Indirect calculation
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When a < b situation applies, the problem a - b can sometimes be modified.
- If only one digit in b is larger than its corresponding digit in a, diminish the offending digit in b until it is equal to its corresponding digit in a. Then subtract further the amount b was diminished by from a. For example, to calculate 872 − 92, turn the problem into 872 − 72 = 800. Then subtract 20 from 800: 780.
- If more than one digit in b is larger than its corresponding digit in a, it may be easier to find how much must be added to b to get a. For example, to calculate 8192 − 732, add 8 to 732 (resulting in 740), then add 60 (to get 800), then 200 (for 1000). Next, add 192 to arrive at 1192, and, finally, add 7000 to get 8192. The final answer is 7460.
- Another useful technique is rounding off one of the digits (Either the larger digit or the smaller digit to the nearest number preferably containing a single non-zero digit). For example, to calculate 8192 - 732, round off 732 to 1000 by adding 268 (the value 268 can be found by subtracting 732 from 1000 mentally. The human brain finds it easier in dealing with rounded figures) to it. Then subtract 1000 from 8192 and obtain 7192 as the answer. Adding 268 to 7192 will lead to obtaining 7460 as the answer.
- Alternatively exchange numbers to round off figures as in the given problem. For example, for calculating 8192 - 732 one can simply add 268 to both sides resulting in 8460 - 1000, which is easier to calculate, resulting in 7460.
- One needs to be prudent in selecting which number to be rounded off. For calculating 8192 - 732 one can round off 8192 to 9000 by adding 808. Then calculate 9000-732 resulting in 8268. Then subtract 808 from 8268 to get 7460 as the answer. But as it can observed, this makes the calculations difficult and lengthy.
- One may also perform the calculation in the traditional way but in a smart manner. For calculating 8192 - 732, eliminate the 2 in units place i.e. replace them with 0. Then subtract 3 from 9 yielding in 6. Finally subtract 7 from 81 yielding in 74. Then rearrange the pieces to get 7460 as the answer.
- It might be easier to start from the left (the big numbers) first.
One may guess what is needed, and accumulate one's guesses. A guess is good as long as it hasn't gone beyond the "target" number. 8192 − 732, mentally, one must add 8000 but that would be too much, so add 7000, then 700 to 1100, is 400 (so far one has 7400), and 32 to 92 can easily be recognized as 60. The result is 7460.
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