Question

1287 запишите обыкновенную дробь в виде десятичной.вычислите: 1) 5 17/20-3,52+4/5; 2) 6 4/25+2,81-1 3/4; 3) 9 7/10+5,92-3 9/20 4) 41,7-8 3/5+2 1/4; 5) 36,63+9 3/4-6 9/10; 6) 58,75-21 9/10+4 8/25.

Answer 1

1)

$\tt\displaystyle 5\frac{17}{20}-3,52+\frac{4}{5}=\frac{5*20+17}{20}-3\frac{52}{100}+\frac{4}{5}=\\\\\\=\frac{117}{20}-\frac{3*100+52}{100}+\frac{4*20}{5*20}=\\\\\\=\frac{117*5}{20*5}-\frac{352}{100}+\frac{80}{100}=\frac{585}{100}-\frac{352}{100}+\frac{80}{100}=\\\\\\=\frac{585-352+80}{100}=\frac{313}{100}=3\frac{13}{100}=3,13$

ответ: 3,13

2)

$\tt\displaystyle 6\frac{4}{25}+2,81-1\frac{3}{4}=\frac{6*25+4}{25}+2\frac{81}{100}-\frac{1*4+3}{4}=\\\\\\=\frac{154}{25}+\frac{2*100+81}{100}-\frac{7}{4}=\frac{154*4}{25*4}+\frac{281}{100}-\frac{7*25}{4*25}=\\\\\\=\frac{616}{100}+\frac{281}{100}-\frac{175}{100}=\frac{616+281-175}{100}=\frac{722}{100}=7\frac{22}{100}=7,22$

ответ: 7,22

3)

$\tt\displaystyle 9\frac{7}{10}+5,92-3\frac{9}{20}=\frac{9*10+7}{10}+5\frac{92}{100}-\frac{3*20+9}{20}=\\\\\\=\frac{97}{10}+\frac{5*100+92}{100}-\frac{69}{20}=\frac{97*10}{10*10}+\frac{592}{100}-\frac{69*5}{20*5}=\\\\\\=\frac{970}{100}+\frac{592}{100}-\frac{345}{100}=\frac{970+592-345}{100}=\frac{1217}{100}=12\frac{17}{100}=12,17$

ответ: 12,17

4)

$\tt\displaystyle 41,7-8\frac{3}{5}+2\frac{1}{4}=41\frac{7}{10}-\frac{8*5+3}{5}+\frac{2*4+1}{4}=\\\\\\=\frac{41*10+7}{10}-\frac{43}{5}+\frac{9}{4}=\frac{417}{10}-\frac{43}{5}+\frac{9}{4}=\\\\\\=\frac{417*2}{10*2}-\frac{43*4}{5*4}+\frac{9*5}{4*5}=\frac{834}{20}-\frac{172}{20}+\frac{45}{20}=\\\\\\=\frac{834-172+45}{20}=\frac{707}{20}=35\frac{7}{20}=35\frac{7*5}{20*5}=35\frac{35}{100}=35,35$

ответ: 35,35

5)

$\tt\displaystyle 36,63+9\frac{3}{4}-6\frac{9}{10}=36\frac{63}{100}+\frac{9*4+3}{4}-\frac{6*10+9}{10}=\\\\=\frac{36*100+63}{100}+\frac{39}{4}-\frac{69}{10}=\frac{3663}{100}+\frac{39*25}{4*25}-\frac{69*10}{10*10}=\\\\\\=\frac{3663}{100}+\frac{975}{100}-\frac{690}{100}=\frac{3948}{100}=39\frac{48}{100}=39,48$

ответ: 39,48

6)

$\tt\displaystyle 58,75-21\frac{9}{10}+4\frac{8}{25}=58\frac{75}{100}-\frac{21*10+9}{10}+\frac{4*25+8}{25}=\\\\\\=\frac{58*100+75}{100}-\frac{219}{10}+\frac{108}{25}=\frac{5875}{100}-\frac{219*10}{10*10}+\frac{108*4}{25*4}=\\\\\\=\frac{5875}{100}-\frac{2910}{100}+\frac{432}{100}=\frac{5875-2910+432}{100}=\frac{3397}{100}=\\\\\\=33\frac{97}{100}=33,97$

ответ: 33,97