Question

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Answer 1

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1).

$3\frac{2}{5} : x= 6\frac{4}{5} : 1 \frac{1}{3}\\\\6\frac{4}{5}*x=3\frac{2}{5} * 1 \frac{1}{3}\\\\\frac{34}{5}*x=\frac{17}{5} *\frac{4}{3}\\\\x= \frac{17}{5} * \frac{4}{3}:\frac{34}{5}\\\\x= \frac{17}{5} *\frac{4}{3}*\frac{5}{34}\\\\x=\frac{17*4*5}{5*3*34} \\\\x=\frac{1*4*1}{1*3*2} \\\\x=\frac{2}{3}$

2).

$7\frac{1}{3} : 2 \frac{1}{2} = 3\frac{2}{3} : y\\\\y*7\frac{1}{3} =2 \frac{1}{2}*3\frac{2}{3}\\\\y=2 \frac{1}{2}*3\frac{2}{3}: 7\frac{1}{3} \\\\y=\frac{5}{2} *\frac{11}{3} *\frac{3}{22}\\\\y=\frac{5*11*3}{2*3*22} \\\\y=\frac{5*1*1}{2*1*2} \\\\y=\frac{5}{4} \\\\y=1\frac{1}{4}$

3).

$4\frac{2}{5} : x=8\frac{4}{5} : 2\frac{1}{2} \\\\8\frac{4}{5} *x=2\frac{1}{2} *4\frac{2}{5} \\\\x=2\frac{1}{2} *4\frac{2}{5} : 8\frac{4}{5} \\\\x=\frac{5}{2} *\frac{22}{5} *\frac{8}{44} \\\\x=\frac{5*22*8}{2*5*44} \\\\x=\frac{1*1*4}{1*1*2} \\\\x=\frac{4}{2} \\\\x=2$

4).

$6\frac{1}{2} : 3\frac{3}{4} =3\frac{1}{4} :y\\\\6\frac{1}{2}*y= 3\frac{3}{4} *3\frac{1}{4}\\\\y= 3\frac{3}{4}*3\frac{1}{4} :6\frac{1}{2}\\\\y=\frac{15}{4} *\frac{13}{4} *\frac{2}{13} \\\\y=\frac{15*13*2}{4*4*13} \\\\y=\frac{15*1*1}{2*4*1} \\\\y=\frac{15}{8} \\\\y=1\frac{7}{8}$