Читать книгу All the Math You'll Ever Need - Steve Slavin - Страница 23

Subtraction is the inverse, or opposite, of addition. Addition puts together. Subtraction takes apart. If you buy a carton of 12 eggs and you use 4 of them to make breakfast, how many eggs are left? 12 – 4 = 8 if you count the remaining eggs. That subtraction problem is another way of thinking about the addition problem 4 + 8 = 12. Each subtraction problem has a related addition problem. 17 – 9 = ? is related to 9 + what = 17? Sometimes it's easier to think about the addition version. If you have 9 and you want 17, you need 1 to make 10 and then 7 more to get up to 17. That's a total of 8.

For larger problems, you'll work column by column, starting from the ones, just like addition, but sometimes you'll need to “borrow,” which means you'll regroup but in the other direction.

In the following example, the ones column is easy: 8 – 3 = 5. But trying to take 9 away from 3 in the tens column is a problem. If you only have 3, how can you take away 9? (There's more than one answer to that question. We'll look at one now and another one in Chapter 6, “Positive and Negative Numbers.”)

We only have 3 tens in our tens column, and we need more, so we're going to borrow 1 hundred from the hundreds column and exchange it for 10 tens. There are 6 hundreds, so if we borrow 1, there will be 5 left. We'll exchange the 1 hundred for 10 tens and add them to our 3 tens so we have 13 tens. We can subtract 9 tens from 13 tens and get 4 tens, then subtract 1 hundred from the remaining 5 hundreds to get 4 hundreds.