\(4.28 + 3.57\)
Decimal addition: Align decimal points and add column by column, carrying over when needed
- Align decimal points vertically
- Add zeros if necessary to make columns equal
- Add column by column from right to left
- Carry over when sum exceeds 9
Tenths: 2
Hundredths: 8
Tenths: 5
Hundredths: 7
\(4.28 + 3.57\) becomes:
\(\begin{array}{r} 4.28 \\ + 3.57 \\ \hline \end{array}\)
\(8 + 7 = 15\), write down 5, carry over 1
\(2 + 5 + 1 = 8\)
\(4 + 3 = 7\)
\(4.28 + 3.57 = 7.85\)
• Decimal alignment: Always align decimal points before adding
• Place value: Add digits in the same place value columns
• Carrying: When sum exceeds 9, carry the extra to the next column
\(5.69 + 2.74\)
Decimal addition: Align decimal points and add column by column, carrying over when needed
Tenths: 6
Hundredths: 9
Tenths: 7
Hundredths: 4
\(5.69 + 2.74\) becomes:
\(\begin{array}{r} 5.69 \\ + 2.74 \\ \hline \end{array}\)
\(9 + 4 = 13\), write down 3, carry over 1
\(6 + 7 + 1 = 14\), write down 4, carry over 1
\(5 + 2 + 1 = 8\)
\(5.69 + 2.74 = 8.43\)
• Decimal alignment: Always align decimal points before adding
• Place value: Add digits in the same place value columns
• Carrying: When sum exceeds 9, carry the extra to the next column
\(6.4 + 2.75\)
Decimal addition: Align decimal points and add column by column, carrying over when needed
\(6.4 + 2.75\) becomes \(6.40 + 2.75\):
\(\begin{array}{r} 6.40 \\ + 2.75 \\ \hline \end{array}\)
\(0 + 5 = 5\)
\(4 + 7 = 11\), write down 1, carry over 1
\(6 + 2 + 1 = 9\)
\(6.4 + 2.75 = 9.15\)
• Decimal alignment: Always align decimal points before adding
• Zero padding: Add zeros to make decimal places equal
• Carrying: When sum exceeds 9, carry the extra to the next column
• 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
- Add column by column: Start from the rightmost column (hundredths)
- Carry over: When sum ≥ 10, carry the extra to the next column
- Place decimal point: Put the decimal point in the answer directly below others
• Align: 3.45 + 2.67
• Add hundredths: 5 + 7 = 12 (write 2, carry 1)
• Add tenths: 4 + 6 + 1 = 11 (write 1, carry 1)
• Add units: 3 + 2 + 1 = 6
• Align: 4.80 + 1.25 (add zero)
• Add hundredths: 0 + 5 = 5
• Add tenths: 8 + 2 = 10 (write 0, carry 1)
• Add units: 4 + 1 + 1 = 6
• Align: 7.92 + 3.48
• Add hundredths: 2 + 8 = 10 (write 0, carry 1)
• Add tenths: 9 + 4 + 1 = 14 (write 4, carry 1)
• Add units: 7 + 3 + 1 = 11
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: Add 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
• Carrying rule: When sum in a column is ≥10, carry the excess to the next column
• Decimal placement: Decimal point in answer aligns with those in the problem
Questions & Answers
Question: Why do I need to align decimal points when adding decimals? Can't I just add them like regular numbers?
Answer: You absolutely must align decimal points when adding decimals! Here's why:
When you align decimal points, you're making sure you're adding digits in the same place value columns. For example:
Without alignment (wrong):
\(\begin{array}{r} 4.56 \\ + 2.78 \\ \hline 6.134 \text{ (WRONG!)} \end{array}\)
With alignment (correct):
\(\begin{array}{r} 4.56 \\ + 2.78 \\ \hline 7.34 \text{ (CORRECT!)} \end{array}\)
If you don't align decimal points, you'll be adding tenths to units and hundredths to tenths, which gives incorrect answers!
Question: What if one number has more decimal places than the other? How do I handle that when adding?
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 of the number!
Example: 3.4 + 2.57
Step 1: Add a zero to 3.4 to make it 3.40
Step 2: Now you have 3.40 + 2.57
Step 3: Align decimal points and add:
\(\begin{array}{r} 3.40 \\ + 2.57 \\ \hline 5.97 \end{array}\)
Remember: 3.4 = 3.40 = 3.400, so adding zeros just makes the addition easier without changing the value!
Question: When do I need to carry over in decimal addition? How do I know where to put the carried number?
Answer: You need to carry over when the sum in any column is 10 or greater. Here's how to handle it:
Carry over happens when:
- Hundredths column: 7 + 8 = 15 (carry the 1 to tenths)
- Tenths column: 6 + 5 = 11 (carry the 1 to units)
- Units column: 9 + 8 = 17 (carry the 1 to tens)
Example: 4.78 + 2.54
\(\begin{array}{r} 4.78 \\ + 2.54 \\ \hline 7.32 \end{array}\)
• 8 + 4 = 12, write down 2, carry 1 to tenths
• 7 + 5 + 1 = 13, write down 3, carry 1 to units
• 4 + 2 + 1 = 7
Always carry to the next column to the left!