Решебник по математике 6 класс Виленкин Часть 1, 2 Часть 1. Параграф 3. Отношения и пропорции Задание 180

\[\boxed{\mathbf{3.180}}\]

\[\frac{a}{b} = \frac{c}{d}\]

\[1)\ c = \frac{\text{ad}}{b} = \frac{15}{3} = 5.\]

\[2)\ b = \frac{\text{ad}}{c} = \frac{2 \cdot 10,5}{3,5} = 2 \cdot 3 = 6.\]

\[3)\ d = \frac{\text{bc}}{a} = \frac{4,8 \cdot 1}{2,4} = 2.\]

\[4)\ c = \frac{\text{ad}}{b} = 1\frac{1}{2} \cdot 5,2\ :2\frac{1}{4} =\]

\[= \frac{3}{2} \cdot \frac{52}{10}\ :\frac{9}{4} = \frac{3 \cdot 26 \cdot 4}{2 \cdot 5 \cdot 9} =\]

\[= \frac{13 \cdot 4}{5 \cdot 3} = \frac{52}{15} = 3\frac{7}{15}.\]

\[5)\ a = \frac{\text{bc}}{d} = \frac{4}{5} \cdot 2\frac{1}{3}\ :2,8 =\]

\[= \frac{4}{5} \cdot \frac{7}{3}\ :\frac{14}{5} = \frac{4 \cdot 7 \cdot 5}{5 \cdot 3 \cdot 14} = \frac{2}{3}.\]

\[6)\ c = \frac{\text{ad}}{b} = \frac{3x \cdot 0,7}{2x} = \frac{2,1}{2} =\]

\[= 1,05.\]

\[7)\ b = \frac{\text{ad}}{c} = \frac{5,2a \cdot 0,6}{2,1} =\]

\[= \frac{5,2a \cdot 2}{7} = \frac{10,4a}{7} = \frac{104}{70}a =\]

\[= \frac{52}{35}a = 1\frac{17}{35}\text{a.}\]

\[8)\ 3\frac{2}{5}\ :1,5 = c\ :d\]

\[\frac{17}{5}\ :\frac{15}{10} = c\ :d\]

\[\frac{17 \cdot 10}{5 \cdot 15} = c\ :d\]

\[\frac{c}{d} = \frac{34}{15}.\]

\[c = 34;\ \ d = 15.\]

\[9)\ a\ :b = 2\frac{3}{4}\ :3\frac{2}{3}\]

\[a\ :b = \frac{11}{4}\ :\frac{11}{3}\]

\[a\ :b = \frac{11}{4} \cdot \frac{3}{11}\]

\[\frac{a}{b} = \frac{3}{4}.\]

\[a = 3;\ \ b = 4.\]