Lutasin ang 70!*70!/80!*60!+70!*70!*100/80!*61!

$$\frac{ 70 ! \times 70 ! }{ 80 ! \times 60 ! } + \frac{ 70 ! \times 70 ! \times 100 }{ 80 ! \times 61 ! }$$

I-evaluate

$$\frac{915244589}{1439241355}\approx 0.635921547$$

Mga Hakbang ng Solution

I-multiply ang 70! at 70! para makuha ang \left(70!\right)^{2}.

$$\frac{\left(70!\right)^{2}}{80!\times 60!}+\frac{70!\times 70!\times 100}{80!\times 61!}$$

I-multiply ang 70! at 70! para makuha ang \left(70!\right)^{2}.

$$\frac{\left(70!\right)^{2}}{80!\times 60!}+\frac{\left(70!\right)^{2}\times 100}{80!\times 61!}$$

Ang factorial ng 70 ay 11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000.

$$\frac{11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000^{2}}{80!\times 60!}+\frac{\left(70!\right)^{2}\times 100}{80!\times 61!}$$

Kalkulahin ang 11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000 sa power ng 2 at kunin ang 143486179252605282342806635197268128186483973356654097161524529227261957403344906950524588163677475732975695571390639580290806725956789181304836309777641976540401395302400000000000000000000000000000000.

$$\frac{143486179252605282342806635197268128186483973356654097161524529227261957403344906950524588163677475732975695571390639580290806725956789181304836309777641976540401395302400000000000000000000000000000000}{80!\times 60!}+\frac{\left(70!\right)^{2}\times 100}{80!\times 61!}$$

Ang factorial ng 80 ay 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000.

$$\frac{143486179252605282342806635197268128186483973356654097161524529227261957403344906950524588163677475732975695571390639580290806725956789181304836309777641976540401395302400000000000000000000000000000000}{71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000\times 60!}+\frac{\left(70!\right)^{2}\times 100}{80!\times 61!}$$

Ang factorial ng 60 ay 8320987112741390144276341183223364380754172606361245952449277696409600000000000000.

$$\frac{143486179252605282342806635197268128186483973356654097161524529227261957403344906950524588163677475732975695571390639580290806725956789181304836309777641976540401395302400000000000000000000000000000000}{71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000\times 8320987112741390144276341183223364380754172606361245952449277696409600000000000000}+\frac{\left(70!\right)^{2}\times 100}{80!\times 61!}$$

I-multiply ang 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000 at 8320987112741390144276341183223364380754172606361245952449277696409600000000000000 para makuha ang 595528529747859576732551720067744655471974906375437967027891579389978351058077643608066119727979258178207029727548544024718296431927079222747502820344753912504981127168000000000000000000000000000000000.

$$\frac{143486179252605282342806635197268128186483973356654097161524529227261957403344906950524588163677475732975695571390639580290806725956789181304836309777641976540401395302400000000000000000000000000000000}{595528529747859576732551720067744655471974906375437967027891579389978351058077643608066119727979258178207029727548544024718296431927079222747502820344753912504981127168000000000000000000000000000000000}+\frac{\left(70!\right)^{2}\times 100}{80!\times 61!}$$

Bawasan ang fraction \frac{143486179252605282342806635197268128186483973356654097161524529227261957403344906950524588163677475732975695571390639580290806725956789181304836309777641976540401395302400000000000000000000000000000000}{595528529747859576732551720067744655471974906375437967027891579389978351058077643608066119727979258178207029727548544024718296431927079222747502820344753912504981127168000000000000000000000000000000000} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 413779473247459302427112178184835896041894173041906489011283016801569289994503836090831422592063621030544268739101471986759508054802301885459303537275548834201600000000000000000000000000000000.

$$\frac{346769689}{1439241355}+\frac{\left(70!\right)^{2}\times 100}{80!\times 61!}$$

Ang factorial ng 70 ay 11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000.

$$\frac{346769689}{1439241355}+\frac{11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000^{2}\times 100}{80!\times 61!}$$

Kalkulahin ang 11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000 sa power ng 2 at kunin ang 143486179252605282342806635197268128186483973356654097161524529227261957403344906950524588163677475732975695571390639580290806725956789181304836309777641976540401395302400000000000000000000000000000000.

$$\frac{346769689}{1439241355}+\frac{143486179252605282342806635197268128186483973356654097161524529227261957403344906950524588163677475732975695571390639580290806725956789181304836309777641976540401395302400000000000000000000000000000000\times 100}{80!\times 61!}$$

I-multiply ang 143486179252605282342806635197268128186483973356654097161524529227261957403344906950524588163677475732975695571390639580290806725956789181304836309777641976540401395302400000000000000000000000000000000 at 100 para makuha ang 14348617925260528234280663519726812818648397335665409716152452922726195740334490695052458816367747573297569557139063958029080672595678918130483630977764197654040139530240000000000000000000000000000000000.

$$\frac{346769689}{1439241355}+\frac{14348617925260528234280663519726812818648397335665409716152452922726195740334490695052458816367747573297569557139063958029080672595678918130483630977764197654040139530240000000000000000000000000000000000}{80!\times 61!}$$

Ang factorial ng 80 ay 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000.

$$\frac{346769689}{1439241355}+\frac{14348617925260528234280663519726812818648397335665409716152452922726195740334490695052458816367747573297569557139063958029080672595678918130483630977764197654040139530240000000000000000000000000000000000}{71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000\times 61!}$$

Ang factorial ng 61 ay 507580213877224798800856812176625227226004528988036003099405939480985600000000000000.

$$\frac{346769689}{1439241355}+\frac{14348617925260528234280663519726812818648397335665409716152452922726195740334490695052458816367747573297569557139063958029080672595678918130483630977764197654040139530240000000000000000000000000000000000}{71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000\times 507580213877224798800856812176625227226004528988036003099405939480985600000000000000}$$

I-multiply ang 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000 at 507580213877224798800856812176625227226004528988036003099405939480985600000000000000 para makuha ang 36327240314619434180685654924132423983790469288901715988701386342788679414542736260092033303406734748870628813380461185507816082347551832587597672041029988662803848757248000000000000000000000000000000000.

$$\frac{346769689}{1439241355}+\frac{14348617925260528234280663519726812818648397335665409716152452922726195740334490695052458816367747573297569557139063958029080672595678918130483630977764197654040139530240000000000000000000000000000000000}{36327240314619434180685654924132423983790469288901715988701386342788679414542736260092033303406734748870628813380461185507816082347551832587597672041029988662803848757248000000000000000000000000000000000}$$

Bawasan ang fraction \frac{14348617925260528234280663519726812818648397335665409716152452922726195740334490695052458816367747573297569557139063958029080672595678918130483630977764197654040139530240000000000000000000000000000000000}{36327240314619434180685654924132423983790469288901715988701386342788679414542736260092033303406734748870628813380461185507816082347551832587597672041029988662803848757248000000000000000000000000000000000} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 126202739340475087240269214346374948292777722777781479148441320124478633448323670007703583890579404414316001965425948955961649956714702075065087578869042394431488000000000000000000000000000000000.

$$\frac{346769689}{1439241355}+\frac{113694980}{287848271}$$

Ang least common multiple ng 1439241355 at 287848271 ay 1439241355. I-convert ang \frac{346769689}{1439241355} at \frac{113694980}{287848271} sa mga fraction na may denominator na 1439241355.

$$\frac{346769689}{1439241355}+\frac{568474900}{1439241355}$$

Dahil may parehong denominator ang \frac{346769689}{1439241355} at \frac{568474900}{1439241355}, pagsamahin ang mga ito sa pamamagitan ng pagsasama sa mga numerator ng mga ito.

$$\frac{346769689+568474900}{1439241355}$$

Idagdag ang 346769689 at 568474900 para makuha ang 915244589.

$$\frac{915244589}{1439241355}$$

I-factor

$$\frac{7 ^ {2} \cdot 17 \cdot 23 ^ {2} \cdot 31 \cdot 67}{5 \cdot 19 \cdot 37 \cdot 71 \cdot 73 \cdot 79} = 0.6359215470153023$$