Addition and Subtraction

Borrowing

Can you solve this problem?

5 - 9

Of course not — 5 is smaller than 9. If you have five, it's impossible to subtract nine. In other words, you can't subtract a larger number from a smaller number.

How could you solve this next problem, then?

There's that 5 again, and 9 is beneath it. But we know that 75 is larger than 29, so we have to be able to subtract it somehow. The trick is a technique called borrowing.

Let's see how it works.

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  First, we'll make sure the expression is set up correctly. The larger number is stacked on top of the smaller number.

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  As with all stacked subtraction problems, begin with the digits farthest to the right. Here, they are 5 and 9.

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  5 is smaller than 9, so we'll need to borrow to make 5 larger.

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  We'll borrow from the digit to the left of 5. Here, it's 7. We'll take 1 from it....

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  7 - 1 = 6. To help us remember that we subtracted 1, we'll cross out the 7 and write 6 above it.

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  Then, we'll place the 1 we took next to the 5...

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  5 becomes 15. See how it looks like 15?

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  15 is larger than 9, which means we can subtract. We'll solve for 15 - 9.

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  15 - 9 = 6. We'll write 6 beneath the line.

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  Next, find the difference of the digits to the left: 6 - 2.

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  6 - 2 = 4. We'll write 4 beneath the line.

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  Our answer is 46. 75 - 29 = 46.

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As you borrow, always cross out the digit you borrow from and write the new value above it. Remember to always place the 1 next to the smaller digit.

Try these problems to practice borrowing. Click the B button to borrow.

Sometimes the top number might have two or more digits that are smaller than the digits beneath them. In that case, you'll need to borrow more than once. It will always work the same way. You'll always subtract 1 from the digit to the left and place 1 next to the smaller digit.

Try solving these subtraction problems to practice borrowing more than one time.