Mental Subtraction Techniques
Being able to subtract quickly in your head is a skill worth building. These techniques help you work smarter, not harder.
1. Compensation Method
Round one number to the nearest ten or hundred, subtract, then adjust.
Why it works: Subtracting a round number like 40 or 100 is instant, but subtracting an awkward number like 39 or 98 is not. Round the number you're subtracting up to the nearest ten or hundred, subtract that instead, then add back the extra amount you subtracted — since rounding up means you took away too much.
Steps:
- Look at the number you are subtracting and find the nearest ten or hundred.
- Work out the adjustment — how much you rounded up by.
- Subtract the rounded number instead of the original one.
- Add back the adjustment, since rounding up made you subtract too much.
2. Bridging Through Tens
Break the subtrahend to reach the nearest ten first, then subtract the rest.
Why it works: It's much easier to subtract down to a friendly round ten than to subtract an awkward two-digit number in one go. Split the amount you're subtracting into two pieces — "just enough to reach the ten below" and "whatever's left" — and subtract each piece in turn.
Steps:
- Look at the number you're subtracting from and find the nearest ten below it.
- Work out how much you need to subtract to land exactly on that ten.
- Subtract that first small piece to bridge down to the round ten.
- Subtract whatever is left of the original subtrahend from that ten.
3. Counting Up (Shopkeeper Method)
Instead of subtracting, count forward from the smaller number to the larger.
Why it works: This is how a shopkeeper works out your change — instead of subtracting, they count forward from the price to the amount you paid. Counting up in friendly jumps (to the nearest ten, then the nearest hundred, then the rest) is often faster than subtracting directly, especially when the two numbers are close together.
Steps:
- Start at the smaller number.
- Count up to the next friendly round number (like the nearest ten), and note the size of that jump.
- Keep counting up in easy jumps (tens, then hundreds if needed) until you reach the larger number.
- Add up all your jumps — that total is the difference.
4. Breaking Down the Subtrahend
Split the number you're subtracting into place values and take them away one at a time.
Why it works: Subtracting a big two-digit or three-digit number all at once is hard to hold in your head. Breaking it into hundreds, tens, and ones lets you subtract one simple chunk at a time, so you're never juggling more than one step of borrowing at once.
Steps:
- Split the number you are subtracting into its place values (hundreds, tens, ones).
- Subtract the largest chunk (hundreds) first.
- Subtract the next chunk (tens) from that running result.
- Subtract the smallest chunk (ones) to reach the final answer.
5. Left-to-Right Subtraction
Subtract the largest place value first, then work through the smaller ones.
Why it works: Just like with addition, thinking left to right matches how we naturally picture numbers, and gives you a running total at every step. It works best when each digit on top is bigger than the matching digit below, so there's no borrowing to slow you down.
Steps:
- Split both numbers into their place values (hundreds, tens, ones).
- Subtract the hundreds first to get a starting total.
- Subtract the tens from that running total.
- Subtract the ones last to get the final answer.
Comparison Table
| Technique | Best for |
|---|---|
| Compensation | Numbers near a ten or hundred |
| Bridging | Crossing tens boundaries |
| Counting up | Finding differences (e.g., change) |
| Breaking down | Multi-digit mental subtraction |
Key Takeaways
- Choose the method that suits the numbers involved.
- Compensation works best when one number is just above or below a round number.
- Counting up is great for differences between close numbers.
- Practice these regularly to build confidence and speed.
Practice: Try a Technique
A random technique from the list above is tested each time. If you get it wrong (or leave it blank), we'll show exactly how that technique works.