To tackle the expression “1 1 2 divided by 2,” let’s break it down step by step to ensure clarity and accuracy in our calculation.
First, we interpret the expression as (1 + 1 + 2) / 2, following the order of operations which dictates that we should perform addition before division.
- Addition: The first step is to add the numbers together: 1 + 1 + 2 = 4.
- Division: After obtaining the sum, we then divide this result by 2: 4 / 2 = 2.
Therefore, the simplified result of “1 1 2 divided by 2” is 2.
Understanding the Order of Operations
The order of operations is a fundamental concept in mathematics that helps us understand how to perform calculations in the correct order when faced with multiple operations. It is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
In the expression given, we first perform the addition because there are no parentheses, exponents, multiplication, or division operations that need to be addressed first. After adding the numbers, we then proceed to division, as per the order of operations.
Practical Applications
Understanding and applying the order of operations is crucial in various mathematical and real-world contexts. For instance, in algebra, chemistry, physics, and engineering, complex calculations are constantly performed. Knowing how to prioritize operations ensures that calculations are accurate and reliable.
Moreover, real-world applications such as financial calculations, architectural designs, and scientific research heavily rely on correct mathematical operations. A small mistake in the order of operations can lead to significant errors in outcomes, emphasizing the importance of adhering to mathematical principles.
Conclusion
In conclusion, simplifying expressions like “1 1 2 divided by 2” involves a straightforward application of the order of operations. By first adding the numbers together and then dividing by 2, we arrive at a clear and simple answer. This demonstrates how mathematical principles can be applied universally to solve problems, regardless of their complexity.
By grasping these fundamental concepts, we can tackle more complex expressions and problems with confidence, ensuring accuracy and precision in our calculations.
What is the order of operations in mathematics?
+The order of operations, remembered by the acronym PEMDAS, is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This rule dictates the order in which operations should be performed when there are multiple operations in an expression.
Why is understanding the order of operations important?
+Understanding the order of operations is crucial for performing mathematical calculations accurately. It ensures that operations are carried out in the correct order, preventing errors and mistakes in calculations, which is vital in various fields such as science, engineering, finance, and more.
