Упр.482 ГДЗ Муравин 7 класс (Алгебра)

1. $$\left(1\frac{5}{12}-\frac{29}{30}\right)\cdot 1\frac{13}{27}-\frac{1}{6}$$
   $$=\left(\frac{85}{60}-\frac{58}{60}\right)\cdot \frac{40}{27}-\frac{1}{6}$$
   $$=\frac{27}{60}\cdot \frac{40}{27}-\frac{1}{6}=\frac{40}{60}-\frac{1}{6}=\frac{2}{3}-\frac{1}{6}=\frac{1}{2}$$
2. $$\frac{2}{5}+\frac{24}{25}:\left(\frac{7}{45}-1\frac{1}{18}\right)$$
   $$=\frac{2}{5}+\frac{24}{25}:\left(\frac{14}{90}-\frac{95}{90}\right)$$
   $$=\frac{2}{5}+\frac{24}{25}:\left(-\frac{81}{90}\right)=\frac{2}{5}+\frac{24}{25}:\left(-\frac{9}{10}\right)$$
   $$=\frac{2}{5}-\frac{24}{25}\cdot \frac{10}{9}=\frac{2}{5}-\frac{16}{15}=-\frac{2}{3}$$
3. $$\left(\frac{19}{42}-\frac{3}{35}\right)\cdot \left(1-\frac{7}{22}\right)$$
   $$=\left(\frac{95}{210}-\frac{18}{210}\right)\cdot \frac{15}{22}=\frac{77}{210}\cdot \frac{15}{22}$$
   $$=\frac{11}{30}\cdot \frac{15}{22}=\frac{1}{4}$$
4. $$\left(\frac{17}{66}+\frac{7}{44}\right)\cdot \left(\frac{1}{5}-5\right)$$
   $$=\left(\frac{34}{132}+\frac{21}{132}\right)\cdot \left(-4\frac{4}{5}\right)$$
   $$=\frac{55}{132}\cdot \left(-\frac{24}{5}\right)=-2$$
5. $$\left(\frac{11}{36}-\frac{5}{24}\right)\cdot 1\frac{1}{35}+0,4$$
   $$=\left(\frac{22}{72}-\frac{15}{72}\right)\cdot \frac{36}{35}+0,4$$
   $$=\frac{7}{72}\cdot \frac{36}{35}+0,4=\frac{1}{10}+0,4=0,5$$
6. $$\left(2\frac{11}{15}-1\frac{19}{30}\right)\cdot 0,4-0,57$$
   $$=\left(2\frac{22}{30}-1\frac{19}{30}\right)\cdot 0,4-0,57$$
   $$=1\frac{3}{30}\cdot 0,4-0,57=1,1\cdot 0,4-0,57$$
   $$=0,44-0,57=-0,13$$
7. $$0,43+0,3\cdot \left(1\frac{5}{12}-\frac{9}{20}\right)$$
   $$=0,43+0,3\cdot \left(\frac{85}{60}-\frac{27}{60}\right)$$
   $$=0,43+0,3\cdot \frac{58}{60}=0,43+\frac{3}{10}\cdot \frac{58}{60}$$
   $$=0,43+\frac{29}{100}=0,72$$
8. $$\left(\frac{11}{35}-\frac{4}{21}\right):3\frac{7}{15}+\frac{3}{14}$$
   $$=\left(\frac{33}{105}-\frac{20}{105}\right):\frac{52}{15}+\frac{3}{14}$$
   $$=\frac{13}{105}:\frac{52}{15}+\frac{3}{14}=\frac{13}{105}\cdot \frac{15}{52}+\frac{3}{14}$$
   $$=\frac{1}{28}+\frac{3}{14}=\frac{1}{28}+\frac{6}{28}=\frac{7}{28}=\frac{1}{4}$$
9. $$\left(\frac{9}{45}-0,24\right)\cdot 4,5-0,82$$
   $$=\left(\frac{1}{5}-0,24\right)\cdot 4,5-0,82$$
   $$=(0,2-0,24)\cdot 4,5-0,82=(-0,04)\cdot 4,5-0,82$$
   $$=-0,18-0,82=-1$$
10. $$\left(\frac{2}{3}-1,3+\frac{3}{4}\right):1,4+\frac{1}{6}$$
    $$=\left(\frac{8}{12}+\frac{9}{12}-\frac{13}{10}\right):\frac{14}{10}+\frac{1}{6}$$
    $$=\left(\frac{17}{12}-\frac{13}{10}\right):\frac{14}{10}+\frac{1}{6}$$
    $$=\left(\frac{85}{60}-\frac{78}{60}\right):\frac{7}{5}+\frac{1}{6}=\frac{7}{60}:\frac{7}{5}+\frac{1}{6}$$
    $$=\frac{7}{60}\cdot \frac{5}{7}+\frac{1}{6}=\frac{1}{12}+\frac{1}{6}=\frac{1}{4}$$
11. $$0,3+0,029:\left(\frac{6}{35}-0,13\right)$$
    $$=0,3+0,029:\left(\frac{6}{35}-\frac{13}{100}\right)$$
    $$=0,3+0,029:\left(\frac{120}{700}-\frac{91}{700}\right)$$
    $$=0,3+0,029:\frac{29}{700}=0,3+\frac{29}{1000}\cdot \frac{700}{29}$$
    $$=0,3+0,7=1$$
12. $$2,6-0,038:\left(\frac{12}{65}-0,17\right)$$
    $$=2,6-0,038:\left(\frac{12}{65}-\frac{17}{100}\right)$$
    $$=2,6-0,038:\left(\frac{240}{1300}-\frac{221}{1300}\right)$$
    $$=2,6-0,038:\frac{19}{1300}$$
    $$=2,6-\frac{38}{1000}\cdot \frac{1300}{19}=2,6-\frac{26}{10}=2,6-2,6=0$$

Ответ

1) $$\frac{1}{2}$$; 2) $$-\frac{2}{3}$$; 3) $$\frac{1}{4}$$; 4) $$-2$$; 5) $$0,5$$; 6) $$-0,13$$; 7) $$0,72$$; 8) $$\frac{1}{4}$$; 9) $$-1$$; 10) $$\frac{1}{4}$$; 11) $$1$$; 12) $$0$$.