Question

Stiind ca x/y=5/7, calculeaza
a.x+y/y
b.2x+y/2y
c.5x-3y/4y
d.4x-y/y

Answer 1

 

$\displaystyle\bf\\\frac{x}{y}=\frac{5}{7}\\\\a)\\\\\frac{x+y}{y}=\frac{x}{y}+\frac{y}{y}=\frac{5}{7}+1=1\frac{5}{7}=\frac{1\times7+5}{7}=\frac{12}{7}\\\\b)\\\\\frac{2x+y}{2y}=\frac{2x}{2y}+\frac{y}{2y}=\frac{5}{7}+\frac{1}{2}=\frac{10}{14}+\frac{7}{14}=\frac{10+7}{14}=\frac{17}{14}\\\\c)\\\frac{5x+3y}{4y}=\frac{5x}{4y}+\frac{3y}{4y}=\frac{5}{4}\times\frac{5}{7}+\frac{3}{4}=\frac{5\times5}{4\times7}+\frac{3}{4}=\\\\=\frac{25}{28}+\frac{3}{4}=\frac{25}{28}+\frac{21}{28}=\frac{25+21}{28}=\frac{46}{28}$

.

$\displaystyle\bf\\d)\\\\\frac{4x-y}{y}=\frac{4x}{y}-\frac{y}{y}=4\times\frac{5}{7}-1=\frac{4\times5}{7}-\frac{7}{7} =\frac{20}{7}-\frac{7}{7}=\frac{20-7}{7}=\frac{13}{7}$