Basic Math and Pre-Algebra For Dummies (10 page)

 In subtraction, the first number is called the
minuend,
and the second number is called the
subtrahend.
But almost nobody ever remembers which is which, so when I talk about subtraction, I prefer to say
the first number
and
the second number
.

One of the first facts you probably heard about subtraction is that you can't take away more than you start with. In that case, the second number can't be larger than the first. And if the two numbers are the same, the result is always 0. For example, 3 − 3 = 0; 11 − 11 = 0; and 1,776 − 1,776 = 0. Later someone breaks the news that you
can
take away more than you have. When you do, though, you need to place a minus sign in front of the difference to show that you have a negative number, a number below 0:

• 4 − 5 = −1
  
• 10 − 13 = −3
  
• 88 − 99 = −11
  

 When subtracting a larger number from a smaller number, remember the words
switch
and
negate
: You
switch
the order of the two numbers and do the subtraction as you normally would, but at the end, you
negate
the result by attaching a minus sign. For example, to find 10 − 13, you switch the order of these two numbers, giving you 13 − 10, which equals 3; then you negate this result to get −3. That's why 10 − 13 = −3.

 The minus sign does double duty, so don't get confused. When you stick a minus sign between two numbers, it means the first number minus the second number. But when you attach it to the front of a number, it means that this number is a negative number.

Flip to Chapter
1
to see how negative numbers work on the number line. I also go into more detail on negative numbers and the Big Four operations in Chapter
4
.

To subtract larger numbers, stack one on top of the other as you do with addition. (For subtraction, however, don't stack more than two numbers —
put the larger number on top and the smaller one underneath it.) For example, suppose you want to subtract 386 − 54. To start, stack the two numbers and begin subtracting in the ones column: 6 − 4 = 2:

Next, move to the tens column and subtract 8 − 5 to get 3:

Finally, move to the hundreds column. This time, 3 − 0 = 3:

This problem shows you that 386 − 54 = 332.

Sometimes the top digit in a column is smaller than the bottom digit in that column. In that case, you need to borrow from the next column to the left. Borrowing is a two-step process:

1. Subtract 1 from the top number in the column directly to the left.
   

   Cross out the number you're borrowing from, subtract 1, and write the answer above the number you crossed out.
   

2. Add 10 to the top number in the column you were working in.
   

For example, suppose you want to subtract 386 − 94. The first step is to subtract 4 from 6 in the ones column, which gives you 2:

When you move to the tens column, however, you find that you need to subtract 8 − 9. Because 8 is smaller than 9, you need to borrow from the hundreds column. First, cross out the 3 and replace it with a 2, because 3 − 1 = 2:

Next, place a 1 in front of the 8, changing it to an 18, because 8 + 10 = 18:

Now you can subtract in the tens column: 18 − 9 = 9:

The final step is simple: 2 − 0 = 2: