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.
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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
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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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Thank You
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