Subtraction - Two Digits | Second Grade
What is Two-Digit Subtraction?
Concept: Two-digit subtraction means subtracting numbers from 10 to 99. We use place value (tens and ones) to subtract these larger numbers!
Two Important Methods:
✓ Without Regrouping: When ones can subtract easily
✓ With Regrouping: When we need to borrow from tens
💡 Tip: Always subtract ones first, then subtract tens!
1. Subtract Multiples of 10
Concept: Multiples of 10 are numbers like 10, 20, 30, 40... When subtracting these, we only work with the tens place!
Pattern Rule:
Subtract the tens, keep the zero!
\( 70 - 30 = ? \)
Think: 7 tens − 3 tens = 4 tens
70 − 30 = 40
Examples
50 − 20 = 30
5 tens − 2 tens = 3 tens
80 − 30 = 50
8 tens − 3 tens = 5 tens
90 − 40 = 50
9 tens − 4 tens = 5 tens
60 − 10 = 50
6 tens − 1 ten = 5 tens
💡 Tip: Think of it like subtracting single digits, then add a zero at the end!
2. Subtract One-Digit from Two-Digit (Without Regrouping)
Concept: When the ones digit is big enough to subtract from, we don't need to borrow (regroup).
📝 Example: 48 − 3 = ?
Vertical Method:
| T | O | |
| 4 | 8 | |
| − | 0 | 3 |
| 4 | 5 |
Step by Step:
Step 1: Subtract ones
8 − 3 = 5
Step 2: Keep tens
4 tens = 40
Answer: 45
💡 Tip: No regrouping needed when the ones digit is large enough!
3. Subtract One-Digit from Two-Digit (With Regrouping)
Concept: When the ones digit is too small to subtract from, we must borrow 1 ten (10 ones) from the tens place!
Regrouping Rule:
When top ones digit is smaller:
Borrow 1 ten = 10 ones
Add 10 to the ones, subtract 1 from tens
📝 Example: 52 − 7 = ?
Vertical Method:
| 5⁴ | ¹² | |
| T | O | |
| 5 | 2 | |
| − | 0 | 7 |
| 4 | 5 |
Step by Step:
Step 1: Can't subtract!
2 < 7, need to regroup
Step 2: Borrow 1 ten
5 tens → 4 tens
2 ones → 12 ones
Step 3: Subtract
12 − 7 = 5
4 tens = 40
Answer: 45
💡 Tip: Remember - borrowing 1 ten gives you 10 more ones!
4. Subtract Two Two-Digit Numbers (Without Regrouping)
Concept: Subtract the ones, then subtract the tens. No regrouping needed when digits are large enough!
📝 Example: 68 − 24 = ?
Vertical Method:
| T | O | |
| 6 | 8 | |
| − | 2 | 4 |
| 4 | 4 |
Step by Step:
Step 1: Subtract ones
8 − 4 = 4
Step 2: Subtract tens
6 − 2 = 4
Step 3: Combine
40 + 4 = 44
Answer: 44
💡 Tip: Line up the place values - tens under tens, ones under ones!
5. Subtract Two Two-Digit Numbers (With Regrouping)
Concept: When the top ones digit is smaller than the bottom, borrow from the tens place. This is the most important two-digit subtraction skill!
📝 Example: 73 − 48 = ?
Vertical Method:
| 7⁶ | ¹³ | |
| T | O | |
| 7 | 3 | |
| − | 4 | 8 |
| 2 | 5 |
Step by Step:
Step 1: Can't subtract!
3 < 8, need to borrow
Step 2: Borrow 1 ten
7 tens → 6 tens
3 ones → 13 ones
Step 3: Subtract ones
13 − 8 = 5
Step 4: Subtract tens
6 − 4 = 2
Answer: 25
Regrouping Checklist:
✓ Check if top ones < bottom ones
✓ Borrow 1 ten from tens place
✓ Cross out tens digit, write 1 less
✓ Add 10 to ones digit
✓ Now subtract ones, then tens
💡 Tip: Always check if you need to regroup before subtracting!
6. Subtraction Input/Output Tables (Up to Two Digits)
Concept: Find the pattern rule, then apply it to find missing outputs or inputs!
📝 Example: Subtract 12 from each number
| Input | Rule: − 12 | Output |
|---|---|---|
| 45 | 45 − 12 | 33 |
| 58 | 58 − 12 | 46 |
| 76 | 76 − 12 | 64 |
| 89 | 89 − 12 | 77 |
💡 Tip: Look for the pattern - what number is always being subtracted?
7. Ways to Make a Number Using Subtraction
Concept: Any number can be made by subtracting different combinations of numbers!
📝 Example: Different Ways to Make 20
30 − 10 = 20
40 − 20 = 20
50 − 30 = 20
35 − 15 = 20
67 − 47 = 20
85 − 65 = 20
💡 Tip: Start with any larger number and subtract to get your target!
8. Subtraction Word Problems (Up to Two Digits)
Concept: Read carefully, find the numbers, look for subtraction keywords, then solve!
Subtraction Keywords:
✓ take away
✓ left
✓ fewer
✓ difference
✓ how many more
✓ remain
📖 Example Problem
A school library had 85 books. Students borrowed 47 books. How many books are left in the library?
Solution Steps:
Step 1: Find the numbers (85 and 47)
Step 2: Look for keywords ("left" = subtract)
Step 3: Write equation: 85 − 47 = ?
Step 4: 5 < 7, need to regroup
Step 5: Borrow: 8 tens → 7 tens, 5 → 15
Step 6: Subtract: 15 − 7 = 8, 7 − 4 = 3
Answer: 38 books left
💡 Tip: Draw a picture to visualize what's being taken away!
9. Balance Subtraction Equations (Up to Two Digits)
Concept: Both sides of an equation must be equal. Find the missing number to balance!
Balance Concept:
\( 65 - 28 = 58 - 21 \)
Left side: 65 − 28 = 37
Right side: 58 − 21 = 37
Both sides equal 37 ✓ BALANCED!
📝 Practice: Find the Missing Number
\( 82 - 35 = 76 - ? \)
Left side: 82 − 35 = 47
Right side must also equal 47
76 − ? = 47
Think: 76 − 29 = 47
Answer: 29
💡 Tip: Solve one side completely, then find what makes the other side equal!
Important Two-Digit Subtraction Rules
Place Value Subtraction
Subtract ones first, then tens
\( 57 - 23 \)
Ones: 7 − 3 = 4
Tens: 5 − 2 = 3
Answer: 34
Regrouping Rule
When top ones < bottom ones:
Borrow 1 ten = 10 ones
Example: 3 < 7
Borrow: 5 tens → 4 tens
3 ones → 13 ones
Check with Addition
If \( a - b = c \)
Then \( c + b = a \)
45 − 18 = 27
Check: 27 + 18 = 45 ✓
🎯 Tips for Two-Digit Subtraction Success 🎯
- ✓ Always line up place values - ones under ones, tens under tens
- ✓ Check if you need to regroup before subtracting
- ✓ When regrouping: borrow 1 ten = 10 ones
- ✓ Cross out and write new numbers when borrowing
- ✓ Check your answer by adding back
- ✓ Practice every day to become faster and more accurate!
⭐ You're a Two-Digit Subtraction Champion! ⭐
Excellent work mastering two-digit subtraction! You now know how to subtract multiples of 10, subtract with and without regrouping, use vertical methods, solve word problems, balance equations, and work with input/output tables. Two-digit subtraction with regrouping is one of the trickiest skills in second grade - and you've conquered it! Understanding place value and borrowing will help you with all future math. Keep practicing these skills and checking your work. You're building an incredibly strong math foundation. You're doing outstanding work!