Simplify each of the following and write as a rational number of the form
Question:

Simplify each of the following and write as a rational number of the form $\frac{p}{q}$ :

(i) $\frac{3}{4}+\frac{5}{6}+\frac{-7}{8}$

(ii) $\frac{2}{3}+\frac{-5}{6}+\frac{-7}{9}$

(iii) $\frac{-11}{2}+\frac{7}{6}+\frac{-5}{8}$

(iv) $\frac{-4}{5}+\frac{-7}{10}+\frac{-8}{15}$

(v) $\frac{-9}{10}+\frac{22}{15}+\frac{13}{-20}$

(vi) $\frac{5}{3}+\frac{3}{-2}+\frac{-7}{3}+3$

Solution:

(i) $\frac{3}{4}+\frac{5}{6}+\frac{-7}{8}$

$=\frac{18}{24}+\frac{20}{24}+\frac{-21}{24}$

$=\frac{18+20+(-21)}{24}$

$=\frac{18+20-21}{24}$

$=\frac{17}{24}$

(ii) $\frac{2}{3}+\frac{-5}{6}+\frac{-7}{9}$

$=\frac{12}{18}+\frac{-15}{18}+\frac{-14}{18}$

$=\frac{12+(-15)+(-14)}{18}$

$=\frac{12-15-14}{18}$

$=\frac{-17}{18}$

(iii) $\frac{-11}{2}+\frac{7}{6}+\frac{-5}{8}$

$=\frac{-132}{24}+\frac{28}{24}+\frac{-15}{24}$

$=\frac{(-132)+28+(-15)}{24}$

$=\frac{-132+28-15}{24}$

$=\frac{-119}{24}$

(iv) $\frac{-4}{5}+\frac{-7}{10}+\frac{-8}{15}$

$=\frac{-24}{30}+\frac{-21}{30}+\frac{-16}{30}$

$=\frac{(-24)+(-21)+(-16)}{30}$

$=\frac{-24-21-16}{30}$

$=\frac{-61}{30}$

(v) $\frac{-9}{10}+\frac{22}{15}+\frac{13}{-20}$

$=\frac{-54}{60}+\frac{88}{60}+\frac{-39}{60}$

$=\frac{(-54)+88+(-39)}{60}$

$=\frac{-54+88-39}{60}$

$=\frac{-5}{60}$

$=\frac{-1}{12}$

(vi) $\frac{5}{3}+\frac{3}{-2}+\frac{-7}{3}+3$

$=\frac{10}{6}+\frac{-9}{6}+\frac{-14}{6}+\frac{18}{6}$

$=\frac{10+(-9)+(-14)+18}{6}$

$=\frac{10-9-14+18}{6}$

$=\frac{5}{6}$