Subtraction of Decimal Fractions

Subtracting decimal fractions involves aligning the decimal points of the numbers and subtracting as with whole numbers. Ensure that each digit in the columns is correctly aligned according to their place value.

Decimal numbers have two components:

Whole number part: The part of the number to the left of the decimal point.

Fractional part: The part of the number to the right of the decimal point.

When subtracting decimal fractions, students should follow these steps:

Align decimal points: Write the numbers so that their decimal points are vertically aligned.

Zero placeholders: Add zeros to the right of the decimal to ensure each number has the same number of decimal places.

Subtract as whole numbers: Subtract digits column by column as you would with whole numbers.

Simplifying result: The answer should have the decimal point aligned with the numbers you subtracted.

The following methods can be used for the subtraction of decimal fractions: Method 1: Horizontal Method To apply this method, use the following steps:

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

Step 2: Align the decimal points and add zeros if necessary.

Step 3: Subtract the numbers.

Example: Subtract 12.75 from 25.68.

Step 1: 25.68 - 12.75

Step 2: Align decimal points

Step 3: 25.68 - 12.75 = 12.93

Answer: 12.93

Method 2: Column Method

In the column method, write the numbers one below the other, making sure to align the decimal points. Add zeros if necessary to make the numbers have the same number of decimal places. Then subtract as you would with whole numbers.

For example, Subtract 3.456 from 7.89. Solution: Align the decimal points and add zeros for alignment. 7.890 - 3.456 ------- 4.434

Therefore, upon subtracting, we get 4.434.

In subtraction, decimal fractions have characteristic 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. Changing the grouping of numbers changes the result. (A - B) - C ≠ A - (B - C)

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

Here are some tips and tricks for efficiently dealing with the subtraction of decimal fractions:

Tip 1: Always ensure the decimal points are aligned before starting the subtraction.

Tip 2: Use zeros as placeholders to avoid confusion with different numbers of decimal places.

Tip 3: Start subtracting from the rightmost digit (the smallest place value) to avoid errors in calculation.

Subtraction of decimal fractions can be tricky, leading to common mistakes. Being aware of these errors can help students avoid them.