Question

Write down ten rational numbers which are equivalent to $\frac{5}{7}$ and the denominator not exceeding $80$

Answer 1

Firstly, we multiply the numerator and denominator of the given fraction $\frac{5}{7}$ by $2$ and then we clearly see that the denominator is less than $80$

$\frac{5\times 2}{7\times 2}=\frac{10}{14}$

Now, we multiply the numerator and denominator of the given fraction $\frac{5}{7}$ by $3$ and then again the denominator is less than $80$

$\frac{5\times 3}{7\times 3}=\frac{15}{21}$

Similarly, we get the remaining eight rational numbers that are equivalent to $\frac{5}{7}$ and the denominator does not exceeds $80$ as shown below:

$\frac{5\times 4}{7\times 4}=\frac{20}{28}$

$\frac{5\times 5}{7\times 5}=\frac{25}{35}$

$\frac{5\times 6}{7\times 6}=\frac{30}{42}$

$\frac{5\times 7}{7\times 7}=\frac{35}{49}$

$\frac{5\times 8}{7\times 8}=\frac{40}{56}$

$\frac{5\times 9}{7\times 9}=\frac{45}{63}$

$\frac{5\times 10}{7\times 10}=\frac{50}{70}$

$\frac{5\times 11}{7\times 11}=\frac{55}{77}$