Subtraction of Real Numbers

Subtracting real numbers involves adding the additive inverse of the second number to the first. It requires changing the sign of the number being subtracted and then performing the arithmetic operation.

Real numbers include: Integers: Whole numbers, both positive and negative, including zero.

Rational numbers: Numbers that can be expressed as a fraction of two integers.

Irrational numbers: Numbers that cannot be expressed as a simple fraction, such as √2 and π.

When subtracting real numbers, students should follow these rules:

Flip sign: Change the sign of the number being subtracted and perform addition.

Combine like terms: In the context of real numbers, simply perform the arithmetic operation.

Simplifying result: Perform the arithmetic operation to obtain the final result.

The following are methods for subtracting real numbers:

Method 1: Direct Method

To apply the direct method for subtraction of real numbers, use these steps:

Step 1: Write the numbers with a minus sign in between.

Step 2: Change the sign of the second number.

Step 3: Perform the arithmetic operation.

Example: Subtract 5 from 12.

Step 1: 12 - 5

Step 2: Change sign: 12 + (-5)

Step 3: Result: 7

Method 2: Number Line Method

Subtracting real numbers using the number line method involves visualizing the operation on a number line. This method is useful for understanding the concept of subtraction as finding the distance between numbers.

Example: Subtract 4 from -3.

Solution: Start at -3 on the number line, move 4 units to the left.

The result is -7.

In real numbers, subtraction has specific properties:

• Subtraction is not commutative In subtraction, changing the order of the numbers changes the result, i.e., A - B ≠ B - A.

• Subtraction is not associative Unlike addition, we cannot regroup in subtraction. When three or more numbers are involved, changing the grouping changes the result. (A − B) − C ≠ A − (B − C)

• Subtraction is the addition of the opposite sign Subtracting a number is the same as adding its opposite, so to make calculations easier, you can convert subtraction into addition by changing the sign of the second number. A − B = A + (−B)

• Subtracting zero from a number leaves the number as is Subtracting zero from any number results in the same number: A - 0 = A.

Tips and tricks are useful for students to efficiently deal with the subtraction of real numbers. Some helpful tips are listed below:

Tip 1: Always pay attention to signs before performing subtraction.

Tip 2: Use the number line method to visualize subtraction, especially with negative numbers.

Tip 3: For complex subtractions, break them down into simpler steps.

Subtraction of real numbers can be challenging, leading to common mistakes. Being aware of these errors can help students avoid them.