Mental Math Subtraction: Count Up, Compensate and Stop Borrowing
Written subtraction teaches you to borrow, cross out digits and keep track of a trail of little numbers. That works on paper but is clumsy in your head. Fast mental calculators almost never borrow. They use three simple ideas instead: counting up, compensating, and subtracting in chunks. This guide explains each one with worked examples.
Why subtraction feels harder than addition
Addition is forgiving: the order of the numbers does not matter, and carrying only ever moves a small amount to the next column. Subtraction has no such symmetry. 83 − 47 is not the same problem as 47 − 83, and the borrowing step makes you hold a half-finished calculation in memory while you fix the column to its right. Mental methods avoid the problem by changing the question into one that looks more like addition.
Method 1: Count up (the shopkeeper's method)
When the two numbers are close together, do not subtract at all. Ask instead: how far is it from the smaller number up to the larger one? Cashiers used to make change this way, counting up from the price to the amount handed over.
Example: 83 − 47
Start at 47. Add 3 to reach 50. Add 30 to reach 80. Add 3 to reach 83. The total you added is 3 + 30 + 3 = 36.
The trick is to use the nearest "friendly" number, usually the next multiple of ten, as a stepping stone. Counting up is at its best when the answer is small, such as 1,002 − 987 (the answer is just 15) or 5,000 − 4,968 (32). It is also the fastest way to answer "how many years between 1987 and 2026?".
Method 2: Compensate (round, then fix)
Subtracting a number that is just below a multiple of ten is awkward. Subtracting the multiple of ten itself is easy. So round the number you are subtracting up, do the easy subtraction, and then give back what you took too much.
Example: 134 − 69
69 is one less than 70. Compute 134 − 70 = 64. You subtracted 1 too much, so add it back: 64 + 1 = 65.
Example: 502 − 298
298 is 2 less than 300. 502 − 300 = 202, and adding the 2 back gives 204.
The rule to remember: if you round the subtrahend up, the answer from the easy subtraction is too small, so you add the difference back. If you ever round it down instead (for example subtracting 60 rather than 62), the intermediate answer is too large, and you subtract the difference.
Method 3: Subtract in chunks, left to right
Split the number you are subtracting into tens and ones, and take them away one at a time from the left. There is no borrowing because you never need to line up columns.
Example: 92 − 57
Subtract the tens first: 92 − 50 = 42. Then subtract the ones: 42 − 7 = 35. If the second step crosses a ten, bridge it: 42 − 7 is the same as 42 − 2 = 40, then 40 − 5 = 35.
Chunking scales to larger numbers too. For 1,240 − 378, take away 300 (940), then 70 (870), then 8 (862).
Which method should you use?
| Situation | Best method | Why |
|---|---|---|
| The two numbers are close | Count up | The answer is a short hop, so you add small steps. |
| You subtract something like 9, 19, 98, 299 | Compensate | Rounding to a round number removes all the awkward digits. |
| Everything else | Chunk left to right | Always works and never needs borrowing. |
Strong players switch between the three without thinking. Before you start a problem, spend half a second looking at the numbers: are they close, is one of them nearly round, or is it a plain two-digit subtraction? That glance chooses the method for you.
Check your answer by adding back
Subtraction is the reverse of addition, which gives you a free check. If 83 − 47 = 36, then 36 + 47 must equal 83. You can do this check in a couple of seconds, and it catches the most common mistake, a slip of exactly 10 caused by a miscounted tens digit. For a fast sanity check, round both numbers first: 83 − 47 is close to 80 − 50 = 30, so an answer near 36 is believable while 26 or 46 is not. Our guide to estimation and sense-checking goes deeper on this habit.
Practice plan
- Spend one session on count-up problems only: pairs of numbers that differ by less than 30.
- Spend the next on compensation: subtract 9, 19, 29, 98, 99 and 199 from random numbers.
- Then mix all three. Say the method aloud for the first few problems, then let it go silent.
- Finish by timing yourself on a set of twenty subtractions and aim to beat your last time.
The Foundations and Blitz modes are built for this kind of short, repeated practice, and both let you play without an account.