Question

Express the sum in the form of $\frac{p}{q}$: $-\frac{3}{4}+\frac{2}{3}+\frac{-4}{5}$.

Answer 1

Evaluate the given expression

Given expression: $-\frac{3}{4}+\frac{2}{3}+\frac{-4}{5}$.

The least common multiple of the denominators, $4$, $3$ and $5$ is $\left(4\times 3\times 5\right)=60$.

$$\begin{gathered} -\frac{3}{4}+\frac{2}{3}+\frac{-4}{5} \\ =\frac{\left(-3\right)\left(15\right)+\left(2\right)\left(20\right)+\left(-4\right)\left(12\right)}{60} \\ =\frac{-45+40-48}{60} \\ =\frac{-53}{60} \\ =-\frac{53}{60} \end{gathered}$$

Therefore, the sum of the given expression in the form $\frac{\mathbf{p}}{\mathbf{q}}$ is $\left(-\frac{53}{60}\right)$.