Mathematics
gatsby
2015-11-05 11:51:33
Can you divide the number 8,101,265,822,784 by 8 without using either long or short division?
ANSWERS
Naifeh278
2015-11-05 13:37:34

Yes. If we wanted to divide  104 by 8 we could write 104 as sum of multiples of 8 with which we are familiar: 104=80+24 then [latex] frac{104}{8}= frac{80+24}{8}= frac{80}{8}+ frac{24}{8}=10+3=13 [/latex] We use the same procedure to divide the given number by 8: First  We can "decompose" the number as a sum of multiples of 8 which we recognize easily. Then, divide each single one of them with 8. That is   8,101,265,822,784 = 8,000,000,000,000+100,000,000,000+1,000,000,000 +265,822,784 now decompose 265,822,784: 265,822,784=240,000,000+24,000,000+1,000,000+800,000+22,784 now decompose 22,784 22,784=16,000+6,784 decompose 6,784 6,784=6,400+384= 6,400+320+64 Thus:  8,101,265,822,784 : 8 =(8,000,000,000,000+100,000,000,000+1,000,000,000+240,000,000 +24,000,000+1,000,000+800,000+16,000+6,400+320+64):8 =1,000,000,000,000+12,500,000,000+125,000,000+30,000,000+ 3,000,000+125,000+100,000+2,000+800+40+8 =(1,000,000,000,000+12,500,000,000)+(125,000,000+30,000,000)    + 3,227,848 =1,012,500,000,000+155,000,000+3,227,848 =1,012,655,000,000+3,227,848 =1,012,658,227,848

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