Question

Решите примеры : 1)(11/18 - 4/9)* 3/16 2) 11/18 - 4/9 * 3/16 3) 1 3/5*(3/4 * 1 3/8) 4) 1 3/5 * 3/4 + 3/8 5) 13 4/5 - 3 1/5 * 3 3/4 6) 1 3/25 * 2 1/7 - 2 1/9 * 27/190 7) 4 7/9*1 3/11 + 1 1/15 * 45/60 8)(8- 2 7/9 * 1/9)* 27/44 9)(4/5+4/7)(7 11/12-5 7/9) 10) 4/5+ 4/7 * (7 11/12 - 5 7/9)

Answer 1

Первый пример.

$\tt\displaystyle (\frac{11}{18}-\frac{4}{9} )*\frac{3}{16}=\frac{1}{32}\\\\\\1)\ \frac{11}{18}-\frac{4}{9}=\frac{11}{18}-\frac{4*2}{9*2}=\frac{11}{18}-\frac{8}{18}=\frac{11-8}{18}=\frac{3}{18}=\frac{1}{6}\\\\\\2)\ \frac{1}{6}*\frac{3}{16}=\frac{1}{2*16}=\frac{1}{32}$

ответ: 1/32

Второй пример.

$\tt\displaystyle \frac{11}{18}-\frac{4}{9}*\frac{3}{16}=\frac{19}{36}\\\\\\1)\ \frac{4}{9}*\frac{3}{16}=\frac{1}{3*4}=\frac{1}{12}\\\\\\2)\ \frac{11}{18}-\frac{1}{12}=\frac{11*2}{18*2} -\frac{1*3}{12*3}=\frac{22}{36}-\frac{3}{36}=\frac{22-3}{36}=\frac{19}{36}$

ответ: 19/36

Третий пример.

$\tt\displaystyle 1\frac{3}{5}* (\frac{3}{4}*1\frac{3}{8} )=1,65\\\\\\1)\ \frac{3}{4}*1\frac{3}{8}=\frac{3}{4}*\frac{1*8+3}{8}=\frac{3}{4}*\frac{11}{8}=\frac{33}{32}\\\\\\2)\ 1\frac{3}{5}*\frac{33}{32}=\frac{1*5+3}{5}*\frac{33}{32}=\frac{8}{5}*\frac{33}{32}=\frac{33}{5*4}=\frac{33}{20}=1\frac{13}{20}=1,65$

ответ: 1,65

Четвёртый пример.

$\tt\displaystyle 1\frac{3}{5} *\frac{3}{4}+\frac{3}{8} =1,575\\\\\\1)\ 1\frac{3}{5}*\frac{3}{4}=\frac{1*5+3}{5}*\frac{3}{4}=\frac{8}{5}*\frac{3}{4}=\frac{2*3}{5}=\frac{6}{5}=1\frac{1}{5}= 1,2\\\\\\2)\ 1,2+\frac{3}{8}=1,2+0,375=1,575$

ответ: 1,575

Пятый пример.

$\tt\displaystyle 13\frac{4}{5}-3\frac{1}{5}*3\frac{3}{4}=1,8\\\\\\1)\ 3\frac{1}{5}*3\frac{3}{4}=\frac{3*5+1}{5}*\frac{3*4+3}{4}=\frac{16}{5}*\frac{15}{4}=4*3=12\\\\\\2 )\ 13\frac{4}{5}-12=13,8-12=1,8$

ответ: 1,8

Шестой пример.

$\tt\displaystyle 1\frac{3}{25}*2\frac{1}{7}-2\frac{1}{9}*\frac{27}{190}=2,1\\\\\\1)\ 1\frac{3}{25}*2\frac{1}{7}=\frac{1*25+3}{25}*\frac{2*7+1}{7}= \frac{28}{25}*\frac{15}{7}=\frac{4*3}{5}=\frac{12}{5}=2\frac{2}{5}= 2,4\\\\\\2)\ 2\frac{1}{9}*\frac{27}{190}=\frac{2*9+1}{9}* \frac{27}{190}=\frac{19}{9}*\frac{27}{190}=\frac{3}{10}=0,3\\\\\\3 )\ 2,4-0,3=2,1$

ответ: 2,1

Седьмой пример.

$\tt\displaystyle 4\frac{7}{9}*1\frac{3}{11}+1\frac{1}{15}*\frac{45}{60}=6\frac{436}{495}\\\\\\1)\ 4\frac{7}{9}*1\frac{3}{11}=\frac{4*9+7}{9}*\frac{1*11+3}{11}=\frac{43}{9} *\frac{14}{11}=\frac{602}{99}\\\\\\2 )\ 1\frac{1}{15}*\frac{45}{60}=\frac{1*15+1}{15}*\frac{45}{60}=\frac{16}{15}*\frac{45}{60}=\frac{4}{5}\\\\\\3 )\ \frac{602}{99}+\frac{4}{5}=\frac{602*5}{99*5}+\frac{4*99}{5*99}=\frac{3010}{495}+\frac{396}{495}=\frac{3010+396}{495}=\frac{3406}{495}=6\frac{436}{495}$

ответ: 6 436/495

Восьмой пример.

$\tt\displaystyle (8-2\frac{7}{9}*\frac{1}{9})*\frac{27}{44}=4\frac{95}{132}\\\\\\1)\ 2\frac{7}{9}*\frac{1}{9}=\frac{2*9+7}{9}*\frac{1}{9}=\frac{25}{9}*\frac{1}{9}=\frac{25}{81} \\\\\\2)\ 8-\frac{25}{81}=7\frac{81}{81}-\frac{25}{81}=7\frac{56}{81}\\\\\\3)\ 7\frac{56}{81}*\frac{27}{44}=\frac{7*81+56}{81}*\frac{27}{44}=\frac{623}{81}*\frac{27}{44}=\frac{623}{3*44}=\frac{623}{132}=4\frac{95}{132}$

ответ: 4 95/132

Девятый пример.

$\tt\displaystyle(\frac{4}{5}+\frac{4}{7})*(7\frac{11}{12}-5\frac{7}{9})=2\frac{14}{15}\\\\\\1)\ \frac{4}{5}+\frac{4}{7}=\frac{4*7}{5*7}+\frac{4*5}{7*5}=\frac{28}{35}+\frac{20}{35}=\frac{28+20}{35}=\frac{48}{35}\\\\\\2)\ 7\frac{11}{12}-5\frac{7}{9}=(7-5)+(\frac{11}{12}-\frac{7}{9})=2+(\frac{11*3}{12*3}-\frac{7*4}{9*4})=\\\\=2+(\frac{33}{36}-\frac{28}{36})=2+\frac{5}{36}=2\frac{5}{36}\\\\\\3)\ \frac{48}{35}*2\frac{5}{36}=\frac{48}{35}*\frac{2*36+5}{36}=\frac{48}{35}*\frac{77}{36} =\frac{44}{15}$

ответ: 2 14/15

Десятый пример.

$\tt\displaystyle\frac{4}{5}+\frac{4}{7}*(7\frac{11}{12}-5\frac{7}{9})=2\frac{1}{45} \\\\\\1)\ 7\frac{11}{12}-5\frac{7}{9}=(7-5)+(\frac{11}{12}-\frac{7}{9})=2+(\frac{11*3}{12*3}-\frac{7*4}{9*4})=\\\\=2+(\frac{33}{36}-\frac{28}{36})=2+\frac{5}{36}=2\frac{5}{36}\\\\\\2)\ \frac{4}{7}*2\frac{5}{36}=\frac{4}{7}*\frac{2*36+5}{36}=\frac{4}{7}*\frac{77}{36}=\frac{11}{9}\\\\\\3)\ \frac{4}{5}+\frac{11}{9}=\frac{4*9}{5*9}+\frac{11*5}{9*5}=\frac{36}{45}+\frac{55}{45}=\frac{36+55}{45}=\frac{91}{45}=2\frac{1}{45}$

ответ: 2 1/45