Solving 134 + 5 - 14 X 91 Order Of Operations Explained
In the realm of mathematics, order of operations reigns supreme. To solve complex equations accurately, understanding and applying the correct sequence of steps is paramount. In this article, we will delve into the step-by-step solution of the equation 134 + 5 - 14 x 91, unraveling the intricacies of mathematical operations and arriving at the correct answer.
Understanding the Order of Operations: PEMDAS/BODMAS
Before we embark on solving the equation, it is crucial to grasp the fundamental concept of the order of operations. Often remembered by the acronyms PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction), this principle dictates the sequence in which mathematical operations must be performed.
- Parentheses/Brackets: Operations enclosed within parentheses or brackets are always performed first.
- Exponents/Orders: Next, we tackle exponents or orders, such as squares and cubes.
- Multiplication and Division: Multiplication and division are performed from left to right.
- Addition and Subtraction: Finally, addition and subtraction are carried out from left to right.
By adhering to this order, we ensure that we arrive at the correct solution for any mathematical equation.
Step-by-Step Solution of 134 + 5 - 14 x 91
Now, let us apply our knowledge of the order of operations to solve the equation 134 + 5 - 14 x 91.
Step 1: Multiplication
According to PEMDAS/BODMAS, multiplication takes precedence over addition and subtraction. Therefore, we begin by multiplying 14 and 91:
14 x 91 = 1274
Our equation now becomes:
134 + 5 - 1274
Step 2: Addition
Next, we perform the addition operation from left to right:
134 + 5 = 139
Our equation is now simplified to:
139 - 1274
Step 3: Subtraction
Finally, we perform the subtraction operation:
139 - 1274 = -1135
Therefore, the solution to the equation 134 + 5 - 14 x 91 is -1135.
Common Mistakes to Avoid
When solving mathematical equations, it is crucial to be mindful of potential errors. One common mistake is neglecting the order of operations, leading to incorrect results. For instance, in our example, if we were to perform addition before multiplication, we would arrive at a different answer.
Another common pitfall is misinterpreting negative signs. When subtracting a larger number from a smaller number, the result will be negative. It is essential to pay close attention to the signs and ensure they are applied correctly.
Importance of Order of Operations in Mathematics
The order of operations is not merely an arbitrary rule; it is a fundamental principle that ensures consistency and accuracy in mathematical calculations. Without a standardized order, the same equation could yield multiple different answers, leading to confusion and errors.
In various fields, from scientific research to engineering design, accurate mathematical calculations are paramount. Adhering to the order of operations is crucial for obtaining reliable results and making informed decisions.
Real-World Applications of Order of Operations
The principles of order of operations extend beyond the realm of theoretical mathematics and find practical applications in numerous real-world scenarios. Let us explore a few examples:
1. Financial Calculations
In finance, calculations involving interest rates, investments, and loans often require a precise understanding of the order of operations. For instance, calculating compound interest involves raising a number to a power, which must be performed before other operations.
2. Computer Programming
In computer programming, the order of operations is essential for writing accurate code. Programming languages adhere to specific rules regarding operator precedence, ensuring that calculations are performed in the intended sequence.
3. Scientific Experiments
In scientific experiments, data analysis often involves complex calculations. Following the order of operations is crucial for obtaining reliable results and drawing valid conclusions.
4. Everyday Life
Even in everyday situations, we implicitly apply the order of operations. For example, when calculating the total cost of a shopping trip, we multiply the quantity of each item by its price before adding up the individual costs.
Practice Problems
To solidify your understanding of the order of operations, let us tackle a few practice problems:
- 25 + 10 x 3 - 15
- (12 - 4) x 6 ÷ 2
- 18 ÷ (3 + 6) + 7
Try solving these problems on your own, keeping in mind the PEMDAS/BODMAS rule. The solutions are provided at the end of this article.
Conclusion
The equation 134 + 5 - 14 x 91 serves as a compelling illustration of the importance of the order of operations in mathematics. By adhering to the PEMDAS/BODMAS principle, we can systematically solve complex equations and arrive at accurate results. The solution to this particular equation is -1135.
Understanding and applying the order of operations is not merely an academic exercise; it is a fundamental skill that empowers us to navigate various real-world scenarios, from financial calculations to scientific experiments. By mastering this principle, we unlock the door to accurate mathematical reasoning and problem-solving.
Solutions to Practice Problems:
- 25 + 10 x 3 - 15 = 25 + 30 - 15 = 40
- (12 - 4) x 6 ÷ 2 = 8 x 6 ÷ 2 = 24
- 18 ÷ (3 + 6) + 7 = 18 ÷ 9 + 7 = 9
