The product of two fractions is $8\dfrac{7}{25}$. If one of them is $3\dfrac{1}{15}$ find the other.

Given:

Let the two fractions be p and q.

p = $3\dfrac{1}{15} = \dfrac{46}{15}$

Let the other fraction be q.

p x q = $8\dfrac{7}{25} = \dfrac{207}{25}$

q = $\dfrac{207}{25}$ ÷ p $\hspace{2cm}\text{[Solving for q]}$

Substituting the value of p, we get:

q = $\dfrac{207}{25} ÷ \dfrac{46}{15}$

$\begin{array}{ll} = \dfrac{207}{25} \times \dfrac{15}{46} & [\text{Reciprocal of } \dfrac{46}{15} \text{ is } \dfrac{15}{46}] \\ = \dfrac{207}{5} \times \dfrac{3}{46} & \text{[Simplifying 15 and 25 ⇒ Divide by 5]} \\ = \dfrac{9}{5} \times \dfrac{3}{2} & \text{[Simplifying 207 and 46 ⇒ Divide by 23]} \\ = \dfrac{9 \times 3}{5 \times 2} \\ = \dfrac{27}{10} \\ = 2\dfrac{7}{10} \end{array}$

∴ The other fraction = $2\dfrac{7}{10}$