Solved Exercises on Subtracting Decimals with Answers in Grade 4

Definitions of Key Concepts:

Decimal Subtraction: The process of finding the difference between two decimal numbers by subtracting digits in the same place value positions.

Decimal Point: The dot that separates the whole number part from the fractional part in a decimal number.

Place Value: The value of a digit based on its position in a number (ones, tenths, hundredths, etc.).

Minuend: The number from which another number is subtracted.

Subtrahend: The number that is subtracted from the minuend.

Difference: The result obtained when one number is subtracted from another.

Borrowing: The process of taking 1 from a higher place value when the digit in the minuend is smaller than the corresponding digit in the subtrahend.

Verification: The process of checking the correctness of an answer by using the inverse operation.

Core Rules and Laws:

• Decimal Alignment Rule: Decimal points must be aligned vertically before subtracting

• Place Value Rule: Only subtract digits in the same place value positions

• Borrowing Rule: When the top digit is smaller, borrow 1 from the next higher place value

• Zero Addition Rule: Adding zeros to the right of a decimal number does not change its value

• Direction Rule: Subtract from right to left, starting with the smallest place value

• Verification Rule: Difference + Subtrahend = Minuend

Step-by-Step Methods:

Method 1: Basic Decimal Subtraction (No Borrowing):

1. Write the numbers vertically with decimal points aligned
2. Subtract digits in each place value from right to left
3. Bring the decimal point straight down in the answer
4. Check your answer by adding the difference to the subtrahend

Method 2: Decimal Subtraction with Borrowing:

1. Align decimal points vertically
2. Starting from the rightmost digit, check if top digit is smaller than bottom digit
3. If so, borrow 1 from the next higher place value
4. Reduce the higher place value by 1 and add 10 to the current place value
5. Continue subtracting from right to left
6. Bring down the decimal point in the answer

Method 3: Verification Process:

1. Add the difference to the subtrahend
2. Check if the result equals the minuend
3. If yes, the answer is correct
4. If no, review the subtraction steps for errors

Examples (Simple → Advanced):

Simple: 4.5 - 2.3 = 2.2 (no borrowing needed)

Intermediate: 7.2 - 3.8 = 3.4 (borrowing needed)

Advanced: 15.75 - 8.29 = 7.46 (borrowing in multiple places)

Complex: 12.3 - 4.786 = 7.514 (different decimal places requiring zero addition)

Tips and Tricks:

• Visual alignment: Draw vertical lines to help align decimal points

• Zero filling: Always add zeros to make decimal places equal when needed

• Verification: Check your answer by adding the difference to the subtrahend to get the minuend

• Place value awareness: Keep track of which place value you're subtracting in

• Borrowing visualization: Think of borrowing as "exchanging" one unit from a higher place value for ten units in the current place value

• Verification: Always verify your answer by performing the inverse operation

Common Pitfalls:

• Misaligning decimal points, leading to incorrect place value subtraction

• Forgetting to add zeros when decimal places are different

• Incorrect borrowing, forgetting to reduce the higher place value by 1

• Placing the decimal point in the wrong position in the answer

• Subtracting the smaller number from the larger number regardless of their position

• Not borrowing when the top digit is smaller than the bottom digit

• Skipping verification steps, leading to unchecked answers

Key Notes for Memorization:

• Always align decimal points before subtracting

• Subtract from right to left by place value

• When borrowing, reduce the higher place value by 1 and add 10 to the current place value

• Add zeros to equalize decimal places when needed

• The decimal point in the answer goes directly below the aligned decimal points

• Check your work by adding the difference to the subtrahend

• Always verify your answers using the inverse operation