\(7.84 - 3.29\)
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: 8
Hundredths: 4
Tenths: 2
Hundredths: 9
\(7.84 - 3.29\) becomes:
\(\begin{array}{r} 7.84 \\ - 3.29 \\ \hline \end{array}\)
\(4 < 9\), so borrow from tenths: \(14 - 9 = 5\)
After borrowing: \(7 - 2 = 5\)
\(7 - 3 = 4\)
\(7.84 - 3.29 = 4.55\)
• 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
\(6.32 - 2.87\)
Decimal subtraction: Align decimal points and subtract column by column, borrowing when needed
Tenths: 3
Hundredths: 2
Tenths: 8
Hundredths: 7
\(6.32 - 2.87\) becomes:
\(\begin{array}{r} 6.32 \\ - 2.87 \\ \hline \end{array}\)
\(2 < 7\), so borrow from tenths: \(12 - 7 = 5\)
After borrowing: \(2 < 8\), so borrow from units: \(12 - 8 = 4\)
After borrowing: \(5 - 2 = 3\)
\(6.32 - 2.87 = 3.45\)
• 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
\(8.4 - 3.75\)
Decimal subtraction: Align decimal points and subtract column by column, borrowing when needed
\(8.4 - 3.75\) becomes \(8.40 - 3.75\):
\(\begin{array}{r} 8.40 \\ - 3.75 \\ \hline \end{array}\)
\(0 < 5\), so borrow from tenths: \(10 - 5 = 5\)
After borrowing: \(3 < 7\), so borrow from units: \(13 - 7 = 6\)
After borrowing: \(7 - 3 = 4\)
\(8.4 - 3.75 = 4.65\)
• 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
• Subtract: 6 - 8 → borrow → 16 - 8 = 8
• Subtract: 4 - 7 → borrow → 14 - 7 = 7
• Subtract: 3 - 1 = 2
• Align decimal points: 4.56 - 1.78
• Subtract: 6 - 8 → borrow → 16 - 8 = 8
• Subtract: 4 - 7 → borrow → 14 - 7 = 7
• Subtract: 3 - 1 = 2
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: How is subtracting decimals similar to subtracting whole numbers? What are the exact same steps?
Answer: Subtracting decimals is almost exactly like subtracting whole numbers! Here are the same steps:
Same steps for both:
- Align numbers vertically (decimal points for decimals, units for whole numbers)
- Subtract column by column from right to left
- Borrow when the top digit is smaller than the bottom digit
- Continue the process for each column
The only difference is that decimal numbers require you to align decimal points, whereas whole numbers align by the units place.
Example comparison:
Whole: 456 - 178 = 278
Decimal: 4.56 - 1.78 = 2.78
Notice how the subtraction process is identical!
Question: Do I still need to borrow when subtracting decimals like I do with whole numbers?
Answer: Yes, exactly! Borrowing works the same way in decimal subtraction as it does in whole number subtraction.
When to borrow:
- When the top digit is smaller than the bottom digit in any column
- When you need to subtract a larger number from a smaller number in that column
Example: 5.23 - 1.78
• In hundredths column: 3 < 8, so borrow from tenths (13 - 8 = 5)
• In tenths column: 1 < 7 (after borrowing), so borrow from units (11 - 7 = 4)
• In units column: 4 - 1 = 3
• Answer: 3.45
The borrowing process is identical to whole numbers!
Question: What if one decimal number has more places than the other? Does that change the subtraction process?
Answer: No, the subtraction process remains the same! When numbers have different decimal places, add zeros to make them equal:
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:
\(\begin{array}{r} 6.40 \\ - 2.75 \\ \hline 3.65 \end{array}\)
The process is still the same:
- Subtract hundredths: 0 < 5, so borrow: 10 - 5 = 5
- Subtract tenths: 3 < 7, so borrow: 13 - 7 = 6
- Subtract units: 5 - 2 = 3
Adding zeros just makes the columns line up properly!