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Longhand Subtraction

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  • pg 1
									                           Longhand Subtraction
Longhand Subtraction

    Introduction
               Small subtractions are easy to remember, such as 4 - 2 or 8 - 5. We don't figure
these out, we simply remember the differences. As numbers get larger, they would be harder
to remember. Did you ever memorize 154 - 31 or 9123 - 1534?

How We Could Do It
     We could start with the first number and count backwards through the rest. For example,
we could start with 154, and then count backwards by one 31 times to subtract 31 from 154.
We would count backwards 31 times from 154: 153, 152, 151, 150, 149, ... all the way down to
123. This works, but we have to admit, it's time-consuming and impractical. It could take hours
to subtract 114,657 from 522,342.

 An Easier Way
      We could use a calculator. A calculator is a great solution; they are fast and accurate.
But what if you had to subtract two really, really large numbers, like
389,475,123,985,234,232,101 from 758,302,375,192,845,629,943? Try that on a calculator.
You probably won't be able to subtract it because most calculators do not allow such large
numbers.
        Know More About      Properties of rational numbers with examples


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The Longhand Way
We can use a pen and paper. We write the numbers onto the paper, one underneath the
other, and subtract them column by column. This way, for two big numbers, we are only
subtracting smaller one-digit numbers at a time. Since we have memorized all of the one-digit
subtractions starting from 0 - 0 = 0 all the way to 9 - 9 = 0, subtracting in columns should be
easy. Let's try one to make this clearer. Let's subtract 31 from 154.

Step 1
Write the two numbers onto the paper. Write them in such a way that the digits line up
underneath each other. Since 154 has more digits than 31, write them in such a way too that
the digits on the right line up underneath each other. The larger number, the minuend, must
always be the upper number. Try it:
1 5 4
    3 1


Step 2
Subtract the column on the far right and write the difference below the subtrahend. 4 - 1 = 3:
1 5 4
   3 1
       3


Step 3
Subtract the next column to the left and write the difference below the subtrahend. 5 - 3 = 2:
1 5 4
   3 1
   2 3




                        Read  More About   Definite integral examples


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Step 4
Subtract the next column to the left and write the sum below the subtrahend. In this case this
is the last column on the left; our subtraction will be finished after this. Since the digit
underneath 1 is blank, we consider the blank as the number 0. 1 - 0 = 1:
1 5 4
    3 1
1 2 3

The subtraction is now complete: 154 - 31 = 123. If you don't believe it, start with 154 and
count down by one 31 times.

The subtraction is now complete: 157 - 28 = 129. You can double-check this on a calculator.




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