➖ Subtraction Algorithms
An algorithm is a step-by-step method. Let's learn how to subtract big numbers using the written column method — including borrowing!
📋 Column Subtraction — No Borrowing
Write numbers in columns (hundreds, tens, ones). Subtract each column starting from the ones (right side).
Example: 478 − 253
- Ones: 8 − 3 = 5
- Tens: 7 − 5 = 2
- Hundreds: 4 − 2 = 2
Answer: 225 ✅
🔄 Borrowing (Regrouping)
Sometimes the top digit is smaller than the bottom digit. We need to borrow (regroup) from the next column to the left.
Example: 352 − 167 (ones: 2 − 7 — can't do it!)
- Ones: 2 − 7? Can't! Borrow 1 ten → 2 becomes 12, tens become 4.
- Ones: 12 − 7 = 5
- Tens: 4 − 6? Can't! Borrow 1 hundred → 4 becomes 14, hundreds become 2.
- Tens: 14 − 6 = 8
- Hundreds: 2 − 1 = 1
Answer: 185 ✅
Worked Examples
Example 1: 635 − 412
Ones: 5 − 2 = 3. Tens: 3 − 1 = 2. Hundreds: 6 − 4 = 2.
635 − 412 = 223 ✅
Example 2: 521 − 348 (with borrowing)
Ones: 1 − 8? Borrow → 11 − 8 = 3. Tens: 1 − 4? Borrow → 11 − 4 = 7. Hundreds: 4 − 3 = 1.
521 − 348 = 173 ✅
Example 3: Check your answer
To check 352 − 167 = 185, add the answer back: 185 + 167 = 352. ✓
Addition is the inverse (opposite) of subtraction — use it to check! ✅
Key Vocabulary
A step-by-step method for solving a problem.
Exchanging 1 ten for 10 ones (or 1 hundred for 10 tens) when the top digit is too small.
The result of a subtraction calculation.
The opposite operation — addition is the inverse of subtraction.
Knowledge Check
Question 1: Calculate 587 − 243 using column subtraction.
Question 2: Calculate 432 − 158 (borrowing required).
Question 3: When do you need to borrow in column subtraction?
Question 4: Calculate 700 − 356.
Question 5: A school has 845 students. 327 are away today. How many are present?
Pax Says:
"Always work from right to left — ones first, then tens, then hundreds. And remember: after subtracting, add your answer back to check!"
Key Concepts Summary
- ✓ Write numbers in columns — hundreds, tens, ones.
- ✓ Subtract from right (ones) to left (hundreds).
- ✓ Borrow from the next column when the top digit is too small.
- ✓ Check your answer by adding the difference back to the subtracted number.