Integer Addition and Subtraction

Welcome to the exciting world of integer addition and subtraction! As you delve into the realm of numbers, you’ll discover that integers are not just limited to positive whole numbers; they encompass negative numbers as well.

Understanding how to add and subtract integers is a fundamental skill that opens doors to a wide range of mathematical concepts and real-life applications.

Table of Contents:

• Integer Addition and Subtraction
• Properties of Integer Addition and Subtraction
• Solved Examples
• FAQs

Integer Addition and Subtraction

Adding Integers: Adding integers involves combining positive and negative numbers to find their sum. When adding integers, we consider the signs of the numbers involved. 

Here are some key rules to remember: If two numbers have the same sign (both positive or negative), add their absolute values and keep the common sign.

If the signs are different (one positive and one negative), subtract the smaller absolute value from the larger absolute value, and keep the sign of the number with the larger absolute value.

Subtracting Integers: Subtracting integers is similar to adding integers, but with a slight twist. We can think of subtraction as the addition of the opposite. 

Here’s what you need to keep in mind: To subtract an integer, change the sign of the number being subtracted and follow the rules of addition.

Subtracting a positive number is the same as adding a negative number.

Subtracting a negative number is the same as adding a positive number.

Using Number Lines and Models: Visualizing integers on a number line or using models can be helpful in understanding addition and subtraction. A number line allows you to move left (negative) or right (positive) to determine the result of an operation.

Models, such as counters or chips, can represent positive and negative values and aid in visualizing the addition and subtraction process.

Properties of Integer Addition and Subtraction

Closure Property: The closure property states that when you add or subtract two integers, the result is always an integer. In other words, the sum or difference of any two integers will always be an integer.

Commutative Property: The commutative property of addition states that changing the order of the numbers being added does not change the result. For example, a + b = b + a. However, this property does not hold for subtraction. Subtraction is not commutative, meaning that changing the order of the numbers being subtracted will result in a different answer.

Associative Property: The associative property of addition states that the grouping of numbers being added does not affect the result. In other words, (a + b) + c = a + (b + c). Similarly, the associative property of subtraction states that the grouping of numbers being subtracted does not affect the result.

Identity Property: The identity property of addition states that adding zero to any integer does not change its value. For example, a + 0 = a. Similarly, the identity property of subtraction states that subtracting zero from any integer does not change its value. For example, a – 0 = a.

Inverse Property: The inverse property of addition states that for every integer a, there exists an additive inverse (-a) such that a + (-a) = 0. In other words, adding an integer to its additive inverse results in zero. Similarly, the inverse property of subtraction states that for every integer a, there exists a subtractive inverse (-a) such that a – (-a) = 0.

Zero Property: The zero property of addition states that if you add zero to any integer, the sum will be the same integer. For example, a + 0 = a. However, the zero property does not hold for subtraction. Subtracting zero from an integer will not change its value.

Solved Examples

Addition Example:
Problem: Calculate the sum of -8 and 5.
Solution: To add -8 and 5, we simply combine the two numbers. (-8) + 5 = -3. Therefore, the sum of -8 and 5 is -3.

Subtraction Example:
Problem: Find the difference between -12 and 7.
Solution: To subtract 7 from -12, we subtract the two numbers. (-12) – 7 = -19. Therefore, the difference between -12 and 7 is -19.

Combination of Addition and Subtraction Example:
Problem: Perform the following calculation: (-5) + 3 – (-7).
Solution: To solve this, we follow the order of operations, which is parentheses first, then addition and subtraction from left to right. (-5) + 3 – (-7) can be rewritten as (-5) + 3 + 7. Now, we can perform the addition: (-5) + 3 + 7 = 5. Therefore, the result of (-5) + 3 – (-7) is 5.
Real-Life Application Example:
Problem: Jane withdraws $40 from her bank account, which has a balance of $120. What is her new account balance?
Solution: To find Jane’s new account balance, we need to subtract the amount she withdrew from her current balance. $120 – $40 = $80. Therefore, her new account balance is $80.

Real-Life Application Example:
Problem: A weather forecast predicts a temperature increase of 6 degrees Celsius. If the current temperature is -2 degrees Celsius, what will be the new temperature?
Solution: To find the new temperature, we need to add the temperature increase to the current temperature. (-2) + 6 = 4. Therefore, the new temperature will be 4 degrees Celsius.

FAQs

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