Subtraction of Decimal Numbers

Subtracting decimal numbers involves aligning the numbers by their decimal points and subtracting each digit starting from the rightmost digit. It requires borrowing when the top digit is smaller than the bottom digit.

There are three components to consider:

Decimal point: The dot that separates the whole number from the fractional part.

Digits: Numerical values from 0–9 that represent the number.

Operators: For subtraction, the operator is the minus (-) symbol.

When subtracting decimal numbers, students should follow these rules:

Align decimal points: Always align the decimal points of the numbers before subtracting.

Borrowing: If a digit in the minuend is smaller than the corresponding digit in the subtrahend, borrow from the next left digit.

Simplifying result: After performing subtraction, remove any trailing zeros and write the final result.

The following are methods for subtracting decimal numbers:

Method 1: Horizontal Method

To apply the horizontal method for subtraction of decimal numbers, use these steps.

Step 1: Write both numbers in a horizontal line with a minus sign in between.

Step 2: Align the decimal points and perform the subtraction.

Step 3: Simplify the result by removing trailing zeros.

Let’s apply these steps to an example: Question: Subtract

Step 1: Write both numbers in the same line, Step 2: Align the decimal points and subtract. Step 3: Simplify the result. Answer:

Method 2: Column Method

When subtracting decimal numbers using the column method, write the numbers one below the other. Ensure the decimal points are aligned in each column. Then perform the subtraction by starting from the rightmost column.

For example, Subtract

Solution: Arrange the numbers vertically with aligned decimal points.

8.75 ← Minuend (from which we subtract) - 3.48 ← Subtrahend (what we subtract) ------- 5.27

Therefore, upon subtracting, we get 5.27.

In arithmetic, subtraction has several characteristic properties that are important to note:

• 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)

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

• Borrowing In decimal subtraction, borrowing is used when a digit in the minuend is smaller than the corresponding digit in the subtrahend.

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

Tip 1: Always pay attention to the decimal points before starting subtraction.

Tip 2: If two numbers have the same digits after the decimal point, consider simplifying before performing subtraction.

Tip 3: Beginners and visual learners can benefit from using the column method to ensure correct alignment of decimal points and avoid mistakes.

Subtraction with decimal numbers can be challenging due to alignment and borrowing, often leading to common mistakes. However, being aware of these errors can help students avoid them.