Question

Add and express the sum as mixed fraction: (i)$\frac{-12}{5}and\frac{43}{10}$ (ii)$\frac{24}{7}and\frac{-11}{4}$ (iii)$\frac{-31}{6}and\frac{-27}{8}$ (iv)$\frac{101}{6}and\frac{7}{8}$

Answer 1

(i)$\frac{-12}{5}and\frac{43}{10}\frac{-12}{5}=\frac{-12\times 2}{5\times 2}=\frac{-24}{10}\therefore \frac{-12}{5}+\frac{43}{10}=\frac{-24}{10}+\frac{43}{10}=\frac{-24+43}{10}=\frac{19}{10}=1\frac{9}{10}$ (ii) $\frac{24}{7}and\frac{-11}{4}LCMof7,4=28\therefore \frac{24}{7}=\frac{24\times 4}{7\times 4}=\frac{96}{28}and\frac{-11}{4}=\frac{-11\times 7}{4\times 7}=\frac{-77}{28}\therefore \frac{24}{7}+\frac{-11}{4}=\frac{96}{28}+\frac{-77}{28}=\frac{96-77}{28}=\frac{19}{28}$ (iii) $\frac{-31}{6}and\frac{-27}{8}LCMof6,8=24\therefore \frac{-31}{6}=\frac{-31\times 4}{6\times 4}=\frac{-124}{24}and\frac{-27}{8}=\frac{-27\times 3}{8\times 3}=\frac{-81}{24}\therefore \frac{-31}{6}+\frac{-27}{8}=\frac{-124}{24}+\frac{-81}{24}=\frac{-124-81}{24}=\frac{-205}{24}=-8\frac{13}{24}$ (iv) $\frac{101}{6}and\frac{7}{8}LCMof6,8=24\therefore \frac{101}{6}=\frac{101\times 4}{6\times 4}=\frac{404}{24}and\frac{7}{8}=\frac{7\times 3}{8\times 3}=\frac{21}{24}\therefore \frac{101}{6}+\frac{7}{8}=\frac{404}{24}+\frac{21}{24}=\frac{404+21}{24}=\frac{425}{24}=17\frac{17}{24}$