Chapter 2: Arithmetic 21Subtraction
Subtraction is often thought of as a separate operation, but it’s really a sort of backward addition.
It’s how you answer the question, “What do you add to A if you want to have B?” What do you
add to 13 to get 20? Well, 20 – 13 is 7, which means 13 + 7 is 20. In this example, 7 is the difference
between 20 and 13.
Subtraction and addition are inverse operations. Remember that shepherd who knows all the
pairs that add to 7? If he looks up and only sees 5 sheep, he needs to know how many sheep are
missing. His question can be phrased in addition terms as 5 + how many = 7? Or you can write it
as a subtraction problem: 7 – 5 = how many? Either way you think about it, compatible numbers
will be helpful with subtraction as well as addition.DEFINITION
The result of a subtraction problem is called a difference. Officially, the number you
start with is the minuend, and the number you take away is the subtrahend, but you
don’t hear many people use that language. In the equation 9 – 2 = 7, 9 is the minuend,
2 is the subtrahend, and 7 is the difference.
An inverse operation is one that reverses the work of another. Putting on your
jacket and taking off your jacket are inverse operations. Subtraction is the inverse
of addition.The “take-away” image of subtraction thinks of the problem as “if you have 12 cookies, and I
take away 4, how many cookies are left?” That works fine for small numbers, and when you’re
working with large numbers, you can apply it one place value column at a time. In the following
subtraction problem, you can work right to left:
7 ones take away 3 ones equals 4 ones
8 tens take away 4 tens equals 4 tens
9 hundreds take away 1 hundred equals 8 hundreds
6 thousands take away 2 thousands equals 4 thousands6,987
2,143
4,844Things get a little more complicated when you try a subtraction like 418 – 293. It starts out
fine in the ones place: 8 – 3 = 5. But when you try to subtract the tens column, you have 1 – 9,
and how can you take 9 away from 1? This is when you need to remember—and undo—the
regrouping you did in addition.
In the process of addition, when the total of one column was more than one digit, too big to fit
in that place, you carried some of it over to the next place. So when you’re subtracting —going
back—and you bump into a column that looks impossible, you’re going to look to the next place
up and take back, or borrow, so that the subtraction becomes possible.