Lesson 90: PEMDAS with Negative Numbers

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• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

This lesson expands on the order of operations by including negative numbers. Students will learn how negative values affect arithmetic operations and how to apply PEMDAS correctly in these cases.

Learning Objectives

• Apply PEMDAS rules to solve problems containing negative numbers.
• Understand how multiplication and division affect the sign of the result.
• Identify common mistakes when combining negative numbers with parentheses and exponents.

Topics Covered

• Negative numbers in addition and subtraction
• Negative numbers in multiplication and division
• Order of operations with parentheses and exponents

Key Terms

• Negative Number: A number less than zero, written with a minus sign (−).
• Sign Rules: Guidelines for determining the result of adding, subtracting, multiplying, or dividing negative numbers.
• PEMDAS: The order of operations—Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

Lesson Examples

Example 1: Negative Number Addition

1. Problem: -5 + 8
2. Step 1: Combine the numbers considering their signs: 8 − 5
3. Step 2: Result = 3

Example 2: Multiplication with Negative Numbers

1. Problem: -4 × 6
2. Step 1: Multiply absolute values: 4 × 6 = 24
3. Step 2: Apply sign rule (negative × positive = negative)
4. Step 3: Result = -24

Example 3: Combined PEMDAS with Negatives

1. Problem: -3 + 2 × (-5)
2. Step 1: Multiply first: 2 × (-5) = -10
3. Step 2: Add: -3 + (-10) = -13
4. Step 3: Result = -13

Practice Problems

1. -7 + 12
2. 5 - (-3)
3. -4 × 3 + 6
4. (-2 + 5) × (-3)

Tips & Common Mistakes

• Remember that subtracting a negative is the same as adding a positive.
• Multiplying or dividing two negative numbers results in a positive number.
• Always follow the order of operations even when negative numbers are involved.

Summary

PEMDAS rules are essential for correctly solving problems with negative numbers. Carefully apply parentheses, exponents, multiplication/division, and addition/subtraction while considering the sign of each number.

Challenge Problems

1. -6 + (-4) × 3
2. (-5 + 2)² - 6
3. 18 ÷ (-3) + (-7)