How this instrument works
Subtracting one two-digit number from another only gets tricky in a single spot: the ones place, when the top figure is smaller than what is being taken away from it. Ten cannot be removed from seven without going negative, so the method reaches left, takes one whole ten from the tens position, and turns it into ten extra ones right where they are needed.
That borrowed ten changes both positions at once. The ones place gains ten before doing its own subtraction — 2 becomes 12, say — while the tens digit loses exactly one, since a full ten was handed over. Whatever the tens column would have produced by itself now has one fewer to work with, on top of whatever was already being subtracted there.
This sheet exists to make that borrow visible rather than buried inside a mental shortcut. Its sibling on this site, long addition, walks through the reverse bookkeeping: sending a surplus forward whenever a column's total tops ten. Together the pair covers both directions of place-by-place arithmetic done by hand.
- Enter the larger number's digits into Number 1 (larger): tens digit and Number 1 (larger): ones digit.
- Enter the number being taken away into Number 2 (subtracted): tens digit and Number 2 (subtracted): ones digit.
- Check Borrow taken from the tens column — it shows 1 whenever the first ones digit is smaller than the second.
- Read Ones digit of the difference for what remains in that column once any borrowing has been applied.
- Read Tens digit of the difference for the tens column's own subtraction, reduced by one whenever a borrow was taken.
Worked example — 52 minus 37, plus two contrasting sums
Take 52 minus 37. In the ones place, 2 minus 7 cannot be done without going negative, so the method borrows a ten from the tens column, turning the problem into 12 minus 7, which equals 5. The tens digit pays for that borrow: 5 minus 3 minus the 1 just taken equals 1. Put the two figures together and the difference reads 15, which checks out against 52−37 by any other method.
Ninety-nine minus eleven needs no borrowing at all: 9 minus 1 is 8 in the ones place, and 9 minus 1 is 8 in the tens position too, for a difference of 88. Forty minus fifteen borrows the same way the first example did: 0 minus 5 becomes 10 minus 5, which is 5, and the tens digit turns 4 minus 1 minus 1 into 2, for a final difference of 25.
Questions
Why does subtraction sometimes need to borrow?
Because a single place cannot go below zero on its own. Whenever the top figure in a position is smaller than the digit being removed from it, the method takes one whole unit from the place to its left — worth ten in the spot that needed it — and only then finishes the subtraction.
What exactly happens to the tens column when a borrow is taken?
It loses one before doing its own subtraction, since a full ten was handed over to the ones place. Fifty-two minus thirty-seven shows this: the tens digit computes 5−3−1=1, that extra −1 being the price of the borrow made in the ones position.
Does every subtraction problem need a borrow?
No — only when the top figure in some place is smaller than what is being subtracted from it. Ninety-nine minus eleven needs none, since 9 is at least as large as 1 in both positions, leaving a plain 8 and 8.
How is this different from long addition?
It moves in the opposite direction. Addition, covered on a separate sheet, sends a surplus to the left whenever a column's total passes ten; subtraction instead reaches left to borrow whenever a column falls short, turning a ten from the neighboring place into ten extra ones.
Can the tens digit of the difference come out negative?
Not for a properly set-up subtraction where the first number is the larger one — tens₁−tens₂−borrow stays at zero or above as long as that holds. Entering a smaller figure as Number 1 will produce a negative result here, which signals the two inputs need to be swapped.
Why walk through borrowing by hand instead of just showing the final difference?
Because the borrow is the step where errors usually happen. Watching 2−7 turn into 12−7=5, and seeing the tens column pay for it with an extra −1, shows precisely where each part of the answer came from and lets the whole calculation be checked by hand.