Order of Operations with Negative Numbers

Understanding the order of operations is a crucial skill in mathematics that helps us solve complex equations and ensure consistent and accurate results.

As Grade 7 students progress in their mathematical journey, they encounter a new challenge: incorporating negative numbers into these calculations.

Table of Contents:

• Order of Operations with Negative Numbers
• Formula
• Real-life Applications
• FAQs

Order of Operations with Negative Numbers

The order of operations is a set of rules that guides us in solving mathematical expressions. It ensures consistency and accuracy in our calculations. Grade 7 students must grasp the concept of performing operations in a specific sequence: parentheses, exponents, multiplication and division (from left to right), and finally, addition and subtraction (from left to right).

Embracing the Negative Numbers: Negative numbers may seem intimidating, but they are an essential part of mathematics. They represent values less than zero and play a crucial role in various real-life scenarios. Understanding how to work with negative numbers allows us to solve a wider range of mathematical problems.

Tackling Parentheses and Exponents: Parentheses and exponents are the building blocks of mathematical expressions. When encountering parentheses, we should simplify the expression within them first. Exponents, on the other hand, involve raising a number to a power. Understanding their order in the overall expression is key to solving equations correctly.

Mastering Multiplication and Division: In the order of operations, multiplication and division have equal priority and are performed from left to right. When negative numbers are involved, it’s important to remember the rules for multiplying and dividing them. Knowing how to handle negative signs in these operations will help you avoid common mistakes.

Navigating Addition and Subtraction: The final step in the order of operations is addition and subtraction, also performed from left to right. With negative numbers, it’s essential to pay attention to signs and apply the appropriate rules. Adding or subtracting negative numbers can sometimes lead to unexpected results, so a solid understanding of these operations is crucial.

Formulas

The order of operations, often remembered by the acronym PEMDAS, stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It represents the sequence in which mathematical operations should be performed within an expression.

Adding and Subtracting Negative Numbers:

To add or subtract negative numbers, we can use the following formulas:

• Adding a negative number: a + (-b) = a – b
• Subtracting a negative number: a – (-b) = a + b
  

Multiplying and Dividing Negative Numbers:

When multiplying or dividing negative numbers, the following formulas apply:

• Multiplying two negative numbers: (-a) * (-b) = ab
• Multiplying a negative and a positive number: (-a) * b = -ab
• Dividing a negative number by a positive number: (-a) / b = -(a/b)
• Dividing a positive number by a negative number: a / (-b) = -(a/b)
  

Power of a Negative Number:

Raising a negative number to an even power results in a positive value, while raising it to an odd power yields a negative value.

The formula is as follows:

• Negative number raised to an even power: (-a)^n = a^n
• Negative number raised to an odd power: (-a)^n = -a^n

Real-life Applications

1. Finances and Banking: Managing money often involves dealing with both positive and negative values. Whether it’s calculating account balances, tracking expenses, or understanding debt and loans, knowing how to apply the order of operations with negative numbers ensures accurate financial calculations.

2. Temperature Changes: Negative numbers frequently appear when measuring temperature changes. For instance, when you see a weather forecast indicating a temperature drop of -5 degrees Celsius, understanding the order of operations allows you to determine the actual temperature after the decrease.

3. Elevations and Altitudes: In geography, negative numbers are commonly used to represent elevations and altitudes below sea level. Whether you’re studying the depth of a lake, the height of a mountain, or the altitude of an airplane, applying the order of operations helps accurately interpret and compare these values.

4. Temperature Scales: Different temperature scales, such as Celsius and Fahrenheit, often involve negative values. Converting between these scales requires correctly applying the order of operations to ensure accurate and meaningful temperature readings.

5. Physics and Mathematics: Concepts in physics and advanced mathematics frequently involve negative numbers. From analyzing vectors and directions to solving equations in calculus, understanding the order of operations with negative numbers is essential for precise calculations and problem-solving.

FAQs

Grade 7 Science Worksheets

• Elements and Compounds
• Solar Energy
• Photosynthesis
• Electricity and Magnetism
• Law of conservation of energy
• Periodic table
• Properties of Matter
• Waves
• Energy Resources 
• Weather and Climate
• Immune, Circulatory and Digestive Systems
• Organs in Multi-cellular Organism
• Sedimentary, Igneous, and Metamorphic Rocks
• Structure of the Earth
• Law of Conservation of Mass
• Physical and Chemical Changes
• Scientific Method
• Human Digestive System
• Environmental Science
• Renewable and Non-renewable energy Resources
• Characteristics of Living Organisms
• Life Science
• Earth and Space Science
• Solar Eclipse
• Heat Technology
• Newton’s Laws of Motions
• Physical Science
• Tools, Measurement and SI Units
• Earth Atmosphere
• Interactions of Living things
• The Earth Ecosystem
• Organelles in Plant and Animal cells
• Layers of the Earth
• Cycles in Nature

Grade 7 Math Worksheets

• Fractions
• Linear equations word problems
• Statistics
• Properties of Parallel Line
• Finding slope from an equation
• Identifying Quadrilaterals
• Percent Change
• Properties of addition and multiplication
• Pythagorean Theorem
• Solving two step inequalities
• Symmetry
• Fractions to Decimals (New)
• Whole Number Exponents with Integer Bases (New)
• Adding and Subtracting Fractions (New)
• Integer Addition and Subtraction (New)
• Dividing Mixed Numbers (New)
• Basics of Coordinate Geometry (New)