Integer Addition And Subtraction

Mathematics is a language; like any language, it has its own rules and syntax that must be understood to effectively communicate and solve problems.

Integer addition and subtraction are fundamental operations in mathematics, forming the basis for more complex concepts like algebra and calculus.

In this blog post, we will delve into the world of integer addition and subtraction, exploring their properties, rules, and practical applications.

Understanding Integers

Before we dive into addition and subtraction, let’s first understand what integers are.

Integers are whole numbers, both positive and negative, including zero.

They are represented on the number line, with positive integers to the right of zero and negative integers to the left. For example, -3, -2, -1, 0, 1, 2, 3 are all integers.

Addition of Integers

Adding integers involves combining numbers to find their sum.

The rules for adding integers are:

1. Same Signs

When adding two integers with the same sign (both positive or both negative), add their absolute values and keep the common sign.

Example: (-3) + (-5) = -(3 + 5) = -8

2. Different Signs

When adding two integers with different signs, subtract the smaller absolute value from the larger absolute value and use the sign of the integer with the larger absolute value.

Example: (-8) + 5 = 5 – 8 = -3

3. Additive Identity

The sum of any integer and zero is the integer itself.

Example: 6 + 0 = 6

Subtraction of Integers

Subtracting integers involves finding the difference between two numbers. The rules for subtracting integers are similar to addition:

1. Subtraction as Addition

To subtract an integer, add its additive inverse (the opposite of the integer).

Example: 8 – (-3) = 8 + 3 = 11

2. Adding the Opposite

To subtract integers with the same sign, change the subtraction sign to addition and change the sign of the integer being subtracted, then follow the rules for addition.

Example: 6 – 3 = 6 + (-3) = 3

Practical Applications

Understanding integer addition and subtraction is essential in various real-world scenarios, such as:

• Accounting: Balancing debits and credits in accounting involves adding and subtracting integers.
• Temperature: Weather forecasts often involve adding and subtracting temperatures to determine changes.
• Finance: Calculating profits and losses in finance requires integer operations.

Tips for Mastery

• Practice: Regular practice with integer addition and subtraction problems will improve your skills.
• Visualize: Use a number line or draw diagrams to visualize integer operations.
• Understand the Concept: Instead of memorizing rules, understand why they work.

Solved Examples

Let’s work through a few examples of integer addition and subtraction to illustrate the concepts discussed.

Example 1: Addition of Integers

Problem: Find the sum of (-6) + (-9).

Solution

1. Same Signs: Since both integers have the same sign (negative), we add their absolute values and keep the negative sign.

(-6) + (-9) = -(6 + 9) = -15

Answer: (-6) + (-9) = -15

Example 2: Subtraction of Integers

Problem: Evaluate 5 – (-3).

Solution

1. Subtraction as Addition: Subtraction is equivalent to adding the additive inverse of the second integer.

5 – (-3) = 5 + 3 = 8

Answer: 5 – (-3) = 8

Example 3: Subtraction with Different Signs

Problem: Calculate (-7) – 4.

Solution

1. Adding the Opposite: Change the subtraction to addition and change the sign of the second integer.

(-7) – 4 = (-7) + (-4) = -(7 + 4) = -11

Answer: (-7) – 4 = -11

Example 4: Combining Addition and Subtraction

Problem: Determine the value of (-5) + 8 – (-2).

Solution

1. Substitution: Substitute subtraction with the addition of the opposite.

(-5) + 8 + 2

2. Combine Like Terms: Add the integers together.

(-5) + 8 + 2 = (-5) + 10 = 5

Answer: (-5) + 8 – (-2) = 5

Integer Addition And Subtraction 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)