Order of Operations: A Step-By-Step Guide | PEMDAS | Math with Mr. J
Table of Contents
Introduction
This tutorial will guide you through the order of operations in mathematics, commonly known by the acronym PEMDAS. Understanding this concept is essential for solving mathematical expressions correctly. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This guide will provide you with step-by-step instructions and examples to clarify how to apply these rules effectively.
Step 1: Understand PEMDAS
To properly apply the order of operations, familiarize yourself with the components of PEMDAS:
- Parentheses: Solve expressions within parentheses first.
- Exponents: Evaluate powers and square roots next.
- Multiplication and Division: Work from left to right.
- Addition and Subtraction: Finally, perform additions and subtractions from left to right.
Practical Tip
: Always look for parentheses first, as they change the standard order of operations.Step 2: Example 1 - Simple Expression
Let's solve a basic expression:
Expression
: ( 3 + 5 \times 2 )- Identify operations
- Addition and Multiplication are present.
- Follow PEMDAS
- First, multiply: ( 5 \times 2 = 10 )
- Then, add: ( 3 + 10 = 13 )
Result
: The answer is 13.Step 3: Example 2 - Including Parentheses
Consider this expression:
Expression
: ( (2 + 3) \times 4 )- Identify operations
- Addition inside parentheses and multiplication.
- Follow PEMDAS
- First, solve the parentheses: ( 2 + 3 = 5 )
- Then, multiply: ( 5 \times 4 = 20 )
Result
: The answer is 20.Step 4: Example 3 - Adding Exponents
Now, let's try an expression with an exponent:
Expression
: ( 2^3 + 4 )- Identify operations
- Exponent and addition.
- Follow PEMDAS
- First, evaluate the exponent: ( 2^3 = 8 )
- Then, add: ( 8 + 4 = 12 )
Result
: The answer is 12.Step 5: Example 4 - Complex Expression
Finally, solve a more complex expression:
Expression
: ( (3 + 5) \times 2^2 - 4 \div 2 )- Identify operations
- Parentheses, exponent, multiplication, division, and subtraction.
- Follow PEMDAS
- Solve the parentheses: ( 3 + 5 = 8 )
- Evaluate the exponent: ( 2^2 = 4 )
- Multiply: ( 8 \times 4 = 32 )
- Divide: ( 4 \div 2 = 2 )
- Finally, subtract: ( 32 - 2 = 30 )
Result
: The answer is 30.Conclusion
Understanding and applying the order of operations is crucial for solving mathematical expressions accurately. Remember the PEMDAS acronym to guide your calculations. Start with parentheses, then move to exponents, followed by multiplication and division, and finish with addition and subtraction. Practice with various examples to enhance your skills, and don't hesitate to revisit this guide for clarification. Happy calculating!