Question

Evaluate:

$\frac{9}{4}+\frac{13}{12}+\frac{15}{8}+\frac{(-11)}{15}$

Answer 1

Evaluate :

First convert all the rational numbers into equivalent form.

$\frac{9}{4}+\frac{13}{12}+\frac{15}{8}+\frac{(-11)}{15}=\frac{9}{4}+\frac{13}{12}+\frac{15}{8}-\frac{11}{15}$

Now LCM (least common multiple) of denominator $4,12,8$ and $15$ is $120$.

So, convert the given rational numbers in equivalent fraction with denominator $120$.

$$\begin{gathered} \frac{9\times 30}{4\times 30}=\frac{270}{120}, \\ \frac{13\times 10}{12\times 10}=\frac{130}{120}, \\ \frac{15\times 15}{8\times 15}=\frac{225}{120} \end{gathered}$$

and $\frac{(-11)\times 8}{15\times 8}=\frac{-88}{120}$

Now, $\frac{9}{4}+\frac{13}{12}+\frac{15}{8}-\frac{11}{15}=\frac{270}{120}+\frac{130}{120}+\frac{225}{120}-\frac{88}{120}$

$$\begin{gathered} =\frac{270+130+225-88}{120} \\ =\frac{537}{120} \end{gathered}$$

Hence, $\frac{9}{4}+\frac{13}{12}+\frac{15}{8}+\frac{(-11)}{15}=\frac{537}{120}$.