Question

Write down $15$ rational numbers which are equivalent to $\frac{11}{5}$ and the numerator not exceeding $180$

Answer 1

We know that A number will be unchanged if you multiply and divide it by same non- zero number.

So multiply and divide given number by 2 to 16

Hence 15 rational numbers which are equivalent to $\frac{11}{5}$ and denominator not exceeding $180$

are $\frac{11\times 2}{5\times 2}$, $\frac{11\times 3}{5\times 3}$, $\frac{11\times 4}{5\times 4}$,$\frac{11\times 5}{5\times 5}$,$\frac{11\times 6}{5\times 6}$,$\frac{11\times 7}{5\times 7}$,$\frac{11\times 7}{5\times 7}$,$\frac{11\times 8}{5\times 8}$$\frac{11\times 9}{5\times 9}$,$\frac{11\times 10}{5\times 11}$,$\frac{11\times 12}{5\times 12}$,$\frac{11\times 13}{5\times 13}$,$\frac{11\times 14}{5\times 14}$,$\frac{11\times 15}{5\times 15}$,$\frac{11\times 16}{5\times 16}$

or $\frac{22}{10}$, $\frac{33}{15}$, $\frac{44}{20}$, $\frac{55}{25}$, $\frac{66}{30}$, $\frac{77}{35}$, $\frac{88}{40}$, $\frac{99}{45}$, $\frac{110}{50}$, $\frac{121}{55}$, $\frac{132}{60}$, $\frac{143}{65}$, $\frac{154}{70}$, $\frac{165}{75}$, $\frac{177}{80}$