# Long Hand Subtraction

Subtraction is the mathematical operation which means to take away. 3 subtracted from 7 means take away 3 from 7, i.e., 7 - 3 = 4. Similarly, 9 - 2 = 7, 3 - 0 = 3, etc. We can also subtract by counting backwards starting from the number we have to subtract. In 7 - 3, we start backward counting from 7 & move back 3 steps as 6, 5 & 4; so we get 4 as the difference between 7 & 3. Similarly 56 – 23, we will count 23 backward starting from 56 & we get 56 – 23 = 33. But for large numbers backward counting is not possible. For subtraction of large numbers we use method of long hand subtraction. Let us know what long hand subtraction is & how to do it.
When we have to subtract large numbers, we first write the minuend & the subtrahend in columns in a way that the digits corresponding to different places are written one under the another; thus taking care that the digits at ones place are in a column, no matter whether there are digits at all the places in the subtrahend or not. Also remember that we always subtract smaller number from the bigger number. After arranging the numbers in columns, we start subtracting from ones place & move the digits to the left. Like 345 – 122.
3    4    5     Starting from ones digit, 5 – 2 = 3, 4 – 2 = 2, 3 – 1 = 2,
-1    2    2
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2    2    3
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Thus, the difference is 223.

As stated above the number to be subtracted should be smaller, so if at any place, a digit in the subtrahend is bigger than the corresponding digit in the minuend, we subtract following subtraction by regrouping in which we proceed by taking a borrow from the place just before the place that falls short.
While doing so 1 borrowed becomes 10 in the next place & is added to the digit already there & then we subtract.

542 - 181 will be written as

4   1   4
5   4   2         2 – 1 = 1, but at tens place, 8 > 4, so we’ll borrow 1 from 5 & it becomes 14. Now 14 – 8 = 6
-  1    8   1
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3   6   1
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Thus the difference is 361. This is how we do long hand subtraction.