Question

Select those which can be written as a rational number with denominator 5 in their standard form:
$\frac{-50}{75},\frac{-15}{25},\frac{45}{-75},\frac{10}{-5},\frac{55}{15},\frac{-20}{65},\frac{-15}{75},$ and $\frac{35}{30}$

Answer 1

A rational number is said to be in its standard form if both the numerator and denominator contain no common factors other than 1, and the denominator should have a positive integer.

$\frac{50}{75}=\frac{-25\times 2}{25\times 3}=\frac{-2}{3}$

$\frac{-15}{25}=\frac{-5\times 3}{5\times 5}=\frac{-3}{5}$

$\frac{45}{-75}=\frac{15\times 3}{-15\times 5}=\frac{-3}{5}$

$\frac{10}{-5}=\frac{5\times 2}{-1\times 5}=-2$

$\frac{55}{15}=\frac{5\times 11}{5\times 3}=\frac{11}{3}$

$\frac{-20}{65}=\frac{-5\times 4}{5\times 13}=\frac{-4}{13}$

$\frac{-15}{75}=\frac{-1\times 15}{5\times 15}=\frac{-1}{5}$

$\frac{-35}{30}=\frac{-5\times 7}{5\times 6}=\frac{-7}{6}$

$\frac{-15}{25},\frac{45}{-75},$ and $\frac{-15}{75}$ can be written in standard form with denominators as 5.