Borrow Across Zero

When you subtract and have to borrow from the next digit to the left, usually that digit is a number greater than zero. But sometimes, that digit is a zero. You can't borrow from zero, so what do you do? You go across the zero to the next digit and borrow from that digit. Look at this example:

Example 1:

Subtract 367 from 804.

As usual, you begin with the column on the right. Here, you'd do 4 - 7, but you can't subtract because 7 is larger than 4.

So go to the next column to borrow. But the next digit is 0, so you can't borrow from that. Instead, go to the next digit, the 8, and borrow from that, to make it 7.

Next, put the 1 you borrowed above the 0, as you normally would. Now, 10 is in the tens place. This seems easy enough, but you're still one column away from where you want to be.

You have to get the 1 back to the 4 so you can subtract the 7. To do this, borrow 1 from the 10 in the tens place to make 9 (cross out both the 1 and the 0), and move the 1 you borrowed from the 10 back to the 4, to make it 14.

Then, subtract as usual.

This takes several steps, but after you complete several problems, you'll find that when you borrow across zero, the 0 always becomes a 9.

So the easy way to borrow across zero is to borrow from the first digit to the left, cancel the 0 and make it a 9, and move the 1 to the next digit.