Subtraction of Integers Rules

Subtracting integers involves adding the additive inverse of the second integer to the first.

This means changing the sign of the integer being subtracted and then performing addition.

The process helps in understanding how positive and negative numbers interact.The rules for subtraction include: Changing the subtraction into addition by using the opposite sign. 

Using the number line for visual representation. Understanding the role of zero in subtraction as a neutral element.

When subtracting integers, students should follow these rules: -

Change the operation: Convert the subtraction problem into an addition problem by changing the sign of the second integer. 

Add the integers: Proceed with the addition of integers by using integer addition rules. 

Simplifying result: The final result is obtained after performing the addition operation.

The following are methods to subtract integers:

Method 1: Number Line Method

To use the number line for subtraction of integers, follow these steps:

Step 1: Locate the first integer on the number line.

Step 2: Move left for subtracting a positive integer or move right for subtracting a negative integer.

Example: Subtract 3 from 5.

Step 1: Locate 5.

Step 2: Move left 3 units to reach 2. Answer: 2

Method 2: Absolute Value Method

When subtracting integers using the absolute value method, consider the following: 

Find the absolute values of both integers. -

Subtract the smaller absolute value from the larger one. -

Assign the sign of the integer with the larger absolute value to the result.

Example: Subtract -4 from 2.

Solution: |2| = 2 and |-4| = 4 4 - 2 = 2, and since -4 has the larger absolute value, the result is -2.

Subtraction of integers has distinct properties: 

Subtraction is not commutative: Changing the order of integers changes the result, i.e., A - B ≠ B - A. 

Subtraction is not associative: Grouping does not apply, so (A − B) − C ≠ A − (B − C). 

Subtraction as addition of the opposite: Subtracting an integer is the same as adding its opposite, A − B = A + (−B). 

Subtracting zero: Subtracting zero from any integer results in the same integer: A - 0 = A.

Here are some tips and tricks for dealing with subtraction of integers:

Tip 1: Always change the subtraction into an addition problem for clarity.

Tip 2: Use a number line for visual learners to help understand movements and directions.

Tip 3: Practice with absolute values to strengthen understanding of integer magnitudes.

Subtraction of integers can be tricky, and students often make errors. Awareness of these mistakes can help avoid them.