Then subtract 23 from 47 using expanded form.
Expanded form: Writing a number as the sum of its place values. For 2-digit numbers: tens + ones
Expanded form subtraction: Subtracting numbers by working with their expanded parts separately
- Write both numbers in expanded form
- Subtract the ones parts
- Subtract the tens parts
- Combine the results
- If needed, regroup/borrow from higher place values
47 = 40 + 7
23 = 20 + 3
7 - 3 = 4
40 - 20 = 20
20 + 4 = 24
47 - 23 = 24
Using expanded form: (40 + 7) - (20 + 3) = 20 + 4 = 24
• Place value rule: Each digit's value depends on its position
• Expanded form rule: Add the values of each place
• Subtraction principle: Subtract same place values separately
• Regrouping rule: If needed, borrow from higher place values
Then subtract 247 from 562 using expanded form.
Number decomposition: Breaking a number into its component parts based on place value
562 = 500 + 60 + 2
247 = 200 + 40 + 7
We need to subtract 7 from 2, but 2 < 7, so we borrow 1 ten (10) from the tens place
New ones: 2 + 10 = 12, New tens: 60 - 10 = 50
Now: 12 - 7 = 5
50 - 40 = 10
500 - 200 = 300
300 + 10 + 5 = 315
562 - 247 = 315
Using expanded form: (500 + 60 + 2) - (200 + 40 + 7) = 300 + 10 + 5 = 315
• Place value identification: Leftmost digit is hundreds, middle is tens, rightmost is ones
• Borrowing principle: When subtracting, if top digit is smaller, borrow from next higher place
• Subtraction by place: Subtract hundreds from hundreds, tens from tens, ones from ones
Then subtract 1,856 from 3,247 using expanded form.
Place value relationship: The position of a digit determines its actual value in the number
3,247 = 3000 + 200 + 40 + 7
1,856 = 1000 + 800 + 50 + 6
7 - 6 = 1
40 - 50: Since 40 < 50, we need to borrow from hundreds
New tens: 40 + 100 = 140, New hundreds: 200 - 100 = 100
Now: 140 - 50 = 90
100 - 800: Since 100 < 800, we need to borrow from thousands
New hundreds: 100 + 1000 = 1100, New thousands: 3000 - 1000 = 2000
Now: 1100 - 800 = 300
2000 - 1000 = 1000
1000 + 300 + 90 + 1 = 1391
3,247 - 1,856 = 1,391
Using expanded form: (3000 + 200 + 40 + 7) - (1000 + 800 + 50 + 6) = 1000 + 300 + 90 + 1 = 1,391
• Position matters: Thousands place is worth 1000 times the digit
• Borrowing rule: When subtracting, if top digit is smaller, borrow from next higher place
• Place-by-place subtraction: Subtract thousands from thousands, hundreds from hundreds, etc.
• Summation: Total value is the sum of all place values after subtraction
Place value: The value of a digit based on its position in a number
Expanded form: Writing a number as the sum of its place values
Expanded form subtraction: Subtracting numbers by working with their expanded parts separately
Thousands: The leftmost digit in a 4-digit number, worth 1000 times its face value
Hundreds: The second digit in a 4-digit number, worth 100 times its face value
Tens: The third digit in a 4-digit number, worth 10 times its face value
Ones: The rightmost digit in a 4-digit number, worth its face value
- Convert to expanded form: Write both numbers as sums of place values
- Subtract by place value: Work with thousands, hundreds, tens, and ones separately
- Apply borrowing: When necessary, borrow from higher place values
- Combine results: Add the subtracted parts together
• Same place values: Always subtract thousands from thousands, hundreds from hundreds, etc.
• Borrowing rule: When top digit is smaller, borrow 10 from the next higher place value
• Value calculation: Subtract place values individually
• Expanded form: Result is the sum of subtracted place values
• Verification: Adding result and subtracted number should equal original number
Then subtract 28,763 from 53,247 using expanded form.
Number composition: Understanding how digits combine to form a whole number
53,247 = 50,000 + 3,000 + 200 + 40 + 7
28,763 = 20,000 + 8,000 + 700 + 60 + 3
7 - 3 = 4
40 - 60: Since 40 < 60, we need to borrow from hundreds
New tens: 40 + 100 = 140, New hundreds: 200 - 100 = 100
Now: 140 - 60 = 80
100 - 700: Since 100 < 700, we need to borrow from thousands
New hundreds: 100 + 1000 = 1100, New thousands: 3000 - 1000 = 2000
Now: 1100 - 700 = 400
2000 - 8000: Since 2000 < 8000, we need to borrow from ten thousands
New thousands: 2000 + 10000 = 12000, New ten thousands: 50000 - 10000 = 40000
Now: 12000 - 8000 = 4000
40000 - 20000 = 20000
20000 + 4000 + 400 + 80 + 4 = 24,884
53,247 - 28,763 = 24,884
Using expanded form: (50,000 + 3,000 + 200 + 40 + 7) - (20,000 + 8,000 + 700 + 60 + 3) = 24,884
• Position identification: Leftmost digit is ten thousands place
• Value multiplication: Each digit multiplied by its place value
• Subtraction with borrowing: When top digit is smaller, borrow from next higher place
• Summation: Add place values to form final result
Then subtract 456,789 from 987,654 using expanded form.
Place value mastery: Understanding how each position contributes to the overall number value
987,654 = 900,000 + 80,000 + 7,000 + 600 + 50 + 4
456,789 = 400,000 + 50,000 + 6,000 + 700 + 80 + 9
4 - 9: Since 4 < 9, we need to borrow from tens
New ones: 4 + 10 = 14, New tens: 50 - 10 = 40
Now: 14 - 9 = 5
40 - 80: Since 40 < 80, we need to borrow from hundreds
New tens: 40 + 100 = 140, New hundreds: 600 - 100 = 500
Now: 140 - 80 = 60
500 - 700: Since 500 < 700, we need to borrow from thousands
New hundreds: 500 + 1000 = 1500, New thousands: 7000 - 1000 = 6000
Now: 1500 - 700 = 800
6000 - 6000 = 0
80,000 - 50,000 = 30,000
900,000 - 400,000 = 500,000
500,000 + 30,000 + 0 + 800 + 60 + 5 = 530,865
987,654 - 456,789 = 530,865
Using expanded form: (900,000 + 80,000 + 7,000 + 600 + 50 + 4) - (400,000 + 50,000 + 6,000 + 700 + 80 + 9) = 530,865
• Place value recognition: Systematic identification of digit positions
• Value computation: Proper multiplication of digits by their place value
• Subtraction with borrowing: When top digit is smaller, borrow from next higher place
• Notation: Expressing as sum of individual place values after subtraction
This comprehensive summary covers all aspects of expanded form subtraction for grade 1 students, providing clear explanations, methods, and examples for mastering place value concepts including ones, tens, hundreds, thousands, ten thousands, and hundred thousands.
Place Value: The value of a digit based on its position in a number. Each position has a different value.
Expanded Form: Writing a number as the sum of its place values (e.g., 532,478 = 500,000 + 30,000 + 2,000 + 400 + 70 + 8).
Expanded Form Subtraction: Subtracting numbers by working with their expanded parts separately (e.g., (500 + 30 + 2) - (200 + 40 + 7) = 300 - 10 - 5 = 285).
Ones Place: The rightmost position in a number, worth the digit's face value.
Tens Place: The second position from the right, worth 10 times the digit's face value.
Hundreds Place: The third position from the right, worth 100 times the digit's face value.
Thousands Place: The fourth position from the right, worth 1,000 times the digit's face value.
Ten Thousands Place: The fifth position from the right, worth 10,000 times the digit's face value.
Hundred Thousands Place: The sixth position from the right, worth 100,000 times the digit's face value.
Digit: Any of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 used to make numbers.
Position Rule: Each position in a number has a specific value that is 10 times the value of the position to its right.
Value Rule: Each digit's value = digit × its place value multiplier.
Subtraction Rule: When subtracting expanded forms, subtract like place values separately.
Borrowing Rule: When the top digit is smaller than the bottom digit, borrow 10 from the next higher place value.
Summation Rule: Expanded form subtraction result is the sum of all subtracted place values.
Verification Rule: Adding the result to the subtracted number should equal the original number.
Consistency Rule: The same method works for any number regardless of size.
Method 1: Standard Approach
- Convert both numbers to expanded form
- Subtract the ones parts
- Subtract the tens parts
- Subtract the hundreds parts
- Subtract the thousands parts
- Continue for higher place values
- Apply borrowing when necessary
- Add all the subtracted values together
Method 2: Verification Approach
- Write expanded form subtraction
- Add the result to the subtracted number
- Check if result equals the original number
Simple Examples:
47 - 23 = (40 + 7) - (20 + 3) = (40 - 20) + (7 - 3) = 20 + 4 = 24
56 - 34 = (50 + 6) - (30 + 4) = (50 - 30) + (6 - 4) = 20 + 2 = 22
Intermediate Examples:
253 - 147 = (200 + 50 + 3) - (100 + 40 + 7) = (200 - 100) + (50 - 40) + (3 - 7) = 100 + 10 - 4 = 106
476 - 283 = (400 + 70 + 6) - (200 + 80 + 3) = (400 - 200) + (70 - 80) + (6 - 3) = 200 - 10 + 3 = 193
Advanced Examples:
3,247 - 1,856 = (3000 + 200 + 40 + 7) - (1000 + 800 + 50 + 6) = (3000 - 1000) + (200 - 800) + (40 - 50) + (7 - 6) = 2000 - 600 - 10 + 1 = 1,391
987,654 - 456,789 = (900,000 + 80,000 + 7,000 + 600 + 50 + 4) - (400,000 + 50,000 + 6,000 + 700 + 80 + 9) = 500,000 + 30,000 + 1,000 - 100 - 30 - 5 = 530,865
Tips:
- Always subtract like place values (thousands from thousands, etc.)
- When borrowing, add 10 to the lower place value and subtract 1 from the higher place value
- Check by adding the result to the subtracted number
- Remember the sequence: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions
Common Mistakes:
- Subtracting different place values (e.g., thousands from hundreds)
- Forgetting to borrow when needed
- Confusing digit positions
Memory Aids:
- "Subtract same place values!" - Always match place values
- "Borrow when smaller!" - If top digit is smaller, borrow from next higher place
- "Each position is 10 times the next smaller position"
- "From right to left: Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands"
Quick Check: Always add the result to the subtracted number to verify it equals the original number.
Pattern Recognition: Each place value is a power of 10: 1, 10, 100, 1,000, 10,000, 100,000, etc.
Questions & Answers
Question: I don't understand why 47 - 23 becomes (40 + 7) - (20 + 3). Why do we need to break it down?
Answer: Great question! Breaking down numbers into expanded form makes subtraction easier because:
- You can subtract the tens from the tens: 40 - 20 = 20
- You can subtract the ones from the ones: 7 - 3 = 4
- Then combine: 20 + 4 = 24
This method helps you understand what's happening in each place value position. Instead of trying to subtract 23 from 47 all at once, you handle each place separately, which is often easier to visualize and compute.
It also reinforces your understanding of place value and how numbers are constructed.
Question: What happens if I need to subtract 7 from 3 in the ones place? Can I do that?
Answer: You cannot subtract 7 from 3 directly because 3 is smaller than 7. In this case, you need to borrow from the next higher place value:
- If you have 43 = 40 + 3 and want to subtract 7 ones, you can't do 3 - 7
- So you borrow 1 ten (which is 10 ones) from the tens place
- New ones: 3 + 10 = 13 ones, New tens: 40 - 10 = 30 tens
- Now you can subtract: 13 - 7 = 6
This borrowing process allows you to perform the subtraction by giving you enough in the lower place value.
Question: What happens if I add the result back to the number I subtracted? Should I get the original number?
Answer: Yes, absolutely! This is a great way to check your work!
When you subtract one number from another, you can verify by adding the result back to the number you subtracted:
- 47 - 23 = 24 → 24 + 23 = 47 ✓
- 562 - 247 = 315 → 315 + 247 = 562 ✓
- 3,247 - 1,856 = 1,391 → 1,391 + 1,856 = 3,247 ✓
This is called the "verification method" - always add your result to the subtracted number to make sure you get the original number. If they don't match, you made a mistake somewhere!
This helps you catch errors and confirms your understanding of place value subtraction.