Question

Simplify:

(2) $\frac{3}{2}+\left(\frac{5}{6}+\frac{-4}{5}\right)$

Answer 1

$$\begin{gathered} \frac{3}{2}+\left(\frac{5}{6}+\frac{-4}{5}\right) \\ =\frac{3}{2}+\left(\frac{5\times 5}{6\times 5}+\frac{-4\times 6}{5\times 6}\right) \\ =\frac{3}{2}+\left(\frac{25}{30}+\frac{-24}{30}\right) \\ =\frac{3}{2}+\left(\frac{25+\left(-24\right)}{30}\right) \\ =\frac{3}{2}+\left(\frac{25-24}{30}\right) \\ =\frac{3}{2}+\frac{1}{30} \\ =\frac{3\times 15}{2\times 15}+\frac{1}{30} \\ =\frac{45}{30}+\frac{1}{30}=\frac{45+1}{30}=\frac{46}{30}=\frac{23}{15} \end{gathered}$$