Question

After expressing the following as a rational number of the form $$\dfrac{p}{q}$$
$$\dfrac{-7}{4}+\dfrac{5}{3}+\dfrac{-1}{2}+\dfrac{-5}{6}+2$$ , then the value equivalent to $$p$$ is ___.

Answer 1

Correct option is A. 7
$$\dfrac{-7}{4}+\dfrac{5}{3}+\dfrac{-1}{2}+\dfrac{-5}{6}+2$$

$$ =\dfrac{-7}{4} - \dfrac{1}{2} + \dfrac{5}{3} - \dfrac{5}{6} + 2 = \dfrac{-7-2}{4} + \dfrac{5\times 2 - 5}{6} + 2$$

$$= \dfrac{-9}{4} + \dfrac{5}{6}+2 = \dfrac{-9\times 3 + 5 \times 2 + 2\times 12}{12}$$

$$= \dfrac{-27+10+24}{12} = \dfrac{7}{12}$$

It is of the form $$\dfrac p q $$ then value equivalent to $$p$$ is $$7$$