How do I subtract quickly in my head?

How does counting up (the shopkeeper's method) work?

Instead of taking the small number away, you count up from it to the big number and track how far you travelled. That distance is the answer. It is the same move a cashier makes handing back change.

For 83 − 67: go from 67 up to 70 (that is 3), then 70 up to 83 (that is 13), so 3 + 13 = 16. Counting up avoids borrowing entirely because every step is an addition.

1. Start at the smaller number.
2. Jump up to the next round number and note the gap.
3. Jump from there to the larger number and note that gap.
4. Add the gaps together.

What are complements and how do they speed up subtraction?

A complement is how far a number sits from a round value like 100 or 1000. Knowing complements to 100 cold makes subtracting from round numbers instant.

For 100 − 63: take the tens digit from 9 (9 − 6 = 3) and the ones digit from 10 (10 − 3 = 7), giving 37. So 1000 − 638 works the same way: 361 + the last digit from 10 is 362.

1. Subtract each digit except the last from 9.
2. Subtract the last digit from 10.
3. Read the digits together as the complement.

How do I use round-and-adjust compensation?

Round the number you are subtracting up to a friendly 10, subtract that, then add back the bit you over-subtracted. This turns an ugly subtraction into an easy one plus a tiny correction.

For 72 − 38: round 38 up to 40, subtract to get 72 − 40 = 32, then add back the 2 you took too much, giving 34. The correction is always small, so it is easy to track.

1. Round the number being subtracted up to the nearest 10 and note how much you added.
2. Subtract the rounded value.
3. Add back the amount you over-subtracted.

How do I subtract in parts by place value?

Peel off the number you are subtracting one place at a time: hundreds first, then tens, then ones. Each step is a single clean subtraction with nothing to borrow.

For 456 − 123: subtract 100 to get 356, subtract 20 to get 336, subtract 3 to get 333. When a step would cross a 10, bridge down to the round number first to stay clean.

1. Split the number being subtracted into hundreds, tens, and ones.
2. Subtract the hundreds, then the tens, then the ones from the running total.

When should I count up versus round and adjust?

Count up when the two numbers are close together, because the distance is small and quick to walk, as in 71 − 68 = 3. Round and adjust when the numbers are far apart but the subtracted number is near a 10, as in 200 − 47.

For 200 − 47: subtract 50 to get 150, then add back 3, giving 153. Matching the method to the numbers is the real skill, and it gets automatic with reps.