Understanding the Order of Operations: Solved Example with 20×3 5
In mathematics, the order of operations is a set of rules that dictate the sequence in which operations in an expression should be performed. Two commonly used acronyms to remember these rules are PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) and BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). These rules are crucial to ensure that everyone arrives at the same answer when solving mathematical expressions. Let's explore how these rules apply to the expression 20×3 5.
Solving the Expression with PEMDAS
Multiplication: PEMDAS stipulates that multiplication should be performed before addition. In the expression 20×3 5, we first perform the multiplication:20×3 60
So the expression becomes:
60 5
Addition: Since there are no other operations to perform, we proceed with the addition:
60 5 65
Thus, the answer to the expression 20×3 5 is 65 according to the PEMDAS rule.
Exploring BODMAS
Brackets/Orders: BODMAS starts with brackets, and then follows orders, which essentially means exponents. In the expression 20×3 5, there are no brackets or exponents, so we proceed to multiplication:20×3 60
So the expression becomes:
60 5
Division and Multiplication: In the absence of brackets or exponents, the next step is multiplication, which we have already performed, and addition, which we proceed with:
60 5 65
Hence, the answer using the BODMAS rule is also 65.
Common Misunderstandings
Misinterpretation of Variables and Coefficients: The expression 3x520 can be confusing because it suggests finding the value of x, which is not the case here. The original expression 20×3 5 does not contain an unknown variable, but only a multiplication and an addition. Thus, the solution is simply the application of the order of operations.Step-by-Step Solution
Let's break down the expression 3×52 20 step by step:
Multiplication: First, we perform the multiplication 3×5:3×5 15First Addition: Next, we add 2 to the result of the multiplication:
15 2 17Final Addition: Finally, we add 20 to the result of the first addition:
17 20 37
Therefore, the answer to the expression 3×52 20 is 37.
Conclusion
The order of operations is a fundamental concept in mathematics that ensures consistency in solving expressions. By following either PEMDAS or BODMAS, we can ensure we arrive at the correct answer. This article provided a clear explanation of how to solve the expression 20×3 5, emphasizing the importance of adhering to the correct order of operations.