\(6.73 - 2.48\)
Decimal subtraction: Align decimal points and subtract column by column, borrowing when needed
- Align decimal points vertically
- Add zeros if necessary to make columns equal
- Subtract column by column from right to left
- Borrow when top digit is smaller than bottom digit
Tenths: 7
Hundredths: 3
Tenths: 4
Hundredths: 8
\(6.73 - 2.48\) becomes:
\(\begin{array}{r} 6.73 \\ - 2.48 \\ \hline \end{array}\)
\(3 < 8\), so borrow from tenths: \(13 - 8 = 5\)
After borrowing: \(6 - 4 = 2\)
\(6 - 2 = 4\)
\(6.73 - 2.48 = 4.25\)
• Decimal alignment: Always align decimal points before subtracting
• Place value: Subtract digits in the same place value columns
• Borrowing: When top digit is smaller, borrow from the next higher place value
\(5.24 - 3.78\)
Decimal subtraction: Align decimal points and subtract column by column, borrowing when needed
Tenths: 2
Hundredths: 4
Tenths: 7
Hundredths: 8
\(5.24 - 3.78\) becomes:
\(\begin{array}{r} 5.24 \\ - 3.78 \\ \hline \end{array}\)
\(4 < 8\), so borrow from tenths: \(14 - 8 = 6\)
After borrowing: \(1 < 7\), so borrow from units: \(11 - 7 = 4\)
After borrowing: \(4 - 3 = 1\)
\(5.24 - 3.78 = 1.46\)
• Decimal alignment: Always align decimal points before subtracting
• Place value: Subtract digits in the same place value columns
• Borrowing: When top digit is smaller, borrow from the next higher place value
\(7.5 - 3.64\)
Decimal subtraction: Align decimal points and subtract column by column, borrowing when needed
\(7.5 - 3.64\) becomes \(7.50 - 3.64\):
\(\begin{array}{r} 7.50 \\ - 3.64 \\ \hline \end{array}\)
\(0 < 4\), so borrow from tenths: \(10 - 4 = 6\)
After borrowing: \(4 < 6\), so borrow from units: \(14 - 6 = 8\)
After borrowing: \(6 - 3 = 3\)
\(7.5 - 3.64 = 3.86\)
• Decimal alignment: Always align decimal points before subtracting
• Zero padding: Add zeros to make decimal places equal
• Borrowing: When top digit is smaller, borrow from the next higher place value
• Decimal number: A number that contains a decimal point separating the whole number part from the fractional part
• Decimal point: The dot that separates the whole number from the fractional part
• Place value: The value of a digit based on its position relative to the decimal point
• Tenths: The first digit to the right of the decimal point (1/10 of a unit)
• Hundredths: The second digit to the right of the decimal point (1/100 of a unit)
- Align decimal points: Write numbers vertically with decimal points lined up
- Add zeros if needed: Make all numbers have the same number of decimal places
- Subtract column by column: Start from the rightmost column (hundredths)
- Borrow when needed: When top digit is smaller, borrow from next column
- Place decimal point: Put the decimal point in the answer directly below others
• Align: 4.57 - 2.38
• Subtract hundredths: 7 < 8, so borrow: 17 - 8 = 9
• Subtract tenths: 4 - 3 = 1
• Subtract units: 4 - 2 = 2
• Align: 5.32 - 1.78
• Subtract hundredths: 2 < 8, so borrow: 12 - 8 = 4
• Subtract tenths: 2 < 7, so borrow: 12 - 7 = 5
• Subtract units: 4 - 1 = 3
• Align: 8.40 - 3.65
• Subtract hundredths: 0 < 5, so borrow: 10 - 5 = 5
• Subtract tenths: 3 < 6, so borrow: 13 - 6 = 7
• Subtract units: 7 - 3 = 4
Decimal system: A base-10 number system where each position represents a power of 10
Place value: The value of a digit based on its position relative to the decimal point
Decimal alignment: Positioning decimal points directly above each other in vertical calculations
- Identify decimal places: Count digits after the decimal point in each number
- Align decimal points: Write numbers vertically with decimal points lined up
- Add zeros if needed: Make all numbers have the same number of decimal places
- Perform operation: Subtract column by column from right to left
- Place decimal point: Put the decimal point in the answer directly below others
- Verify result: Check if the answer makes sense with estimation
• Alignment rule: Always align decimal points vertically before calculating
• Zero padding: Add zeros to match decimal places if necessary
• Borrowing rule: When subtracting and top digit is smaller, borrow from next column
• Decimal placement: Decimal point in answer aligns with those in the problem
Questions & Answers
Question: When do I need to borrow in decimal subtraction? How do I know where to borrow from?
Answer: You need to borrow when the top digit in a column is smaller than the bottom digit. Here's how to know where to borrow from:
Borrowing happens when:
- Hundredths column: 3 < 8, so borrow from tenths
- Tenths column: 4 < 7, so borrow from units
- Units column: 2 < 5, so borrow from tens
Example: 5.23 - 1.78
• Hundredths: 3 < 8, so borrow from tenths: 13 - 8 = 5
• Tenths: 1 < 7 (after borrowing), so borrow from units: 11 - 7 = 4
• Units: 4 - 1 = 3
• Answer: 3.45
Always borrow from the next higher place value column!
Question: What if one number has more decimal places than the other? How do I handle that?
Answer: When numbers have different decimal places, add zeros to the end of the shorter number to make them the same length. This doesn't change the value!
Example: 6.4 - 2.75
Step 1: Add a zero to 6.4 to make it 6.40
Step 2: Now you have 6.40 - 2.75
Step 3: Align decimal points and subtract:
\(\begin{array}{r} 6.40 \\ - 2.75 \\ \hline 3.65 \end{array}\)
Remember: 6.4 = 6.40 = 6.400, so adding zeros just makes the subtraction easier without changing the value!
Question: How can I check if my decimal subtraction is correct? Sometimes I'm not sure if I made a mistake.
Answer: There are several ways to check your decimal subtraction:
Method 1: Add the result back to the subtracted number
If 7.84 - 3.29 = 4.55, then 4.55 + 3.29 should equal 7.84
Method 2: Estimate first
Round decimals to whole numbers: 7.84 ≈ 8, 3.29 ≈ 3, so 8 - 3 = 5. Your answer should be close to 5.
Method 3: Check decimal point placement
Make sure your answer has the decimal point aligned with the original numbers.
Always verify your work using one of these methods!