What is the result for this expression?
4 + 8 * 3 / 4 + 5 % 2
The Correct Answer and Explanation is :
The correct answer is: 11
To evaluate the expression (4 + 8 \times 3 \div 4 + 5 \mod 2), we must follow the order of operations, commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Step-by-Step Calculation
- Identify and Perform Multiplication and Division:
- The first operation we encounter is multiplication: (8 \times 3 = 24).
- The expression now reads: (4 + 24 \div 4 + 5 \mod 2).
- Continue with Division:
- Next, we perform the division: (24 \div 4 = 6).
- The expression simplifies to: (4 + 6 + 5 \mod 2).
- Evaluate the Modulus Operation:
- Now, we compute (5 \mod 2). The modulus operation finds the remainder when 5 is divided by 2. Since (5) divided by (2) gives a quotient of (2) and a remainder of (1), we have (5 \mod 2 = 1).
- The expression now reads: (4 + 6 + 1).
- Perform Addition:
- Finally, we add the numbers together: (4 + 6 = 10) and then (10 + 1 = 11).
Final Result
Therefore, the result of the expression (4 + 8 \times 3 \div 4 + 5 \mod 2) is 11.
Explanation
Understanding the order of operations is crucial for accurately solving mathematical expressions. When multiple operations are involved, failure to adhere to PEMDAS can lead to incorrect results. By breaking down each part of the expression and performing operations in the correct sequence, we can ensure that our calculations are valid. This systematic approach applies not only in mathematics but also in programming and algorithm design, where operations must be prioritized to avoid logical errors.
This expression also illustrates the utility of different mathematical operations, including multiplication, division, and modulus, each serving distinct purposes. While multiplication and division typically alter the magnitude of numbers significantly, the modulus operation offers insights into divisibility and can be particularly useful in computer science and cryptography. Thus, comprehending these fundamentals fosters a more profound appreciation for mathematical reasoning.