining operation is 16 \div 4.
16 \div 4 = 4
So, the value of the expression [((16 \div 4) \times 4) \div 4] is 4.
Final Result
Based on the step-by-step calculation following the order of operations, the value that should come in place of the question mark is 4.
Revision Table: Key Concepts
| Concept | Description |
|---|---|
| Order of Operations | Rules governing the sequence of operations in a mathematical expression (e.g., BODMAS/PEMDAS). |
| Brackets | Operations inside brackets are performed first, from innermost to outermost. |
| Division (÷) | One of the four basic arithmetic operations, the inverse of multiplication. |
| Multiplication (×) | One of the four basic arithmetic operations, repeated addition. |
Additional Information: Related Mathematical Concepts
Understanding the order of operations is fundamental in mathematics to ensure consistent and correct results. Expressions with multiple levels of brackets are common and always require starting from the innermost set. The given expression is a good example of how applying the rules step-by-step leads to the unique correct answer. This process helps simplify complex-looking problems into manageable parts. Proficiency in basic arithmetic operations (addition, subtraction, multiplication, division) is essential for solving such problems accurately.
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