A list of Anomalous Cancellations

Shalosh B. EKHAD Lots and Lots of Anomalous Cancellations By Shalosh B. Ekhad In this book, you will find listed all the anomalous cancellation where the denominator has up to , 3, digits and one digit in the numerator and one in the denominator, that must be the same, gets cancelled, and you still get something correct! Chapter 1 : The denominator has 2 digits Section 1 All the Anomalous Cancellations with the denominator with, 2, digits, and where the , 1, -th digit of the numerator is cancelled out with the, 0, -th digit of the denominator denominator= 26 \frac{6̸5}{26̸} = \frac{5}{2} Section 2 All the Anomalous Cancellations with the denominator with, 2, digits, and where the , 1, -th digit of the numerator is cancelled out with the, 1, -th digit of the denominator denominator= 64 \frac{16̸0}{6̸4} = \frac{10}{4} ————————————————————————- Chapter 2 : The denominator has 3 digits Section 1 All the Anomalous Cancellations with the denominator with, 3, digits, and where the , 1, -th digit of the numerator is cancelled out with the, 0, -th digit of the denominator denominator= 106 \frac{26̸5}{106̸} = \frac{25}{10} denominator= 146 \frac{36̸5}{146̸} = \frac{35}{14} denominator= 186 \frac{46̸5}{186̸} = \frac{45}{18} denominator= 217 \frac{77̸5}{217̸} = \frac{75}{21} denominator= 222 \frac{122̸1}{222̸} = \frac{121}{22} denominator= 226 \frac{56̸5}{226̸} = \frac{55}{22} denominator= 244 \frac{134̸2}{244̸} = \frac{132}{24} denominator= 248 \frac{108̸5}{248̸} = \frac{105}{24} denominator= 266 \frac{66̸5}{266̸} = \frac{65}{26} \frac{146̸3}{266̸} = \frac{143}{26} \frac{226̸1}{266̸} = \frac{221}{26} denominator= 288 \frac{158̸4}{288̸} = \frac{154}{28} denominator= 305 \frac{85̸4}{305̸} = \frac{84}{30} \frac{195̸2}{305̸} = \frac{192}{30} denominator= 306 \frac{76̸5}{306̸} = \frac{75}{30} denominator= 346 \frac{86̸5}{346̸} = \frac{85}{34} denominator= 357 \frac{127̸5}{357̸} = \frac{125}{35} denominator= 386 \frac{96̸5}{386̸} = \frac{95}{38} denominator= 408 \frac{178̸5}{408̸} = \frac{175}{40} denominator= 422 \frac{232̸1}{422̸} = \frac{231}{42} denominator= 426 \frac{106̸5}{426̸} = \frac{105}{42} denominator= 427 \frac{97̸6}{427̸} = \frac{96}{42} \frac{207̸4}{427̸} = \frac{204}{42} \frac{317̸2}{427̸} = \frac{312}{42} denominator= 444 \frac{144̸3}{444̸} = \frac{143}{44} \frac{244̸2}{444̸} = \frac{242}{44} \frac{344̸1}{444̸} = \frac{341}{44} denominator= 466 \frac{116̸5}{466̸} = \frac{115}{46} \frac{256̸3}{466̸} = \frac{253}{46} \frac{396̸1}{466̸} = \frac{391}{46} denominator= 488 \frac{158̸6}{488̸} = \frac{156}{48} \frac{268̸4}{488̸} = \frac{264}{48} \frac{378̸2}{488̸} = \frac{372}{48} denominator= 497 \frac{177̸5}{497̸} = \frac{175}{49} denominator= 506 \frac{126̸5}{506̸} = \frac{125}{50} denominator= 546 \frac{136̸5}{546̸} = \frac{135}{54} denominator= 555 \frac{155̸4}{555̸} = \frac{154}{55} \frac{255̸3}{555̸} = \frac{253}{55} \frac{355̸2}{555̸} = \frac{352}{55} \frac{455̸1}{555̸} = \frac{451}{55} denominator= 568 \frac{248̸5}{568̸} = \frac{245}{56} denominator= 586 \frac{146̸5}{586̸} = \frac{145}{58} denominator= 622 \frac{342̸1}{622̸} = \frac{341}{62} denominator= 626 \frac{156̸5}{626̸} = \frac{155}{62} denominator= 637 \frac{227̸5}{637̸} = \frac{225}{63} denominator= 644 \frac{354̸2}{644̸} = \frac{352}{64} denominator= 666 \frac{166̸5}{666̸} = \frac{165}{66} \frac{366̸3}{666̸} = \frac{363}{66} \frac{566̸1}{666̸} = \frac{561}{66} denominator= 688 \frac{378̸4}{688̸} = \frac{374}{68} denominator= 706 \frac{176̸5}{706̸} = \frac{175}{70} denominator= 728 \frac{318̸5}{728̸} = \frac{315}{72} denominator= 746 \frac{186̸5}{746̸} = \frac{185}{74} denominator= 777 \frac{177̸6}{777̸} = \frac{176}{77} \frac{277̸5}{777̸} = \frac{275}{77} \frac{377̸4}{777̸} = \frac{374}{77} \frac{477̸3}{777̸} = \frac{473}{77} \frac{577̸2}{777̸} = \frac{572}{77} \frac{677̸1}{777̸} = \frac{671}{77} denominator= 786 \frac{196̸5}{786̸} = \frac{195}{78} denominator= 805 \frac{225̸4}{805̸} = \frac{224}{80} \frac{515̸2}{805̸} = \frac{512}{80} denominator= 822 \frac{452̸1}{822̸} = \frac{451}{82} denominator= 826 \frac{206̸5}{826̸} = \frac{205}{82} denominator= 844 \frac{274̸3}{844̸} = \frac{273}{84} \frac{464̸2}{844̸} = \frac{462}{84} \frac{654̸1}{844̸} = \frac{651}{84} denominator= 866 \frac{216̸5}{866̸} = \frac{215}{86} \frac{476̸3}{866̸} = \frac{473}{86} \frac{736̸1}{866̸} = \frac{731}{86} denominator= 888 \frac{188̸7}{888̸} = \frac{187}{88} \frac{288̸6}{888̸} = \frac{286}{88} \frac{388̸5}{888̸} = \frac{385}{88} \frac{488̸4}{888̸} = \frac{484}{88} \frac{588̸3}{888̸} = \frac{583}{88} \frac{688̸2}{888̸} = \frac{682}{88} \frac{788̸1}{888̸} = \frac{781}{88} denominator= 906 \frac{226̸5}{906̸} = \frac{225}{90} denominator= 917 \frac{327̸5}{917̸} = \frac{325}{91} denominator= 946 \frac{236̸5}{946̸} = \frac{235}{94} denominator= 986 \frac{246̸5}{986̸} = \frac{245}{98} ————————————————————————- Section 2 All the Anomalous Cancellations with the denominator with, 3, digits, and where the , 2, -th digit of the numerator is cancelled out with the, 0, -th digit of the denominator denominator= 106 \frac{66̸25}{106̸} = \frac{625}{10} denominator= 124 \frac{54̸25}{124̸} = \frac{525}{12} denominator= 186 \frac{116̸25}{186̸} = \frac{1125}{18} denominator= 217 \frac{7̸75}{217̸} = \frac{75}{21} \frac{77̸50}{217̸} = \frac{750}{21} \frac{147̸25}{217̸} = \frac{1425}{21} denominator= 248 \frac{38̸75}{248̸} = \frac{375}{24} \frac{108̸50}{248̸} = \frac{1050}{24} \frac{178̸25}{248̸} = \frac{1725}{24} denominator= 266 \frac{6̸65}{266̸} = \frac{65}{26} \frac{46̸55}{266̸} = \frac{455}{26} \frac{86̸45}{266̸} = \frac{845}{26} \frac{126̸35}{266̸} = \frac{1235}{26} \frac{166̸25}{266̸} = \frac{1625}{26} \frac{206̸15}{266̸} = \frac{2015}{26} \frac{246̸05}{266̸} = \frac{2405}{26} denominator= 284 \frac{124̸25}{284̸} = \frac{1225}{28} denominator= 346 \frac{216̸25}{346̸} = \frac{2125}{34} denominator= 357 \frac{127̸50}{357̸} = \frac{1250}{35} denominator= 408 \frac{178̸50}{408̸} = \frac{1750}{40} denominator= 426 \frac{266̸25}{426̸} = \frac{2625}{42} denominator= 427 \frac{97̸60}{427̸} = \frac{960}{42} \frac{207̸40}{427̸} = \frac{2040}{42} \frac{317̸20}{427̸} = \frac{3120}{42} denominator= 488 \frac{158̸60}{488̸} = \frac{1560}{48} \frac{378̸20}{488̸} = \frac{3720}{48} denominator= 497 \frac{17̸75}{497̸} = \frac{175}{49} \frac{177̸50}{497̸} = \frac{1750}{49} \frac{337̸25}{497̸} = \frac{3325}{49} denominator= 506 \frac{316̸25}{506̸} = \frac{3125}{50} denominator= 568 \frac{88̸75}{568̸} = \frac{875}{56} \frac{248̸50}{568̸} = \frac{2450}{56} \frac{408̸25}{568̸} = \frac{4025}{56} denominator= 586 \frac{366̸25}{586̸} = \frac{3625}{58} denominator= 604 \frac{264̸25}{604̸} = \frac{2625}{60} denominator= 622 \frac{202̸15}{622̸} = \frac{2015}{62} \frac{482̸05}{622̸} = \frac{4805}{62} denominator= 637 \frac{227̸50}{637̸} = \frac{2250}{63} denominator= 728 \frac{318̸50}{728̸} = \frac{3150}{72} denominator= 746 \frac{466̸25}{746̸} = \frac{4625}{74} denominator= 764 \frac{334̸25}{764̸} = \frac{3325}{76} denominator= 826 \frac{516̸25}{826̸} = \frac{5125}{82} denominator= 844 \frac{274̸30}{844̸} = \frac{2730}{84} \frac{654̸10}{844̸} = \frac{6510}{84} denominator= 906 \frac{566̸25}{906̸} = \frac{5625}{90} denominator= 917 \frac{327̸50}{917̸} = \frac{3250}{91} denominator= 924 \frac{404̸25}{924̸} = \frac{4025}{92} denominator= 986 \frac{616̸25}{986̸} = \frac{6125}{98} ————————————————————————- Section 3 All the Anomalous Cancellations with the denominator with, 3, digits, and where the , 1, -th digit of the numerator is cancelled out with the, 1, -th digit of the denominator denominator= 160 \frac{6̸4}{16̸0} = \frac{4}{10} denominator= 190 \frac{9̸5}{19̸0} = \frac{5}{10} denominator= 192 \frac{9̸6}{19̸2} = \frac{6}{12} denominator= 194 \frac{9̸7}{19̸4} = \frac{7}{14} \frac{29̸1}{19̸4} = \frac{21}{14} denominator= 196 \frac{9̸8}{19̸6} = \frac{8}{16} \frac{29̸4}{19̸6} = \frac{24}{16} \frac{49̸0}{19̸6} = \frac{40}{16} denominator= 222 \frac{122̸1}{22̸2} = \frac{121}{22} denominator= 244 \frac{134̸2}{24̸4} = \frac{132}{24} denominator= 260 \frac{6̸5}{26̸0} = \frac{5}{20} denominator= 266 \frac{66̸5}{26̸6} = \frac{65}{26} \frac{146̸3}{26̸6} = \frac{143}{26} \frac{226̸1}{26̸6} = \frac{221}{26} denominator= 288 \frac{158̸4}{28̸8} = \frac{154}{28} denominator= 291 \frac{9̸7}{29̸1} = \frac{7}{21} \frac{19̸4}{29̸1} = \frac{14}{21} denominator= 294 \frac{9̸8}{29̸4} = \frac{8}{24} \frac{19̸6}{29̸4} = \frac{16}{24} \frac{39̸2}{29̸4} = \frac{32}{24} \frac{49̸0}{29̸4} = \frac{40}{24} denominator= 332 \frac{83̸0}{33̸2} = \frac{80}{32} denominator= 390 \frac{19̸5}{39̸0} = \frac{15}{30} denominator= 392 \frac{9̸8}{39̸2} = \frac{8}{32} \frac{19̸6}{39̸2} = \frac{16}{32} \frac{29̸4}{39̸2} = \frac{24}{32} \frac{49̸0}{39̸2} = \frac{40}{32} denominator= 394 \frac{19̸7}{39̸4} = \frac{17}{34} \frac{59̸1}{39̸4} = \frac{51}{34} denominator= 398 \frac{19̸9}{39̸8} = \frac{19}{38} \frac{59̸7}{39̸8} = \frac{57}{38} \frac{99̸5}{39̸8} = \frac{95}{38} \frac{139̸3}{39̸8} = \frac{133}{38} \frac{179̸1}{39̸8} = \frac{171}{38} denominator= 422 \frac{232̸1}{42̸2} = \frac{231}{42} denominator= 444 \frac{144̸3}{44̸4} = \frac{143}{44} \frac{244̸2}{44̸4} = \frac{242}{44} \frac{344̸1}{44̸4} = \frac{341}{44} denominator= 464 \frac{116̸0}{46̸4} = \frac{110}{44} denominator= 466 \frac{116̸5}{46̸6} = \frac{115}{46} \frac{256̸3}{46̸6} = \frac{253}{46} \frac{396̸1}{46̸6} = \frac{391}{46} denominator= 488 \frac{158̸6}{48̸8} = \frac{156}{48} \frac{268̸4}{48̸8} = \frac{264}{48} \frac{378̸2}{48̸8} = \frac{372}{48} denominator= 490 \frac{9̸8}{49̸0} = \frac{8}{40} \frac{19̸6}{49̸0} = \frac{16}{40} \frac{29̸4}{49̸0} = \frac{24}{40} \frac{39̸2}{49̸0} = \frac{32}{40} denominator= 532 \frac{13̸3}{53̸2} = \frac{13}{52} \frac{93̸1}{53̸2} = \frac{91}{52} \frac{133̸0}{53̸2} = \frac{130}{52} denominator= 555 \frac{155̸4}{55̸5} = \frac{154}{55} \frac{255̸3}{55̸5} = \frac{253}{55} \frac{355̸2}{55̸5} = \frac{352}{55} \frac{455̸1}{55̸5} = \frac{451}{55} denominator= 576 \frac{187̸2}{57̸6} = \frac{182}{56} denominator= 590 \frac{29̸5}{59̸0} = \frac{25}{50} denominator= 591 \frac{19̸7}{59̸1} = \frac{17}{51} \frac{39̸4}{59̸1} = \frac{34}{51} denominator= 592 \frac{29̸6}{59̸2} = \frac{26}{52} denominator= 596 \frac{29̸8}{59̸6} = \frac{28}{56} \frac{89̸4}{59̸6} = \frac{84}{56} \frac{149̸0}{59̸6} = \frac{140}{56} denominator= 597 \frac{19̸9}{59̸7} = \frac{19}{57} \frac{39̸8}{59̸7} = \frac{38}{57} \frac{79̸6}{59̸7} = \frac{76}{57} \frac{99̸5}{59̸7} = \frac{95}{57} \frac{139̸3}{59̸7} = \frac{133}{57} \frac{159̸2}{59̸7} = \frac{152}{57} \frac{199̸0}{59̸7} = \frac{190}{57} denominator= 598 \frac{29̸9}{59̸8} = \frac{29}{58} \frac{89̸7}{59̸8} = \frac{87}{58} \frac{149̸5}{59̸8} = \frac{145}{58} \frac{209̸3}{59̸8} = \frac{203}{58} \frac{269̸1}{59̸8} = \frac{261}{58} denominator= 622 \frac{342̸1}{62̸2} = \frac{341}{62} denominator= 644 \frac{354̸2}{64̸4} = \frac{352}{64} denominator= 664 \frac{16̸6}{66̸4} = \frac{16}{64} \frac{116̸2}{66̸4} = \frac{112}{64} \frac{166̸0}{66̸4} = \frac{160}{64} denominator= 665 \frac{26̸6}{66̸5} = \frac{26}{65} \frac{106̸4}{66̸5} = \frac{104}{65} \frac{146̸3}{66̸5} = \frac{143}{65} \frac{186̸2}{66̸5} = \frac{182}{65} \frac{226̸1}{66̸5} = \frac{221}{65} denominator= 666 \frac{166̸5}{66̸6} = \frac{165}{66} \frac{366̸3}{66̸6} = \frac{363}{66} \frac{566̸1}{66̸6} = \frac{561}{66} denominator= 688 \frac{378̸4}{68̸8} = \frac{374}{68} denominator= 732 \frac{183̸0}{73̸2} = \frac{180}{72} denominator= 775 \frac{217̸0}{77̸5} = \frac{210}{75} denominator= 777 \frac{177̸6}{77̸7} = \frac{176}{77} \frac{277̸5}{77̸7} = \frac{275}{77} \frac{377̸4}{77̸7} = \frac{374}{77} \frac{477̸3}{77̸7} = \frac{473}{77} \frac{577̸2}{77̸7} = \frac{572}{77} \frac{677̸1}{77̸7} = \frac{671}{77} denominator= 790 \frac{39̸5}{79̸0} = \frac{35}{70} denominator= 794 \frac{39̸7}{79̸4} = \frac{37}{74} \frac{119̸1}{79̸4} = \frac{111}{74} denominator= 796 \frac{19̸9}{79̸6} = \frac{19}{76} \frac{39̸8}{79̸6} = \frac{38}{76} \frac{59̸7}{79̸6} = \frac{57}{76} \frac{99̸5}{79̸6} = \frac{95}{76} \frac{119̸4}{79̸6} = \frac{114}{76} \frac{139̸3}{79̸6} = \frac{133}{76} \frac{179̸1}{79̸6} = \frac{171}{76} \frac{199̸0}{79̸6} = \frac{190}{76} denominator= 798 \frac{39̸9}{79̸8} = \frac{39}{78} \frac{119̸7}{79̸8} = \frac{117}{78} \frac{199̸5}{79̸8} = \frac{195}{78} \frac{279̸3}{79̸8} = \frac{273}{78} \frac{359̸1}{79̸8} = \frac{351}{78} denominator= 822 \frac{452̸1}{82̸2} = \frac{451}{82} denominator= 830 \frac{33̸2}{83̸0} = \frac{32}{80} denominator= 844 \frac{274̸3}{84̸4} = \frac{273}{84} \frac{464̸2}{84̸4} = \frac{462}{84} \frac{654̸1}{84̸4} = \frac{651}{84} denominator= 854 \frac{195̸2}{85̸4} = \frac{192}{84} \frac{305̸0}{85̸4} = \frac{300}{84} denominator= 864 \frac{216̸0}{86̸4} = \frac{210}{84} denominator= 866 \frac{216̸5}{86̸6} = \frac{215}{86} \frac{476̸3}{86̸6} = \frac{473}{86} \frac{736̸1}{86̸6} = \frac{731}{86} denominator= 888 \frac{188̸7}{88̸8} = \frac{187}{88} \frac{288̸6}{88̸8} = \frac{286}{88} \frac{388̸5}{88̸8} = \frac{385}{88} \frac{488̸4}{88̸8} = \frac{484}{88} \frac{588̸3}{88̸8} = \frac{583}{88} \frac{688̸2}{88̸8} = \frac{682}{88} \frac{788̸1}{88̸8} = \frac{781}{88} denominator= 894 \frac{29̸8}{89̸4} = \frac{28}{84} \frac{59̸6}{89̸4} = \frac{56}{84} \frac{119̸2}{89̸4} = \frac{112}{84} \frac{149̸0}{89̸4} = \frac{140}{84} denominator= 897 \frac{29̸9}{89̸7} = \frac{29}{87} \frac{59̸8}{89̸7} = \frac{58}{87} \frac{119̸6}{89̸7} = \frac{116}{87} \frac{149̸5}{89̸7} = \frac{145}{87} \frac{209̸3}{89̸7} = \frac{203}{87} \frac{239̸2}{89̸7} = \frac{232}{87} \frac{299̸0}{89̸7} = \frac{290}{87} denominator= 931 \frac{13̸3}{93̸1} = \frac{13}{91} \frac{53̸2}{93̸1} = \frac{52}{91} \frac{133̸0}{93̸1} = \frac{130}{91} denominator= 932 \frac{23̸3}{93̸2} = \frac{23}{92} \frac{163̸1}{93̸2} = \frac{161}{92} \frac{233̸0}{93̸2} = \frac{230}{92} denominator= 976 \frac{207̸4}{97̸6} = \frac{204}{96} \frac{317̸2}{97̸6} = \frac{312}{96} \frac{427̸0}{97̸6} = \frac{420}{96} denominator= 992 \frac{49̸6}{99̸2} = \frac{46}{92} denominator= 994 \frac{49̸7}{99̸4} = \frac{47}{94} \frac{149̸1}{99̸4} = \frac{141}{94} denominator= 995 \frac{19̸9}{99̸5} = \frac{19}{95} \frac{39̸8}{99̸5} = \frac{38}{95} \frac{59̸7}{99̸5} = \frac{57}{95} \frac{79̸6}{99̸5} = \frac{76}{95} \frac{119̸4}{99̸5} = \frac{114}{95} \frac{139̸3}{99̸5} = \frac{133}{95} \frac{159̸2}{99̸5} = \frac{152}{95} \frac{179̸1}{99̸5} = \frac{171}{95} denominator= 996 \frac{49̸8}{99̸6} = \frac{48}{96} \frac{149̸4}{99̸6} = \frac{144}{96} \frac{249̸0}{99̸6} = \frac{240}{96} denominator= 998 \frac{49̸9}{99̸8} = \frac{49}{98} \frac{149̸7}{99̸8} = \frac{147}{98} \frac{249̸5}{99̸8} = \frac{245}{98} \frac{349̸3}{99̸8} = \frac{343}{98} \frac{449̸1}{99̸8} = \frac{441}{98} ————————————————————————- Section 4 All the Anomalous Cancellations with the denominator with, 3, digits, and where the , 2, -th digit of the numerator is cancelled out with the, 1, -th digit of the denominator denominator= 121 \frac{2̸20}{12̸1} = \frac{20}{11} \frac{22̸00}{12̸1} = \frac{200}{11} denominator= 130 \frac{3̸25}{13̸0} = \frac{25}{10} denominator= 132 \frac{3̸30}{13̸2} = \frac{30}{12} \frac{23̸10}{13̸2} = \frac{210}{12} denominator= 143 \frac{4̸40}{14̸3} = \frac{40}{13} \frac{24̸20}{14̸3} = \frac{220}{13} \frac{34̸10}{14̸3} = \frac{310}{13} \frac{44̸00}{14̸3} = \frac{400}{13} denominator= 154 \frac{5̸50}{15̸4} = \frac{50}{14} \frac{25̸30}{15̸4} = \frac{230}{14} \frac{35̸20}{15̸4} = \frac{320}{14} \frac{45̸10}{15̸4} = \frac{410}{14} \frac{55̸00}{15̸4} = \frac{500}{14} denominator= 176 \frac{7̸70}{17̸6} = \frac{70}{16} \frac{27̸50}{17̸6} = \frac{250}{16} \frac{37̸40}{17̸6} = \frac{340}{16} \frac{47̸30}{17̸6} = \frac{430}{16} \frac{57̸20}{17̸6} = \frac{520}{16} \frac{67̸10}{17̸6} = \frac{610}{16} \frac{77̸00}{17̸6} = \frac{700}{16} denominator= 187 \frac{8̸80}{18̸7} = \frac{80}{17} \frac{28̸60}{18̸7} = \frac{260}{17} \frac{38̸50}{18̸7} = \frac{350}{17} \frac{48̸40}{18̸7} = \frac{440}{17} \frac{58̸30}{18̸7} = \frac{530}{17} \frac{68̸20}{18̸7} = \frac{620}{17} \frac{78̸10}{18̸7} = \frac{710}{17} \frac{88̸00}{18̸7} = \frac{800}{17} denominator= 220 \frac{12̸10}{22̸0} = \frac{110}{20} denominator= 231 \frac{3̸30}{23̸1} = \frac{30}{21} \frac{13̸20}{23̸1} = \frac{120}{21} \frac{33̸00}{23̸1} = \frac{300}{21} denominator= 242 \frac{4̸40}{24̸2} = \frac{40}{22} \frac{14̸30}{24̸2} = \frac{130}{22} \frac{34̸10}{24̸2} = \frac{310}{22} \frac{44̸00}{24̸2} = \frac{400}{22} denominator= 253 \frac{5̸50}{25̸3} = \frac{50}{23} \frac{15̸40}{25̸3} = \frac{140}{23} \frac{35̸20}{25̸3} = \frac{320}{23} \frac{45̸10}{25̸3} = \frac{410}{23} \frac{55̸00}{25̸3} = \frac{500}{23} denominator= 260 \frac{6̸50}{26̸0} = \frac{50}{20} \frac{16̸25}{26̸0} = \frac{125}{20} denominator= 262 \frac{6̸55}{26̸2} = \frac{55}{22} denominator= 264 \frac{6̸60}{26̸4} = \frac{60}{24} \frac{16̸50}{26̸4} = \frac{150}{24} \frac{36̸30}{26̸4} = \frac{330}{24} \frac{46̸20}{26̸4} = \frac{420}{24} \frac{56̸10}{26̸4} = \frac{510}{24} denominator= 266 \frac{6̸65}{26̸6} = \frac{65}{26} \frac{46̸55}{26̸6} = \frac{455}{26} \frac{86̸45}{26̸6} = \frac{845}{26} \frac{126̸35}{26̸6} = \frac{1235}{26} \frac{166̸25}{26̸6} = \frac{1625}{26} \frac{206̸15}{26̸6} = \frac{2015}{26} \frac{246̸05}{26̸6} = \frac{2405}{26} denominator= 270 \frac{7̸56}{27̸0} = \frac{56}{20} \frac{17̸28}{27̸0} = \frac{128}{20} denominator= 275 \frac{7̸70}{27̸5} = \frac{70}{25} \frac{17̸60}{27̸5} = \frac{160}{25} \frac{37̸40}{27̸5} = \frac{340}{25} \frac{47̸30}{27̸5} = \frac{430}{25} \frac{57̸20}{27̸5} = \frac{520}{25} \frac{67̸10}{27̸5} = \frac{610}{25} denominator= 286 \frac{8̸80}{28̸6} = \frac{80}{26} \frac{18̸70}{28̸6} = \frac{170}{26} \frac{38̸50}{28̸6} = \frac{350}{26} \frac{48̸40}{28̸6} = \frac{440}{26} \frac{58̸30}{28̸6} = \frac{530}{26} \frac{68̸20}{28̸6} = \frac{620}{26} \frac{78̸10}{28̸6} = \frac{710}{26} \frac{88̸00}{28̸6} = \frac{800}{26} denominator= 291 \frac{9̸70}{29̸1} = \frac{70}{21} \frac{19̸40}{29̸1} = \frac{140}{21} denominator= 294 \frac{9̸80}{29̸4} = \frac{80}{24} \frac{19̸60}{29̸4} = \frac{160}{24} \frac{39̸20}{29̸4} = \frac{320}{24} \frac{49̸00}{29̸4} = \frac{400}{24} denominator= 297 \frac{9̸90}{29̸7} = \frac{90}{27} \frac{19̸80}{29̸7} = \frac{180}{27} \frac{39̸60}{29̸7} = \frac{360}{27} \frac{49̸50}{29̸7} = \frac{450}{27} \frac{69̸30}{29̸7} = \frac{630}{27} \frac{79̸20}{29̸7} = \frac{720}{27} \frac{99̸00}{29̸7} = \frac{900}{27} denominator= 341 \frac{4̸40}{34̸1} = \frac{40}{31} \frac{14̸30}{34̸1} = \frac{130}{31} \frac{24̸20}{34̸1} = \frac{220}{31} \frac{44̸00}{34̸1} = \frac{400}{31} denominator= 352 \frac{5̸50}{35̸2} = \frac{50}{32} \frac{15̸40}{35̸2} = \frac{140}{32} \frac{25̸30}{35̸2} = \frac{230}{32} \frac{45̸10}{35̸2} = \frac{410}{32} \frac{55̸00}{35̸2} = \frac{500}{32} denominator= 354 \frac{115̸05}{35̸4} = \frac{1105}{34} denominator= 363 \frac{6̸60}{36̸3} = \frac{60}{33} \frac{16̸50}{36̸3} = \frac{150}{33} \frac{26̸40}{36̸3} = \frac{240}{33} \frac{46̸20}{36̸3} = \frac{420}{33} \frac{56̸10}{36̸3} = \frac{510}{33} \frac{66̸00}{36̸3} = \frac{600}{33} denominator= 374 \frac{7̸70}{37̸4} = \frac{70}{34} \frac{17̸60}{37̸4} = \frac{160}{34} \frac{27̸50}{37̸4} = \frac{250}{34} \frac{47̸30}{37̸4} = \frac{430}{34} \frac{57̸20}{37̸4} = \frac{520}{34} \frac{67̸10}{37̸4} = \frac{610}{34} \frac{77̸00}{37̸4} = \frac{700}{34} denominator= 385 \frac{8̸80}{38̸5} = \frac{80}{35} \frac{18̸70}{38̸5} = \frac{170}{35} \frac{28̸60}{38̸5} = \frac{260}{35} \frac{48̸40}{38̸5} = \frac{440}{35} \frac{58̸30}{38̸5} = \frac{530}{35} \frac{68̸20}{38̸5} = \frac{620}{35} \frac{78̸10}{38̸5} = \frac{710}{35} \frac{88̸00}{38̸5} = \frac{800}{35} denominator= 390 \frac{9̸75}{39̸0} = \frac{75}{30} \frac{29̸25}{39̸0} = \frac{225}{30} denominator= 392 \frac{9̸80}{39̸2} = \frac{80}{32} \frac{29̸40}{39̸2} = \frac{240}{32} \frac{49̸00}{39̸2} = \frac{400}{32} denominator= 394 \frac{9̸85}{39̸4} = \frac{85}{34} \frac{29̸55}{39̸4} = \frac{255}{34} \frac{49̸25}{39̸4} = \frac{425}{34} denominator= 396 \frac{9̸90}{39̸6} = \frac{90}{36} \frac{29̸70}{39̸6} = \frac{270}{36} \frac{49̸50}{39̸6} = \frac{450}{36} \frac{69̸30}{39̸6} = \frac{630}{36} \frac{89̸10}{39̸6} = \frac{810}{36} denominator= 398 \frac{9̸95}{39̸8} = \frac{95}{38} \frac{29̸85}{39̸8} = \frac{285}{38} \frac{49̸75}{39̸8} = \frac{475}{38} \frac{69̸65}{39̸8} = \frac{665}{38} \frac{89̸55}{39̸8} = \frac{855}{38} \frac{109̸45}{39̸8} = \frac{1045}{38} \frac{129̸35}{39̸8} = \frac{1235}{38} \frac{149̸25}{39̸8} = \frac{1425}{38} \frac{169̸15}{39̸8} = \frac{1615}{38} \frac{189̸05}{39̸8} = \frac{1805}{38} denominator= 440 \frac{14̸30}{44̸0} = \frac{130}{40} \frac{24̸20}{44̸0} = \frac{220}{40} \frac{34̸10}{44̸0} = \frac{310}{40} denominator= 442 \frac{24̸31}{44̸2} = \frac{231}{42} \frac{64̸09}{44̸2} = \frac{609}{42} denominator= 451 \frac{5̸50}{45̸1} = \frac{50}{41} \frac{15̸40}{45̸1} = \frac{140}{41} \frac{25̸30}{45̸1} = \frac{230}{41} \frac{35̸20}{45̸1} = \frac{320}{41} \frac{55̸00}{45̸1} = \frac{500}{41} denominator= 462 \frac{6̸60}{46̸2} = \frac{60}{42} \frac{16̸50}{46̸2} = \frac{150}{42} \frac{26̸40}{46̸2} = \frac{240}{42} \frac{36̸30}{46̸2} = \frac{330}{42} \frac{56̸10}{46̸2} = \frac{510}{42} \frac{66̸00}{46̸2} = \frac{600}{42} denominator= 473 \frac{7̸70}{47̸3} = \frac{70}{43} \frac{17̸60}{47̸3} = \frac{160}{43} \frac{27̸50}{47̸3} = \frac{250}{43} \frac{37̸40}{47̸3} = \frac{340}{43} \frac{57̸20}{47̸3} = \frac{520}{43} \frac{67̸10}{47̸3} = \frac{610}{43} \frac{77̸00}{47̸3} = \frac{700}{43} denominator= 484 \frac{8̸80}{48̸4} = \frac{80}{44} \frac{18̸70}{48̸4} = \frac{170}{44} \frac{28̸60}{48̸4} = \frac{260}{44} \frac{38̸50}{48̸4} = \frac{350}{44} \frac{58̸30}{48̸4} = \frac{530}{44} \frac{68̸20}{48̸4} = \frac{620}{44} \frac{78̸10}{48̸4} = \frac{710}{44} \frac{88̸00}{48̸4} = \frac{800}{44} denominator= 488 \frac{158̸60}{48̸8} = \frac{1560}{48} \frac{378̸20}{48̸8} = \frac{3720}{48} denominator= 530 \frac{13̸25}{53̸0} = \frac{125}{50} denominator= 532 \frac{13̸30}{53̸2} = \frac{130}{52} \frac{33̸25}{53̸2} = \frac{325}{52} \frac{73̸15}{53̸2} = \frac{715}{52} \frac{93̸10}{53̸2} = \frac{910}{52} \frac{113̸05}{53̸2} = \frac{1105}{52} denominator= 550 \frac{15̸40}{55̸0} = \frac{140}{50} \frac{25̸30}{55̸0} = \frac{230}{50} \frac{35̸20}{55̸0} = \frac{320}{50} \frac{45̸10}{55̸0} = \frac{410}{50} denominator= 561 \frac{6̸60}{56̸1} = \frac{60}{51} \frac{16̸50}{56̸1} = \frac{150}{51} \frac{26̸40}{56̸1} = \frac{240}{51} \frac{36̸30}{56̸1} = \frac{330}{51} \frac{46̸20}{56̸1} = \frac{420}{51} \frac{66̸00}{56̸1} = \frac{600}{51} denominator= 572 \frac{7̸70}{57̸2} = \frac{70}{52} \frac{17̸60}{57̸2} = \frac{160}{52} \frac{27̸50}{57̸2} = \frac{250}{52} \frac{37̸40}{57̸2} = \frac{340}{52} \frac{47̸30}{57̸2} = \frac{430}{52} \frac{67̸10}{57̸2} = \frac{610}{52} \frac{77̸00}{57̸2} = \frac{700}{52} denominator= 576 \frac{187̸20}{57̸6} = \frac{1820}{56} denominator= 583 \frac{8̸80}{58̸3} = \frac{80}{53} \frac{18̸70}{58̸3} = \frac{170}{53} \frac{28̸60}{58̸3} = \frac{260}{53} \frac{38̸50}{58̸3} = \frac{350}{53} \frac{48̸40}{58̸3} = \frac{440}{53} \frac{68̸20}{58̸3} = \frac{620}{53} \frac{78̸10}{58̸3} = \frac{710}{53} \frac{88̸00}{58̸3} = \frac{800}{53} denominator= 591 \frac{9̸85}{59̸1} = \frac{85}{51} \frac{19̸70}{59̸1} = \frac{170}{51} \frac{39̸40}{59̸1} = \frac{340}{51} \frac{49̸25}{59̸1} = \frac{425}{51} denominator= 594 \frac{9̸90}{59̸4} = \frac{90}{54} \frac{19̸80}{59̸4} = \frac{180}{54} \frac{39̸60}{59̸4} = \frac{360}{54} \frac{49̸50}{59̸4} = \frac{450}{54} \frac{69̸30}{59̸4} = \frac{630}{54} \frac{79̸20}{59̸4} = \frac{720}{54} \frac{99̸00}{59̸4} = \frac{900}{54} denominator= 597 \frac{9̸95}{59̸7} = \frac{95}{57} \frac{19̸90}{59̸7} = \frac{190}{57} \frac{39̸80}{59̸7} = \frac{380}{57} \frac{49̸75}{59̸7} = \frac{475}{57} \frac{69̸65}{59̸7} = \frac{665}{57} \frac{79̸60}{59̸7} = \frac{760}{57} \frac{99̸50}{59̸7} = \frac{950}{57} \frac{109̸45}{59̸7} = \frac{1045}{57} \frac{129̸35}{59̸7} = \frac{1235}{57} \frac{139̸30}{59̸7} = \frac{1330}{57} \frac{159̸20}{59̸7} = \frac{1520}{57} \frac{169̸15}{59̸7} = \frac{1615}{57} \frac{189̸05}{59̸7} = \frac{1805}{57} \frac{199̸00}{59̸7} = \frac{1900}{57} denominator= 622 \frac{202̸15}{62̸2} = \frac{2015}{62} \frac{482̸05}{62̸2} = \frac{4805}{62} denominator= 660 \frac{16̸50}{66̸0} = \frac{150}{60} \frac{36̸30}{66̸0} = \frac{330}{60} \frac{56̸10}{66̸0} = \frac{510}{60} denominator= 662 \frac{16̸55}{66̸2} = \frac{155}{62} \frac{36̸41}{66̸2} = \frac{341}{62} \frac{56̸27}{66̸2} = \frac{527}{62} \frac{76̸13}{66̸2} = \frac{713}{62} denominator= 664 \frac{16̸60}{66̸4} = \frac{160}{64} \frac{36̸52}{66̸4} = \frac{352}{64} \frac{56̸44}{66̸4} = \frac{544}{64} \frac{76̸36}{66̸4} = \frac{736}{64} \frac{96̸28}{66̸4} = \frac{928}{64} \frac{116̸20}{66̸4} = \frac{1120}{64} \frac{136̸12}{66̸4} = \frac{1312}{64} \frac{156̸04}{66̸4} = \frac{1504}{64} denominator= 671 \frac{7̸70}{67̸1} = \frac{70}{61} \frac{17̸60}{67̸1} = \frac{160}{61} \frac{27̸50}{67̸1} = \frac{250}{61} \frac{37̸40}{67̸1} = \frac{340}{61} \frac{47̸30}{67̸1} = \frac{430}{61} \frac{57̸20}{67̸1} = \frac{520}{61} \frac{77̸00}{67̸1} = \frac{700}{61} denominator= 682 \frac{8̸80}{68̸2} = \frac{80}{62} \frac{18̸70}{68̸2} = \frac{170}{62} \frac{28̸60}{68̸2} = \frac{260}{62} \frac{38̸50}{68̸2} = \frac{350}{62} \frac{48̸40}{68̸2} = \frac{440}{62} \frac{58̸30}{68̸2} = \frac{530}{62} \frac{78̸10}{68̸2} = \frac{710}{62} \frac{88̸00}{68̸2} = \frac{800}{62} denominator= 693 \frac{9̸90}{69̸3} = \frac{90}{63} \frac{19̸80}{69̸3} = \frac{180}{63} \frac{29̸70}{69̸3} = \frac{270}{63} \frac{39̸60}{69̸3} = \frac{360}{63} \frac{49̸50}{69̸3} = \frac{450}{63} \frac{59̸40}{69̸3} = \frac{540}{63} \frac{79̸20}{69̸3} = \frac{720}{63} \frac{89̸10}{69̸3} = \frac{810}{63} \frac{99̸00}{69̸3} = \frac{900}{63} denominator= 754 \frac{245̸05}{75̸4} = \frac{2405}{74} denominator= 770 \frac{17̸60}{77̸0} = \frac{160}{70} \frac{27̸50}{77̸0} = \frac{250}{70} \frac{37̸40}{77̸0} = \frac{340}{70} \frac{47̸30}{77̸0} = \frac{430}{70} \frac{57̸20}{77̸0} = \frac{520}{70} \frac{67̸10}{77̸0} = \frac{610}{70} denominator= 781 \frac{8̸80}{78̸1} = \frac{80}{71} \frac{18̸70}{78̸1} = \frac{170}{71} \frac{28̸60}{78̸1} = \frac{260}{71} \frac{38̸50}{78̸1} = \frac{350}{71} \frac{48̸40}{78̸1} = \frac{440}{71} \frac{58̸30}{78̸1} = \frac{530}{71} \frac{68̸20}{78̸1} = \frac{620}{71} \frac{88̸00}{78̸1} = \frac{800}{71} denominator= 790 \frac{19̸75}{79̸0} = \frac{175}{70} \frac{59̸25}{79̸0} = \frac{525}{70} denominator= 792 \frac{9̸90}{79̸2} = \frac{90}{72} \frac{19̸80}{79̸2} = \frac{180}{72} \frac{29̸70}{79̸2} = \frac{270}{72} \frac{49̸50}{79̸2} = \frac{450}{72} \frac{59̸40}{79̸2} = \frac{540}{72} \frac{69̸30}{79̸2} = \frac{630}{72} \frac{89̸10}{79̸2} = \frac{810}{72} \frac{99̸00}{79̸2} = \frac{900}{72} denominator= 794 \frac{19̸85}{79̸4} = \frac{185}{74} \frac{59̸55}{79̸4} = \frac{555}{74} \frac{99̸25}{79̸4} = \frac{925}{74} denominator= 796 \frac{9̸95}{79̸6} = \frac{95}{76} \frac{19̸90}{79̸6} = \frac{190}{76} \frac{29̸85}{79̸6} = \frac{285}{76} \frac{49̸75}{79̸6} = \frac{475}{76} \frac{59̸70}{79̸6} = \frac{570}{76} \frac{69̸65}{79̸6} = \frac{665}{76} \frac{89̸55}{79̸6} = \frac{855}{76} \frac{99̸50}{79̸6} = \frac{950}{76} \frac{109̸45}{79̸6} = \frac{1045}{76} \frac{129̸35}{79̸6} = \frac{1235}{76} \frac{139̸30}{79̸6} = \frac{1330}{76} \frac{149̸25}{79̸6} = \frac{1425}{76} \frac{169̸15}{79̸6} = \frac{1615}{76} \frac{179̸10}{79̸6} = \frac{1710}{76} \frac{189̸05}{79̸6} = \frac{1805}{76} denominator= 798 \frac{19̸95}{79̸8} = \frac{195}{78} \frac{59̸85}{79̸8} = \frac{585}{78} \frac{99̸75}{79̸8} = \frac{975}{78} \frac{139̸65}{79̸8} = \frac{1365}{78} \frac{179̸55}{79̸8} = \frac{1755}{78} \frac{219̸45}{79̸8} = \frac{2145}{78} \frac{259̸35}{79̸8} = \frac{2535}{78} \frac{299̸25}{79̸8} = \frac{2925}{78} \frac{339̸15}{79̸8} = \frac{3315}{78} \frac{379̸05}{79̸8} = \frac{3705}{78} denominator= 830 \frac{3̸32}{83̸0} = \frac{32}{80} \frac{13̸28}{83̸0} = \frac{128}{80} \frac{23̸24}{83̸0} = \frac{224}{80} \frac{43̸16}{83̸0} = \frac{416}{80} \frac{53̸12}{83̸0} = \frac{512}{80} \frac{63̸08}{83̸0} = \frac{608}{80} \frac{73̸04}{83̸0} = \frac{704}{80} denominator= 844 \frac{274̸30}{84̸4} = \frac{2730}{84} \frac{654̸10}{84̸4} = \frac{6510}{84} denominator= 854 \frac{195̸20}{85̸4} = \frac{1920}{84} \frac{305̸00}{85̸4} = \frac{3000}{84} denominator= 880 \frac{18̸70}{88̸0} = \frac{170}{80} \frac{28̸60}{88̸0} = \frac{260}{80} \frac{38̸50}{88̸0} = \frac{350}{80} \frac{48̸40}{88̸0} = \frac{440}{80} \frac{58̸30}{88̸0} = \frac{530}{80} \frac{68̸20}{88̸0} = \frac{620}{80} \frac{78̸10}{88̸0} = \frac{710}{80} denominator= 882 \frac{48̸51}{88̸2} = \frac{451}{82} denominator= 884 \frac{28̸73}{88̸4} = \frac{273}{84} \frac{48̸62}{88̸4} = \frac{462}{84} \frac{68̸51}{88̸4} = \frac{651}{84} \frac{108̸29}{88̸4} = \frac{1029}{84} \frac{128̸18}{88̸4} = \frac{1218}{84} \frac{148̸07}{88̸4} = \frac{1407}{84} denominator= 886 \frac{48̸73}{88̸6} = \frac{473}{86} \frac{128̸47}{88̸6} = \frac{1247}{86} \frac{208̸21}{88̸6} = \frac{2021}{86} denominator= 891 \frac{9̸90}{89̸1} = \frac{90}{81} \frac{19̸80}{89̸1} = \frac{180}{81} \frac{29̸70}{89̸1} = \frac{270}{81} \frac{39̸60}{89̸1} = \frac{360}{81} \frac{49̸50}{89̸1} = \frac{450}{81} \frac{59̸40}{89̸1} = \frac{540}{81} \frac{69̸30}{89̸1} = \frac{630}{81} \frac{79̸20}{89̸1} = \frac{720}{81} \frac{99̸00}{89̸1} = \frac{900}{81} denominator= 894 \frac{29̸80}{89̸4} = \frac{280}{84} \frac{59̸60}{89̸4} = \frac{560}{84} \frac{119̸20}{89̸4} = \frac{1120}{84} \frac{149̸00}{89̸4} = \frac{1400}{84} denominator= 897 \frac{29̸90}{89̸7} = \frac{290}{87} \frac{59̸80}{89̸7} = \frac{580}{87} \frac{119̸60}{89̸7} = \frac{1160}{87} \frac{149̸50}{89̸7} = \frac{1450}{87} \frac{209̸30}{89̸7} = \frac{2030}{87} \frac{239̸20}{89̸7} = \frac{2320}{87} \frac{299̸00}{89̸7} = \frac{2900}{87} denominator= 930 \frac{23̸25}{93̸0} = \frac{225}{90} denominator= 931 \frac{13̸30}{93̸1} = \frac{130}{91} \frac{33̸25}{93̸1} = \frac{325}{91} \frac{53̸20}{93̸1} = \frac{520}{91} \frac{73̸15}{93̸1} = \frac{715}{91} \frac{113̸05}{93̸1} = \frac{1105}{91} \frac{133̸00}{93̸1} = \frac{1300}{91} denominator= 932 \frac{23̸30}{93̸2} = \frac{230}{92} \frac{163̸10}{93̸2} = \frac{1610}{92} denominator= 976 \frac{207̸40}{97̸6} = \frac{2040}{96} \frac{317̸20}{97̸6} = \frac{3120}{96} \frac{427̸00}{97̸6} = \frac{4200}{96} ————————————————————————- Section 5 All the Anomalous Cancellations with the denominator with, 3, digits, and where the , 1, -th digit of the numerator is cancelled out with the, 2, -th digit of the denominator denominator= 120 \frac{1̸2}{1̸20} = \frac{2}{20} denominator= 130 \frac{1̸3}{1̸30} = \frac{3}{30} denominator= 140 \frac{1̸4}{1̸40} = \frac{4}{40} denominator= 150 \frac{1̸5}{1̸50} = \frac{5}{50} denominator= 160 \frac{1̸6}{1̸60} = \frac{6}{60} denominator= 170 \frac{1̸7}{1̸70} = \frac{7}{70} denominator= 180 \frac{1̸8}{1̸80} = \frac{8}{80} denominator= 190 \frac{1̸9}{1̸90} = \frac{9}{90} denominator= 210 \frac{2̸1}{2̸10} = \frac{1}{10} denominator= 222 \frac{122̸1}{2̸22} = \frac{121}{22} denominator= 240 \frac{2̸4}{2̸40} = \frac{4}{40} denominator= 260 \frac{2̸6}{2̸60} = \frac{6}{60} denominator= 280 \frac{2̸8}{2̸80} = \frac{8}{80} denominator= 310 \frac{3̸1}{3̸10} = \frac{1}{10} denominator= 320 \frac{3̸2}{3̸20} = \frac{2}{20} denominator= 325 \frac{13̸0}{3̸25} = \frac{10}{25} denominator= 332 \frac{83̸0}{3̸32} = \frac{80}{32} denominator= 360 \frac{3̸6}{3̸60} = \frac{6}{60} denominator= 370 \frac{3̸7}{3̸70} = \frac{7}{70} denominator= 380 \frac{3̸8}{3̸80} = \frac{8}{80} denominator= 390 \frac{3̸9}{3̸90} = \frac{9}{90} denominator= 410 \frac{4̸1}{4̸10} = \frac{1}{10} denominator= 420 \frac{4̸2}{4̸20} = \frac{2}{20} denominator= 430 \frac{4̸3}{4̸30} = \frac{3}{30} denominator= 444 \frac{144̸3}{4̸44} = \frac{143}{44} \frac{244̸2}{4̸44} = \frac{242}{44} \frac{344̸1}{4̸44} = \frac{341}{44} denominator= 510 \frac{5̸1}{5̸10} = \frac{1}{10} denominator= 520 \frac{5̸2}{5̸20} = \frac{2}{20} denominator= 530 \frac{5̸3}{5̸30} = \frac{3}{30} denominator= 540 \frac{5̸4}{5̸40} = \frac{4}{40} denominator= 555 \frac{155̸4}{5̸55} = \frac{154}{55} \frac{255̸3}{5̸55} = \frac{253}{55} \frac{355̸2}{5̸55} = \frac{352}{55} \frac{455̸1}{5̸55} = \frac{451}{55} denominator= 610 \frac{6̸1}{6̸10} = \frac{1}{10} denominator= 620 \frac{6̸2}{6̸20} = \frac{2}{20} denominator= 630 \frac{6̸3}{6̸30} = \frac{3}{30} denominator= 640 \frac{6̸4}{6̸40} = \frac{4}{40} \frac{16̸0}{6̸40} = \frac{10}{40} denominator= 644 \frac{16̸1}{6̸44} = \frac{11}{44} denominator= 648 \frac{16̸2}{6̸48} = \frac{12}{48} denominator= 650 \frac{6̸5}{6̸50} = \frac{5}{50} \frac{26̸0}{6̸50} = \frac{20}{50} denominator= 652 \frac{16̸3}{6̸52} = \frac{13}{52} denominator= 655 \frac{26̸2}{6̸55} = \frac{22}{55} denominator= 656 \frac{16̸4}{6̸56} = \frac{14}{56} denominator= 664 \frac{16̸6}{6̸64} = \frac{16}{64} \frac{116̸2}{6̸64} = \frac{112}{64} \frac{166̸0}{6̸64} = \frac{160}{64} denominator= 665 \frac{26̸6}{6̸65} = \frac{26}{65} \frac{106̸4}{6̸65} = \frac{104}{65} \frac{146̸3}{6̸65} = \frac{143}{65} \frac{186̸2}{6̸65} = \frac{182}{65} \frac{226̸1}{6̸65} = \frac{221}{65} denominator= 666 \frac{166̸5}{6̸66} = \frac{165}{66} \frac{366̸3}{6̸66} = \frac{363}{66} \frac{566̸1}{6̸66} = \frac{561}{66} denominator= 710 \frac{7̸1}{7̸10} = \frac{1}{10} denominator= 720 \frac{7̸2}{7̸20} = \frac{2}{20} denominator= 730 \frac{7̸3}{7̸30} = \frac{3}{30} denominator= 740 \frac{7̸4}{7̸40} = \frac{4}{40} denominator= 750 \frac{7̸5}{7̸50} = \frac{5}{50} denominator= 756 \frac{27̸0}{7̸56} = \frac{20}{56} denominator= 760 \frac{7̸6}{7̸60} = \frac{6}{60} denominator= 775 \frac{217̸0}{7̸75} = \frac{210}{75} denominator= 777 \frac{177̸6}{7̸77} = \frac{176}{77} \frac{277̸5}{7̸77} = \frac{275}{77} \frac{377̸4}{7̸77} = \frac{374}{77} \frac{477̸3}{7̸77} = \frac{473}{77} \frac{577̸2}{7̸77} = \frac{572}{77} \frac{677̸1}{7̸77} = \frac{671}{77} denominator= 810 \frac{8̸1}{8̸10} = \frac{1}{10} denominator= 820 \frac{8̸2}{8̸20} = \frac{2}{20} denominator= 830 \frac{8̸3}{8̸30} = \frac{3}{30} denominator= 840 \frac{8̸4}{8̸40} = \frac{4}{40} denominator= 850 \frac{8̸5}{8̸50} = \frac{5}{50} denominator= 860 \frac{8̸6}{8̸60} = \frac{6}{60} denominator= 870 \frac{8̸7}{8̸70} = \frac{7}{70} denominator= 888 \frac{188̸7}{8̸88} = \frac{187}{88} \frac{288̸6}{8̸88} = \frac{286}{88} \frac{388̸5}{8̸88} = \frac{385}{88} \frac{488̸4}{8̸88} = \frac{484}{88} \frac{588̸3}{8̸88} = \frac{583}{88} \frac{688̸2}{8̸88} = \frac{682}{88} \frac{788̸1}{8̸88} = \frac{781}{88} denominator= 910 \frac{9̸1}{9̸10} = \frac{1}{10} denominator= 920 \frac{9̸2}{9̸20} = \frac{2}{20} denominator= 930 \frac{9̸3}{9̸30} = \frac{3}{30} denominator= 940 \frac{9̸4}{9̸40} = \frac{4}{40} denominator= 950 \frac{9̸5}{9̸50} = \frac{5}{50} \frac{19̸0}{9̸50} = \frac{10}{50} denominator= 955 \frac{19̸1}{9̸55} = \frac{11}{55} denominator= 960 \frac{9̸6}{9̸60} = \frac{6}{60} \frac{19̸2}{9̸60} = \frac{12}{60} denominator= 965 \frac{19̸3}{9̸65} = \frac{13}{65} denominator= 970 \frac{9̸7}{9̸70} = \frac{7}{70} \frac{19̸4}{9̸70} = \frac{14}{70} \frac{29̸1}{9̸70} = \frac{21}{70} denominator= 975 \frac{19̸5}{9̸75} = \frac{15}{75} \frac{39̸0}{9̸75} = \frac{30}{75} denominator= 980 \frac{9̸8}{9̸80} = \frac{8}{80} \frac{19̸6}{9̸80} = \frac{16}{80} \frac{29̸4}{9̸80} = \frac{24}{80} \frac{39̸2}{9̸80} = \frac{32}{80} \frac{49̸0}{9̸80} = \frac{40}{80} denominator= 982 \frac{49̸1}{9̸82} = \frac{41}{82} denominator= 984 \frac{49̸2}{9̸84} = \frac{42}{84} denominator= 985 \frac{19̸7}{9̸85} = \frac{17}{85} \frac{39̸4}{9̸85} = \frac{34}{85} \frac{59̸1}{9̸85} = \frac{51}{85} denominator= 986 \frac{49̸3}{9̸86} = \frac{43}{86} denominator= 988 \frac{49̸4}{9̸88} = \frac{44}{88} denominator= 992 \frac{49̸6}{9̸92} = \frac{46}{92} denominator= 994 \frac{49̸7}{9̸94} = \frac{47}{94} \frac{149̸1}{9̸94} = \frac{141}{94} denominator= 995 \frac{19̸9}{9̸95} = \frac{19}{95} \frac{39̸8}{9̸95} = \frac{38}{95} \frac{59̸7}{9̸95} = \frac{57}{95} \frac{79̸6}{9̸95} = \frac{76}{95} \frac{119̸4}{9̸95} = \frac{114}{95} \frac{139̸3}{9̸95} = \frac{133}{95} \frac{159̸2}{9̸95} = \frac{152}{95} \frac{179̸1}{9̸95} = \frac{171}{95} denominator= 996 \frac{49̸8}{9̸96} = \frac{48}{96} \frac{149̸4}{9̸96} = \frac{144}{96} \frac{249̸0}{9̸96} = \frac{240}{96} denominator= 998 \frac{49̸9}{9̸98} = \frac{49}{98} \frac{149̸7}{9̸98} = \frac{147}{98} \frac{249̸5}{9̸98} = \frac{245}{98} \frac{349̸3}{9̸98} = \frac{343}{98} \frac{449̸1}{9̸98} = \frac{441}{98} ————————————————————————- Section 6 All the Anomalous Cancellations with the denominator with, 3, digits, and where the , 2, -th digit of the numerator is cancelled out with the, 2, -th digit of the denominator denominator= 220 \frac{12̸10}{2̸20} = \frac{110}{20} denominator= 432 \frac{14̸04}{4̸32} = \frac{104}{32} denominator= 436 \frac{14̸17}{4̸36} = \frac{117}{36} denominator= 438 \frac{24̸09}{4̸38} = \frac{209}{38} denominator= 440 \frac{14̸30}{4̸40} = \frac{130}{40} \frac{24̸20}{4̸40} = \frac{220}{40} \frac{34̸10}{4̸40} = \frac{310}{40} denominator= 442 \frac{24̸31}{4̸42} = \frac{231}{42} \frac{64̸09}{4̸42} = \frac{609}{42} denominator= 540 \frac{15̸12}{5̸40} = \frac{112}{40} denominator= 545 \frac{15̸26}{5̸45} = \frac{126}{45} \frac{25̸07}{5̸45} = \frac{207}{45} denominator= 550 \frac{15̸40}{5̸50} = \frac{140}{50} \frac{25̸30}{5̸50} = \frac{230}{50} \frac{35̸20}{5̸50} = \frac{320}{50} \frac{45̸10}{5̸50} = \frac{410}{50} denominator= 640 \frac{16̸00}{6̸40} = \frac{100}{40} denominator= 642 \frac{16̸05}{6̸42} = \frac{105}{42} denominator= 644 \frac{16̸10}{6̸44} = \frac{110}{44} denominator= 646 \frac{16̸15}{6̸46} = \frac{115}{46} denominator= 648 \frac{16̸20}{6̸48} = \frac{120}{48} denominator= 650 \frac{16̸25}{6̸50} = \frac{125}{50} denominator= 652 \frac{16̸30}{6̸52} = \frac{130}{52} denominator= 654 \frac{16̸35}{6̸54} = \frac{135}{54} denominator= 656 \frac{16̸40}{6̸56} = \frac{140}{56} \frac{36̸08}{6̸56} = \frac{308}{56} denominator= 658 \frac{16̸45}{6̸58} = \frac{145}{58} \frac{36̸19}{6̸58} = \frac{319}{58} denominator= 660 \frac{16̸50}{6̸60} = \frac{150}{60} \frac{36̸30}{6̸60} = \frac{330}{60} \frac{56̸10}{6̸60} = \frac{510}{60} denominator= 662 \frac{16̸55}{6̸62} = \frac{155}{62} \frac{36̸41}{6̸62} = \frac{341}{62} \frac{56̸27}{6̸62} = \frac{527}{62} \frac{76̸13}{6̸62} = \frac{713}{62} denominator= 664 \frac{16̸60}{6̸64} = \frac{160}{64} \frac{36̸52}{6̸64} = \frac{352}{64} \frac{56̸44}{6̸64} = \frac{544}{64} \frac{76̸36}{6̸64} = \frac{736}{64} \frac{96̸28}{6̸64} = \frac{928}{64} \frac{116̸20}{6̸64} = \frac{1120}{64} \frac{136̸12}{6̸64} = \frac{1312}{64} \frac{156̸04}{6̸64} = \frac{1504}{64} denominator= 749 \frac{17̸12}{7̸49} = \frac{112}{49} denominator= 756 \frac{17̸28}{7̸56} = \frac{128}{56} \frac{27̸00}{7̸56} = \frac{200}{56} denominator= 763 \frac{17̸44}{7̸63} = \frac{144}{63} \frac{27̸25}{7̸63} = \frac{225}{63} \frac{37̸06}{7̸63} = \frac{306}{63} denominator= 770 \frac{17̸60}{7̸70} = \frac{160}{70} \frac{27̸50}{7̸70} = \frac{250}{70} \frac{37̸40}{7̸70} = \frac{340}{70} \frac{47̸30}{7̸70} = \frac{430}{70} \frac{57̸20}{7̸70} = \frac{520}{70} \frac{67̸10}{7̸70} = \frac{610}{70} denominator= 848 \frac{18̸02}{8̸48} = \frac{102}{48} denominator= 856 \frac{18̸19}{8̸56} = \frac{119}{56} denominator= 864 \frac{18̸36}{8̸64} = \frac{136}{64} \frac{28̸08}{8̸64} = \frac{208}{64} denominator= 868 \frac{28̸21}{8̸68} = \frac{221}{68} denominator= 872 \frac{18̸53}{8̸72} = \frac{153}{72} \frac{28̸34}{8̸72} = \frac{234}{72} \frac{38̸15}{8̸72} = \frac{315}{72} denominator= 874 \frac{48̸07}{8̸74} = \frac{407}{74} denominator= 876 \frac{28̸47}{8̸76} = \frac{247}{76} \frac{48̸18}{8̸76} = \frac{418}{76} denominator= 878 \frac{48̸29}{8̸78} = \frac{429}{78} denominator= 880 \frac{18̸70}{8̸80} = \frac{170}{80} \frac{28̸60}{8̸80} = \frac{260}{80} \frac{38̸50}{8̸80} = \frac{350}{80} \frac{48̸40}{8̸80} = \frac{440}{80} \frac{58̸30}{8̸80} = \frac{530}{80} \frac{68̸20}{8̸80} = \frac{620}{80} \frac{78̸10}{8̸80} = \frac{710}{80} denominator= 882 \frac{48̸51}{8̸82} = \frac{451}{82} denominator= 884 \frac{28̸73}{8̸84} = \frac{273}{84} \frac{48̸62}{8̸84} = \frac{462}{84} \frac{68̸51}{8̸84} = \frac{651}{84} \frac{108̸29}{8̸84} = \frac{1029}{84} \frac{128̸18}{8̸84} = \frac{1218}{84} \frac{148̸07}{8̸84} = \frac{1407}{84} denominator= 886 \frac{48̸73}{8̸86} = \frac{473}{86} \frac{128̸47}{8̸86} = \frac{1247}{86} \frac{208̸21}{8̸86} = \frac{2021}{86} ————————————————————————- This ends this book that took, 2.980, seconds to generate.

References

Shalosh B. Ekhad, c/o D. Zeilberger, Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen Rd., Piscataway, NJ 08854-8019, USA.

Email: ShaloshBEkhad at gmail dot com .