Question

Which of the following fraction is the smallest? $\frac{7}{6},\frac{7}{9},\frac{4}{5},\frac{5}{7}$

• A. $\frac{7}{6}$
• B. $\frac{7}{9}$
• C. $\frac{4}{5}$
• D. $\frac{5}{7}$

Answer 1

The correct option is D $\frac{5}{7}$

let the fractions be a, b, c, d

$\frac{a}{b}=\frac{7}{6}\times \frac{9}{7}=\frac{9}{6}>1\Rightarrow a>b$

a is not smallest

$\frac{b}{c}=\frac{7}{9}\times \frac{4}{5}=\frac{28}{45}<1\Rightarrow c>b$

c is not smallest

$\frac{b}{d}=\frac{7}{9}\times \frac{7}{5}=\frac{49}{45}>1\Rightarrow b>d$

$\Rightarrow$ d is smallest $\Rightarrow \left(D\right)$