Решебник по математике 6 класс Мерзляк ФГОС Задание 384

 

\[\boxed{\mathbf{384\ (384).}\mathbf{\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\frac{124}{279} = \frac{2 \cdot 2 \cdot 31}{3 \cdot 3 \cdot 31} = \frac{4}{9}\]

\[2)\frac{324}{378} = \frac{2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3}{2 \cdot 3 \cdot 3 \cdot 3 \cdot 7} =\]

\[= \frac{2 \cdot 3}{7} = \frac{6}{7}\]

\[3)\ \frac{888}{999} = \frac{111 \cdot 8}{111 \cdot 9} = \frac{8}{9}\]

\[4)\frac{1111}{111111} = \frac{11 \cdot 101}{3 \cdot 7 \cdot 11 \cdot 13 \cdot 37} =\]

\[= \frac{101}{21 \cdot 13 \cdot 37} = \frac{101}{10101}\]

\[5)\frac{2323}{3434} = \frac{23 \cdot 101}{2 \cdot 17 \cdot 101} = \frac{23}{34}\]

\[6)\frac{121212}{191919} =\]

\[= \frac{2 \cdot 2 \cdot 3 \cdot 3 \cdot 7 \cdot 13 \cdot 37}{3 \cdot 7 \cdot 13 \cdot 19 \cdot 37} =\]

\[= \frac{2 \cdot 2 \cdot 3}{19} = \frac{12}{19}\]

\[\boxed{\mathbf{384}\mathbf{.}}\]

\[1)\ 1\frac{5^{\backslash 4}}{7} + 3\frac{11^{\backslash 2}}{14} - 2\frac{1^{\backslash 7}}{4} =\]

\[= 2 + \frac{20 + 22 - 7}{28} = 3 + \frac{35}{28} =\]

\[= 3 + 1\frac{7}{28} = 3 + 1\frac{1}{4} = 4\frac{1}{4}\]

\[2)\ 17\frac{2}{3} - \left( 6\frac{1^{\backslash 2}}{36} - 4\frac{3^{\backslash 9}}{8} \right) =\]

\[= 17\frac{2}{3} - \left( 6\frac{2}{72} - 4\frac{27}{72} \right) =\]

\[= 17\frac{2}{3} - \left( 5\frac{74}{72} - 4\frac{27}{72} \right) =\]

\[= 17\frac{2^{\backslash 24}}{3} - 1\frac{47}{72} =\]

\[= 17\frac{48}{72} - 1\frac{47}{72} = 16\frac{1}{72}\]