Mathematics can often appear complex, especially when various operations are grouped together in an equation. To aid in systematically solving such problems, mathematicians developed the PEMDAS rule. This rule outlines the order in which mathematical operations should be performed to get the correct result.
Definition of the PEMDAS Rule
The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. It is a mnemonic that helps individuals remember the order of operations in mathematics. It’s important to note that this order of operations is standardized across mathematics worldwide, ensuring everyone is calculating in a consistent way.
- Parentheses: This refers to terms within brackets. According to the PEMDAS rule, operations within parentheses should be performed first before any other operations.
- Exponents: After parentheses, any exponents (or powers) should be resolved.
- Multiplication and Division: The next operations to be carried out are multiplication and division. They are considered to have the same level of precedence and should be performed from left to right in the equation.
- Addition and Subtraction: Lastly, perform the addition and subtraction operations. Just like multiplication and division, these operations also have the same level of precedence and are carried out from left to right.
Examples of the PEMDAS Rule
Let’s consider a few examples to understand the application of the PEMDAS rule.
Consider the mathematical expression: 5 + (6 * 3)² – 4
First, following the PEMDAS rule, we perform the operation in the parentheses: 6 * 3 = 18. The expression becomes:
5 + (18)² – 4
Next, we deal with the exponent (²). So, 18² = 324. Now, our expression looks like this:
5 + 324 – 4
Finally, we perform the addition and subtraction from left to right:
329 – 4 = 325
Let’s take a slightly more complex expression: (3 + 2) * 6 – 2² + 4 / 2
First, we resolve the operation within the parentheses: 3 + 2 = 5. The expression now becomes:
5 * 6 – 2² + 4 / 2
Next, we perform the operation involving the exponent: 2² = 4. The expression becomes:
5 * 6 – 4 + 4 / 2
Then, we perform the multiplication and division from left to right: 5 * 6 = 30 and 4 / 2 = 2. Our expression is now:
30 – 4 + 2
Lastly, we perform the subtraction and addition from left to right:
30 – 4 = 26; 26 + 2 = 28
So, the result of the expression (3 + 2) * 6 – 2² + 4 / 2 is 28.
Understanding the PEMDAS rule is fundamental to carrying out mathematical operations correctly. This rule provides a systematic approach that ensures consistency in mathematical calculations, irrespective of their complexity. As you delve deeper into mathematics, these foundational principles like the PEMDAS rule become increasingly significant. So, remember, Parentheses first, then Exponents, followed by Multiplication and Division, and lastly, Addition and Subtraction.