ដោះស្រាយ {l}{23/16*(336/7-312/3)+47/27div2frac{4}{21}}{(5frac{2}{9}+1frac{1}{2})*2frac{18}{22}-5frac{1}{2}div5frac{2}{2}}

$$\left. \begin{array} { l } { 2 \frac { 3 } { 16 } \times ( 33 \frac { 6 } { 7 } - 31 \frac { 2 } { 3 } ) + 4 \frac { 7 } { 27 } \div 2 \frac { 4 } { 21 } } \\ { ( 5 \frac { 2 } { 9 } + 1 \frac { 1 } { 2 } ) \times 2 \frac { 18 } { 22 } - 5 \frac { 1 } { 2 } \div 5 \frac { 2 } { 2 } } \end{array} \right.$$

តម្រៀប

$$\frac{485}{72},\ \frac{649}{36}$$

ជំហានចម្លើយ

គុណ 2 និង 16 ដើម្បីបាន 32។

$$sort(\frac{32+3}{16}\left(\frac{33\times 7+6}{7}-\frac{31\times 3+2}{3}\right)+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

បូក 32 និង 3 ដើម្បីបាន 35។

$$sort(\frac{35}{16}\left(\frac{33\times 7+6}{7}-\frac{31\times 3+2}{3}\right)+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

គុណ 33 និង 7 ដើម្បីបាន 231។

$$sort(\frac{35}{16}\left(\frac{231+6}{7}-\frac{31\times 3+2}{3}\right)+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

បូក 231 និង 6 ដើម្បីបាន 237។

$$sort(\frac{35}{16}\left(\frac{237}{7}-\frac{31\times 3+2}{3}\right)+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

គុណ 31 និង 3 ដើម្បីបាន 93។

$$sort(\frac{35}{16}\left(\frac{237}{7}-\frac{93+2}{3}\right)+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

បូក 93 និង 2 ដើម្បីបាន 95។

$$sort(\frac{35}{16}\left(\frac{237}{7}-\frac{95}{3}\right)+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

ផលគុណរួមតូចបំផុតនៃ 7 និង 3 គឺ 21។ ប​ម្លែង \frac{237}{7} និង \frac{95}{3} ទៅជាប្រភាគជាមួយភាគបែង 21។

$$sort(\frac{35}{16}\left(\frac{711}{21}-\frac{665}{21}\right)+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

ដោយសារ \frac{711}{21} និង \frac{665}{21} មានភាគបែងដូចគ្នា សូមដកពួកវាដោយការដកភាគយករបស់ពួកវា។

$$sort(\frac{35}{16}\times \frac{711-665}{21}+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

ដក​ 665 ពី 711 ដើម្បីបាន 46។

$$sort(\frac{35}{16}\times \frac{46}{21}+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

គុណ \frac{35}{16} ដង \frac{46}{21} ដោយការគុណភាគយក​ចំនួនដងនៃភាគយក និងភាគបែងចំនួនដងនៃភាគបែង។

$$sort(\frac{35\times 46}{16\times 21}+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

ធ្វើផល​គុណនៅក្នុងប្រភាគ \frac{35\times 46}{16\times 21}។

$$sort(\frac{1610}{336}+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

កាត់បន្ថយប្រភាគ \frac{1610}{336} ទៅតួដែលតូចបំផុតដោយ​ដក និងលុបចេញ 14។

$$sort(\frac{115}{24}+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

ចែក \frac{4\times 27+7}{27} នឹង \frac{2\times 21+4}{21} ដោយការគុណ \frac{4\times 27+7}{27} នឹងប្រភាគផ្ទុយគ្នានៃ \frac{2\times 21+4}{21}.

$$sort(\frac{115}{24}+\frac{\left(4\times 27+7\right)\times 21}{27\left(2\times 21+4\right)},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

សម្រួល 3 ទាំងនៅក្នុងភាគយក និងភាគបែង។

$$sort(\frac{115}{24}+\frac{7\left(7+4\times 27\right)}{9\left(4+2\times 21\right)},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

គុណ 4 និង 27 ដើម្បីបាន 108។

$$sort(\frac{115}{24}+\frac{7\left(7+108\right)}{9\left(4+2\times 21\right)},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

បូក 7 និង 108 ដើម្បីបាន 115។

$$sort(\frac{115}{24}+\frac{7\times 115}{9\left(4+2\times 21\right)},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

គុណ 7 និង 115 ដើម្បីបាន 805។

$$sort(\frac{115}{24}+\frac{805}{9\left(4+2\times 21\right)},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

គុណ 2 និង 21 ដើម្បីបាន 42។

$$sort(\frac{115}{24}+\frac{805}{9\left(4+42\right)},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

បូក 4 និង 42 ដើម្បីបាន 46។

$$sort(\frac{115}{24}+\frac{805}{9\times 46},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

គុណ 9 និង 46 ដើម្បីបាន 414។

$$sort(\frac{115}{24}+\frac{805}{414},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

កាត់បន្ថយប្រភាគ \frac{805}{414} ទៅតួដែលតូចបំផុតដោយ​ដក និងលុបចេញ 23។

$$sort(\frac{115}{24}+\frac{35}{18},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

ផលគុណរួមតូចបំផុតនៃ 24 និង 18 គឺ 72។ ប​ម្លែង \frac{115}{24} និង \frac{35}{18} ទៅជាប្រភាគជាមួយភាគបែង 72។

$$sort(\frac{345}{72}+\frac{140}{72},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

ដោយសារ \frac{345}{72} និង \frac{140}{72} មានភាគបែងដូចគ្នា សូមបូកពួកវាដោយការបូកភាគយករបស់ពួកវា។

$$sort(\frac{345+140}{72},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

បូក 345 និង 140 ដើម្បីបាន 485។

$$sort(\frac{485}{72},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

គុណ 5 និង 9 ដើម្បីបាន 45។

$$sort(\frac{485}{72},\left(\frac{45+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

បូក 45 និង 2 ដើម្បីបាន 47។

$$sort(\frac{485}{72},\left(\frac{47}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

គុណ 1 និង 2 ដើម្បីបាន 2។

$$sort(\frac{485}{72},\left(\frac{47}{9}+\frac{2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

បូក 2 និង 1 ដើម្បីបាន 3។

$$sort(\frac{485}{72},\left(\frac{47}{9}+\frac{3}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

ផលគុណរួមតូចបំផុតនៃ 9 និង 2 គឺ 18។ ប​ម្លែង \frac{47}{9} និង \frac{3}{2} ទៅជាប្រភាគជាមួយភាគបែង 18។

$$sort(\frac{485}{72},\left(\frac{94}{18}+\frac{27}{18}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

ដោយសារ \frac{94}{18} និង \frac{27}{18} មានភាគបែងដូចគ្នា សូមបូកពួកវាដោយការបូកភាគយករបស់ពួកវា។

$$sort(\frac{485}{72},\frac{94+27}{18}\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

បូក 94 និង 27 ដើម្បីបាន 121។

$$sort(\frac{485}{72},\frac{121}{18}\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

គុណ 2 និង 22 ដើម្បីបាន 44។

$$sort(\frac{485}{72},\frac{121}{18}\times \frac{44+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

បូក 44 និង 18 ដើម្បីបាន 62។

$$sort(\frac{485}{72},\frac{121}{18}\times \frac{62}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

កាត់បន្ថយប្រភាគ \frac{62}{22} ទៅតួដែលតូចបំផុតដោយ​ដក និងលុបចេញ 2។

$$sort(\frac{485}{72},\frac{121}{18}\times \frac{31}{11}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

គុណ \frac{121}{18} ដង \frac{31}{11} ដោយការគុណភាគយក​ចំនួនដងនៃភាគយក និងភាគបែងចំនួនដងនៃភាគបែង។

$$sort(\frac{485}{72},\frac{121\times 31}{18\times 11}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

ធ្វើផល​គុណនៅក្នុងប្រភាគ \frac{121\times 31}{18\times 11}។

$$sort(\frac{485}{72},\frac{3751}{198}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

កាត់បន្ថយប្រភាគ \frac{3751}{198} ទៅតួដែលតូចបំផុតដោយ​ដក និងលុបចេញ 11។

$$sort(\frac{485}{72},\frac{341}{18}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})$$

ចែក \frac{5\times 2+1}{2} នឹង \frac{5\times 2+2}{2} ដោយការគុណ \frac{5\times 2+1}{2} នឹងប្រភាគផ្ទុយគ្នានៃ \frac{5\times 2+2}{2}.

$$sort(\frac{485}{72},\frac{341}{18}-\frac{\left(5\times 2+1\right)\times 2}{2\left(5\times 2+2\right)})$$

សម្រួល 2 ទាំងនៅក្នុងភាគយក និងភាគបែង។

$$sort(\frac{485}{72},\frac{341}{18}-\frac{1+2\times 5}{2+2\times 5})$$

គុណ 2 និង 5 ដើម្បីបាន 10។

$$sort(\frac{485}{72},\frac{341}{18}-\frac{1+10}{2+2\times 5})$$

បូក 1 និង 10 ដើម្បីបាន 11។

$$sort(\frac{485}{72},\frac{341}{18}-\frac{11}{2+2\times 5})$$

គុណ 2 និង 5 ដើម្បីបាន 10។

$$sort(\frac{485}{72},\frac{341}{18}-\frac{11}{2+10})$$

បូក 2 និង 10 ដើម្បីបាន 12។

$$sort(\frac{485}{72},\frac{341}{18}-\frac{11}{12})$$

ផលគុណរួមតូចបំផុតនៃ 18 និង 12 គឺ 36។ ប​ម្លែង \frac{341}{18} និង \frac{11}{12} ទៅជាប្រភាគជាមួយភាគបែង 36។

$$sort(\frac{485}{72},\frac{682}{36}-\frac{33}{36})$$

ដោយសារ \frac{682}{36} និង \frac{33}{36} មានភាគបែងដូចគ្នា សូមដកពួកវាដោយការដកភាគយករបស់ពួកវា។

$$sort(\frac{485}{72},\frac{682-33}{36})$$

ដក​ 33 ពី 682 ដើម្បីបាន 649។

$$sort(\frac{485}{72},\frac{649}{36})$$

ភាគបែងរួមតូចបំផុតនៃលេខនៅក្នុងបញ្ជី \frac{485}{72},\frac{649}{36} គឺ 72។ បម្លែងលេខនៅក្នុងបញ្ជីទៅជាប្រភាគជាមួយភាគបែង 72។

$$\frac{485}{72},\frac{1298}{72}$$

វាយតម្លៃ

$$\frac{485}{72},\ \frac{649}{36}$$