# A treatise on elementary algebra by by James Hamblin Smith

By by James Hamblin Smith

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This fear more than anything else worries people about division. The possibility that a division will not come out even is something that produces nervousness. There is always a certain fear that a fraction will spring out suddenly, and a certain relief when a division does come out even and no fraction appears. It might therefore be comfortable, in doing divisions, if you could tell in advance, and with very little trouble, if the problem were to come out even or not. It would make very little difference arithmetically, but it might make a great deal of difference psychologically, and that is important.

Consider 5712, which has a digit sum of 6. If you subtract the 6 from 5712, you will have 5706, Quick and Easy Math 94 Division 95 which is divisible by 9. The remainder has been safely division remains the most difficult of the four arith­ extracted before the division has even been begun. metical operations. In like manner you can subtract enough to make the Division is a backward process, based on our knowl­ digit sum either 0, 3, or 6 ( whichever is closest ) and edge of multiplication. Everyone memorizes the multi­ ensure divisibility by 3.

Other combinations are possi�le, too. If the multi­ plier is 21, that can be expressed lis 20 + 1. To multiply by 20 we need only double and add a zero. Hence 52 X 21 = 52 X ( 20 + 1 ) = 1040 + 52 = 1092. As for 19, that is 20 - 1. Therefore. 64 X 19 = 64 X ( 20 - 1 ) = 1280 - 64 = 1216. Doubling ( or multiplying by 2 ) is so much simpler than multiplying �y any number higher than 2 that we ' f' ,. ought to n· -ke use of it whene\fer we can. Sometimes doing this enables us to multiply by numbers that would otherwise be tricky to handle.