Basic Math and Pre-Algebra For Dummies Read Online Free PDF Page B

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
    Â 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.
    Â 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 .
Columns and stacks: Subtracting larger numbers
    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.
Can you spare a ten? Borrowing to subtract
    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:
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.
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:

    Therefore, 386 − 94 = 292.
    In some cases, the column directly to the left may not have anything to lend. Suppose, for instance, that you want to subtract 1,002 − 398. Beginning in the ones column, you find that you need to subtract 2 − 8. Because 2 is smaller than 8, you need to borrow from the next column to the left. But the digit in the tens column is a 0, so you can't borrow from there because the cupboard is bare, so to speak:

    Â When borrowing from the next column isn't an option, you need to borrow from the nearest nonzero column to the left.
    In this example, the column you need to borrow from is the thousands column. First, cross out the 1 and replace it with a 0. Then place a 1 in front of the 0 in the hundreds column:

    Now cross out the 10 and replace it with a 9. Place a 1 in front of the 0 in the tens column:

    Finally, cross out the 10 in the tens column and replace it with a 9. Then place a 1 in front of the 2:

    At last, you can begin subtracting in the ones column: 12 − 8 = 4:

    Then subtract in the tens column: 9 − 9 = 0:

    Then subtract in the