By what number must $-\dfrac{3}{4}$ be multiplied so that the product is $-\dfrac{9}{16}$?

Let the number be $x$

$-\dfrac{3}{4} \times x = -\dfrac{9}{16}\\[1em] \Rightarrow x = -\dfrac{9}{16} ÷ -\dfrac{3}{4}\\[1em] \Rightarrow x = \dfrac{9}{16} \times \dfrac{4}{3}\\[1em] \Rightarrow x = \dfrac{9 \times 4}{16 \times 3}\\[1em] \Rightarrow x = \dfrac{36}{48}\\[1em] \Rightarrow x = \dfrac{3}{4}$

$-\dfrac{3}{4}$ must be multiplied by $\dfrac{3}{4}$ so that the product is $-\dfrac{9}{16}$.