Solving the Example Problem

Oct 13, 2025 by recoveryshake.com 135 views

Introduction

The order of operations is a fundamental concept in mathematics that helps students solve complex expressions by following a specific sequence of steps. In Grade 4, students are introduced to the order of operations, which is essential for solving mathematical problems involving multiple operations. In this article, we will delve into the world of order of operations, focusing on the Grade 4 level, and provide a comprehensive guide to help students master this crucial concept.

What is the Order of Operations?

The order of operations is a set of rules that dictates the order in which mathematical operations should be performed when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Solving the Example Problem

Let's solve the example problem given at the beginning of this article:

42 \div 6 + 9 \times (5 - 2) =

To solve this problem, we need to follow the order of operations:

Evaluate the expression inside the parentheses: $5 - 2 = 3$
Multiply 9 by the result: $9 \times 3 = 27$
Divide 42 by 6: $42 \div 6 = 7$
Add the results of the multiplication and division: $7 + 27 = 34$

Therefore, the final answer is:

42 \div 6 + 9 \times (5 - 2) = 34

Step-by-Step Guide to Solving Order of Operations Problems

Here's a step-by-step guide to help students solve order of operations problems:

Identify the operations: Look for parentheses, exponents, multiplication, division, addition, and subtraction operations in the expression.
Evaluate expressions inside parentheses: Follow the order of operations and evaluate any expressions inside parentheses first.
Evaluate exponents: Evaluate any exponential expressions next.
Evaluate multiplication and division: Evaluate multiplication and division operations from left to right.
Evaluate addition and subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Check your work: Once you have finished solving the problem, check your work to ensure that you have followed the order of operations correctly.

Practice Problems

Here are some practice problems to help students master the order of operations:

$24 \div 4 + 3 \times (6 - 2) =$
$9 \times 2 + 12 \div (3 + 1) =$
$15 \div 3 + 2 \times (8 - 4) =$
$6 \times 9 + 24 \div (4 + 2) =$
$12 \div 4 + 9 \times (3 - 1) =$

Conclusion

Mastering the order of operations is a crucial skill for students to develop in Grade 4. By following the steps outlined in this article, students can solve complex expressions with confidence. Remember to always follow the order of operations, and practice, practice, practice to become proficient in solving order of operations problems.

Additional Resources

For additional resources and practice problems, check out the following websites:

Khan Academy: Order of Operations
Mathway: Order of Operations
IXL: Order of Operations

Frequently Asked Questions

Q: What is the order of operations? A: The order of operations is a set of rules that dictates the order in which mathematical operations should be performed when there are multiple operations in an expression.

Q: What is PEMDAS? A: PEMDAS is an acronym that stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I solve order of operations problems? A: To solve order of operations problems, follow the steps outlined in this article: identify the operations, evaluate expressions inside parentheses, evaluate exponents, evaluate multiplication and division, evaluate addition and subtraction, and check your work.

Introduction

The order of operations is a fundamental concept in mathematics that helps students solve complex expressions by following a specific sequence of steps. In Grade 4, students are introduced to the order of operations, which is essential for solving mathematical problems involving multiple operations. In this article, we will answer some of the most frequently asked questions about the order of operations, providing a comprehensive guide to help students master this crucial concept.

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that dictates the order in which mathematical operations should be performed when there are multiple operations in an expression.

Q: What is PEMDAS?

A: PEMDAS is an acronym that stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. It is a helpful tool for remembering the order of operations.

Q: How do I solve order of operations problems?

A: To solve order of operations problems, follow the steps outlined below:

Identify the operations: Look for parentheses, exponents, multiplication, division, addition, and subtraction operations in the expression.
Evaluate expressions inside parentheses: Follow the order of operations and evaluate any expressions inside parentheses first.
Evaluate exponents: Evaluate any exponential expressions next.
Evaluate multiplication and division: Evaluate multiplication and division operations from left to right.
Evaluate addition and subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Check your work: Once you have finished solving the problem, check your work to ensure that you have followed the order of operations correctly.

Q: What are some common mistakes to avoid when solving order of operations problems?

A: Some common mistakes to avoid when solving order of operations problems include:

Forgetting to evaluate expressions inside parentheses
Not following the order of operations
Not checking your work
Getting confused between multiplication and division
Getting confused between addition and subtraction

Q: How can I practice order of operations problems?

A: There are many ways to practice order of operations problems, including:

Using online resources such as Khan Academy, Mathway, and IXL
Working with a tutor or teacher
Practicing with worksheets and puzzles
Solving real-world problems that involve the order of operations

Q: Why is the order of operations important?

A: The order of operations is important because it helps students solve complex expressions by following a specific sequence of steps. It is essential for solving mathematical problems involving multiple operations and is used in many real-world applications.

Q: Can I use a calculator to solve order of operations problems?

A: While calculators can be helpful for solving mathematical problems, it is still important to understand the order of operations and how to solve problems manually. This will help you to develop problem-solving skills and to understand the underlying math concepts.

Q: How can I apply the order of operations to real-world problems?

A: The order of operations can be applied to many real-world problems, including:

Solving financial problems, such as calculating interest rates and investments
Solving scientific problems, such as calculating the area and perimeter of shapes
Solving engineering problems, such as designing and building structures
Solving everyday problems, such as calculating the cost of groceries and the time it takes to complete a task

Conclusion

The order of operations is a fundamental concept in mathematics that helps students solve complex expressions by following a specific sequence of steps. By understanding the order of operations and how to apply it to real-world problems, students can develop problem-solving skills and become proficient in solving mathematical problems involving multiple operations. Remember to practice regularly and to seek help when needed.

Additional Resources

For additional resources and practice problems, check out the following websites:

Khan Academy: Order of Operations
Mathway: Order of Operations
IXL: Order of Operations

Frequently Asked Questions (FAQs)

Q: What is PEMDAS? A: PEMDAS is an acronym that stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I solve order of operations problems? A: To solve order of operations problems, follow the steps outlined in this article.

Q: What are some common mistakes to avoid when solving order of operations problems? A: Some common mistakes to avoid when solving order of operations problems include forgetting to evaluate expressions inside parentheses, not following the order of operations, and not checking your work.

Q: How can I practice order of operations problems? A: There are many ways to practice order of operations problems, including using online resources, working with a tutor or teacher, and practicing with worksheets and puzzles.

Q: Why is the order of operations important? A: The order of operations is important because it helps students solve complex expressions by following a specific sequence of steps.

Q: Can I use a calculator to solve order of operations problems? A: While calculators can be helpful for solving mathematical problems, it is still important to understand the order of operations and how to solve problems manually.

Q: How can I apply the order of operations to real-world problems? A: The order of operations can be applied to many real-world problems, including solving financial problems, solving scientific problems, and solving everyday problems.