Subtraction Strategies
Build confidence with mental and written strategies for subtracting multi-digit numbers.
Mental Subtraction Strategies
Just like with addition, there are smart strategies that help you subtract numbers in your head.
1. Jump Strategy (Counting Back)
Start with the larger number and jump backwards in easy steps.
Example: 835 − 320
2. Compensation Strategy
Round the number you are subtracting to make it easier, then adjust.
Example: 742 − 198
Think: 198 is close to 200.
We subtracted 2 too many, so we add 2 back.
3. Same Difference Strategy
Add or subtract the same amount from both numbers to make the subtraction easier. The difference stays the same!
Example: 523 − 297
Add 3 to both numbers:
Written Subtraction (Vertical Algorithm)
For larger numbers, use the vertical subtraction method. Line up the digits by place value and subtract from right to left. When the top digit is smaller, you need to regroup (borrow).
Example: 7,304 − 2,856
Ones: 4 − 6? Can't do it. Borrow from tens. But tens is 0, so borrow from hundreds.
Regroup: 3 hundreds becomes 2 hundreds + 10 tens. Then 10 tens becomes 9 tens + 10 ones.
Now: 14 − 6 = 8, 9 − 5 = 4, 2 − 8? Borrow again: 12 − 8 = 4, 6 − 2 = 4.
Answer: 4,448
Top tip: Always check your subtraction by adding the answer to the bottom number. If you get the top number, you know it's correct! 4,448 + 2,856 = 7,304 ✓
Estimation: Is My Answer Reasonable?
Round each number to the nearest hundred or thousand before subtracting to get a quick estimate.
Example: Estimate 6,218 − 2,793
Exact answer: 3,425. Our estimate of 3,000 is close, so the answer looks right!
Key Vocabulary
Difference
The result of subtracting one number from another.
Regroup (Borrow)
When the top digit is too small, take 1 from the next column to the left (1 ten = 10 ones).
Minuend
The starting number (the number you subtract from), written on top.
Subtrahend
The number being taken away, written on the bottom.
Worked Examples
Use compensation to solve 863 − 399.
Step 1: Round 399 up to 400 (that is 1 more).
Step 2: 863 − 400 = 463.
Step 3: We subtracted 1 too many, so add 1 back: 463 + 1 = 464.
Use the same difference strategy to solve 614 − 298.
Step 1: Add 2 to both numbers to turn 298 into 300.
Step 2: 616 − 300 = 316.
Check: 316 + 298 = 614 ✓
Use the vertical method to solve 5,003 − 1,867.
Ones: 3 − 7? Can't. Borrow from tens (0), which borrows from hundreds (0), which borrows from thousands.
After regrouping: 13 − 7 = 6, 9 − 6 = 3, 9 − 8 = 1, 4 − 1 = 3.
Answer: 3,136
Knowledge Check
Select the correct answer for each question.
Question 1
What is 6,502 − 3,247?
Question 2
Using compensation, what is 725 − 198?
Question 3
What is the best estimate for 8,345 − 4,672?
Question 4
A library has 4,200 books. If 1,875 are borrowed, how many remain?
Question 5
Which strategy adds the same amount to both numbers to make subtraction easier?
Key Concepts Summary
- ●The jump strategy counts back in easy steps (hundreds, then tens, then ones).
- ●The compensation strategy rounds the subtrahend, then adjusts the answer.
- ●The same difference strategy shifts both numbers by the same amount.
- ●The vertical method subtracts column by column, regrouping when needed.
- ●Check your answer by adding the result to the subtrahend — it should equal the minuend.