(i) Find the equivalent fraction of $\dfrac{15}{35}$ with denominator 7

(ii) Find the equivalent fraction of $\dfrac{2}{9}$ with denominator 63

(i) Equivalent fraction of $\dfrac{15}{35}$ with denominator 7

To get 7 from 35, we have to divide 35 by 5.

So, divide both numerator and denominator by 5.

$\Rightarrow \dfrac{15}{35} = \dfrac{15 \div 5}{35 \div 5} \\[1em] = \dfrac{3}{7}.$

Hence, the required equivalent fraction = $\dfrac{3}{7}$.

(ii) Equivalent fraction of $\dfrac{2}{9}$ with denominator 63

To get 63 from 9, we have to multiply 9 by 7.

So, multiply both numerator and denominator by 7.

$\Rightarrow \dfrac{2}{9} = \dfrac{2 \times 7}{9 \times 7} \\[1em] = \dfrac{14}{63}.$

Hence, the required equivalent fraction = $\dfrac{14}{63}$.