By what fraction should $\dfrac{9}{35}$ be multiplied to get $\dfrac{7}{15}$ ?

Given:

The fraction by which $\dfrac{9}{35}$ must be multiplied to get $\dfrac{7}{15}$ = ?

Let the required fraction be x

Now we have,

$\dfrac{9}{35} \times x = \dfrac{7}{15}$

x = $\dfrac{7}{15} ÷ \dfrac{9}{35}$

$\begin{array}{ll} = \dfrac{7}{15} \times \dfrac{35}{9} & [\text{Reciprocal of } \dfrac{9}{35} \text{ is } \dfrac{35}{9}] \\ = \dfrac{7}{3} \times \dfrac{7}{9} & \text{[Simplifying 35 and 15 ⇒ Divide by 5]} \\ = \dfrac{7 \times 7}{3 \times 9} \\ = \dfrac{49}{27} \\ = 1\dfrac{22}{27} \end{array}$

∴ The answer is $1\dfrac{22}{27}$