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МатематикаРешебник по математике 6 класс Мерзляк ФГОС Задание 463
Задание 463
\[\boxed{\mathbf{463\ (463).}\mathbf{\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ 5\frac{11}{14}x - \frac{8}{15} = \frac{5}{21}\]
\[5\frac{11}{14}x = \frac{5^{\backslash 5}}{21} + \frac{8^{\backslash 7}}{15}\]
\[\frac{81}{14}x = \frac{25 + 56}{105}\]
\[\frac{81}{14}x = \frac{81}{105}\]
\[x = \frac{81}{105}\ :\frac{81}{14}\]
\[x = \frac{81}{105} \cdot \frac{14}{81}\]
\[x = \frac{2}{15}\]
\[Ответ:\ \frac{2}{15}.\]
\[2)\ 7\frac{3}{10} + \frac{25}{28}x = 8\frac{13}{35}\]
\[\frac{25}{28}x = 8\frac{13^{\backslash 2}}{35} - 7\frac{3^{\backslash 7}}{10}\]
\[\frac{25}{28}x = 1\ \frac{26 - 21}{70}\]
\[\frac{25}{28}x = 1\frac{5}{70}\]
\[\frac{25}{28}x = \frac{75}{70}\]
\[x = \frac{75}{70}\ :\frac{25}{28}\]
\[x = \frac{75}{70} \cdot \frac{28}{25}\]
\[x = \frac{6}{5} = 1\frac{1}{5}\]
\[Ответ:\ \ 1\frac{1}{5}.\]
\[3)\ 3\frac{1}{3} - 1\frac{1}{20}x = 1\frac{14}{15}\]
\[\frac{21}{20}x = \frac{10^{\backslash 5}}{3} - \frac{29}{15}\]
\[\frac{21}{20}x = \frac{50 - 29}{15}\]
\[\frac{21}{20}x = \frac{21}{15}\]
\[x = \frac{21}{15}\ :\frac{21}{20}\]
\[x = \frac{21}{15} \cdot \frac{20}{21}\]
\[x = \frac{4}{3} = 1\frac{1}{3}\]
\[Ответ:1\frac{1}{3}.\]
\[4)\frac{3^{\backslash 3}}{8}x + \frac{7^{\backslash 2}}{12}x - \frac{5^{\backslash 4}}{6}x = \frac{9}{32}\]
\[\frac{9 + 14 - 20}{24}x = \frac{9}{32}\]
\[\frac{3}{24}x = \frac{9}{32}\]
\[x = \frac{9}{32}\ :\frac{3}{24}\]
\[x = \frac{9}{32} \cdot \frac{24}{3}\]
\[x = \frac{9}{4} = 2\frac{1}{4}\]
\[Ответ:2\frac{1}{4}.\]
\[5)\ 2\frac{1}{3}\ :x - 1\frac{1}{6} = 1\frac{5}{9}\]
\[\frac{7}{3}\ :x = 1\frac{5}{9} + 1\frac{1}{6}\]
\[\frac{7}{3}\ :x = \frac{14^{\backslash 2}}{9} + \frac{7^{\backslash 3}}{6}\]
\[\frac{7}{3}\ :x = \frac{28 + 21}{18}\]
\[\frac{7}{3}\ :x = \frac{49}{18}\]
\[x = \frac{7}{3}\ :\frac{49}{18}\]
\[x = \frac{7}{3} \cdot \frac{18}{49}\]
\[x = \frac{6}{7}\]
\[Ответ:\ \frac{6}{7}.\]
\[6)\ 2\frac{1}{3}\ :\left( x - 1\frac{1}{6} \right) = 1\frac{5}{9}\]
\[\frac{7}{3}\ :\left( x - \frac{7}{6} \right) = \frac{14}{9}\]
\[x - \frac{7}{6} = \frac{7}{3}\ :\frac{14}{9}\]
\[x - \frac{7}{6} = \frac{7}{3} \cdot \frac{9}{14}\]
\[x = \frac{3^{\backslash 3}}{2} + \frac{7}{6}\]
\[x = \frac{9 + 7}{6} = \frac{16}{6}\]
\[x = \frac{8}{3} = 2\frac{2}{3}\]
\[Ответ:\ 2\frac{2}{3}.\]
\[7)\ 27\ :\left( 31\frac{3}{7} - 2\frac{11}{14}x \right) = 1\frac{1}{8}\]
\[31\frac{3}{7} - 2\frac{11}{14}x = 27\ :\frac{9}{8}\]
\[\frac{39}{14}x = 31\frac{3}{7} - 24\]
\[\frac{39}{14}x = 7\frac{3}{7}\]
\[x = \frac{52}{7}\ :\frac{39}{14}\]
\[x = 2\frac{2}{3}\]
\[Ответ:2\frac{2}{3}.\]
\[8)\ 48\ :\left( 3\frac{4}{5}x - 25 \right) = 1\frac{1}{2}\]
\[3\frac{4}{5}x - 25 = 48\ :\frac{3}{2}\]
\[\frac{19}{5}x - 25 = 48 \cdot \frac{2}{3}\]
\[\frac{19}{5}x = 32 + 25\]
\[\frac{19}{5}x = 57\]
\[x = 57\ :\frac{19}{5}\]
\[x = 57 \cdot \frac{5}{19}\]
\[Ответ:15.\]
\[\boxed{\mathbf{463}.}\]
\[1)\ 17,5\ :7 = 175\ :70 = 2,5\]
\[2)\ 20,4\ :24 = 204\ :240 = 0,85\]
\[3)\ 453,2\ :22 =\]
\[= 4532\ :220 = 20,6\]
\[4)\ 5,49\ :6 = 549\ :600 = 0,915\]
\[5)\ 0,1242\ :6,9 =\]
\[= 1242\ :69\ 000 = 0,018\]
\[6)\ 0,02592\ :0,048 =\]
\[= 2592\ :4800 = 0,54\]
