This isnt just random numbers. It makes long numbers more readable and reduces chances of making an error. It does this by making the less significant digits of the numbers youre working with end in 5 or 0 (since most of us regularly work and think in the decimal number system, this simplifies the appearance of numbers a little). So, starting with 12, you add 3 to make 15. Add 5 to 15 to make 20. Add 10 to 20 to make 30. Add 2 to 30 to make 32. The sum of everything you added at each step is equal to the difference between the two numbers (3 + 5 + 10 + 2 = 20). And actually this example could (should) have combined the second and third step (15 + 15 = 30; 3 + 15 + 2 = 20). For short numbers, or when you dont need to borrow, this is not the most efficient way to do it. But its not a worse way, just a different way than were used to. A similar method, and how I personally do it in my head, is to knock off the least significant digits and add their difference later. 32 - 12 = (30 - 10) + (2 - 2) = 20 + 0 = 20 578 - 279 = (570 - 270) + (8 - 9) = 300 + -1 = 299 2 - 158 = -(150) + (2 - 8) = -150 + -6 = -156 For really large numbers, you can even do this several times: 10,788,383,839 - 1,847,447 = 10,780,000,000 + (8,383,000 - 1,847,000) + (839 - 447) = 10,780,000,000 + 6,536,000 + 392 = 10,786,536,000 + 392 = 10,786,536,392 Theres also an alternative way to do addition much along the same lines.
Posted on: Sat, 08 Mar 2014 06:36:08 +0000
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