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Line, Line Segment and Ray

Simplify:i 89...

Question

Simplify:
(i) $\frac{8}{9} + \frac{- 11}{6}$
(ii) $\frac{- 5}{16} + \frac{7}{24}$
(iii) $\frac{1}{- 12} + \frac{2}{- 15}$
(iv) $\frac{- 8}{19} + \frac{- 4}{57}$

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Solution

$(i) \frac{8}{9} + \frac{- 11}{6} LCM of the denominators 9 and 6 is 18 . Now, we express \frac{8}{9} and \frac{- 11}{6} into forms in which both of them have the same denominator as LCM . \frac{8}{9} = \frac{8 \times 2}{9 \times 2} \frac{- 11}{6} = \frac{- 11 \times 3}{6 \times 3} Therefore, \frac{8 \times 2}{9 \times 2} + \frac{- 11 \times 3}{6 \times 3} = \frac{16 - 33}{18} = \frac{- 17}{18}$

$(ii) \frac{- 5}{16} + \frac{7}{24} LCM of the denominators 16 and 24 is 48 . Now, we express \frac{- 5}{16} and \frac{7}{24} into forms in which both of them have the same denominator as LCM . \frac{- 5}{16} = \frac{- 5 \times 3}{16 \times 3} \frac{7}{24} = \frac{7 \times 2}{24 \times 2} Therefore, \frac{- 5 \times 3}{16 \times 3} + \frac{7 \times 2}{24 \times 2} = \frac{- 15 + 14}{48} = \frac{- 1}{48} (iii) \frac{1}{- 12} + \frac{2}{- 15} LCM of the denominators 12 and 15 is 60 . Now, we express \frac{- 1}{12} and \frac{- 2}{15} into forms in which both of them have the same denominator as LCM . \frac{- 1}{12} = \frac{- 1 \times 5}{12 \times 5} \frac{- 2}{15} = \frac{- 2 \times 4}{15 \times 4} Therefore, \frac{- 1 \times 5}{12 \times 5} + \frac{- 2 \times 4}{15 \times 4} = \frac{- 5 - 8}{60} = \frac{- 13}{60}$

$(iv) \frac{- 8}{19} + \frac{- 4}{57} LCM of the denominators 19 and 57 is 57 . Now, we express \frac{- 8}{19} and \frac{- 4}{57} into forms in which both of them have the same denominator as LCM . \frac{8}{9} = \frac{- 8 \times 3}{19 \times 3} \frac{- 4}{57} = \frac{- 4 \times 1}{57 \times 1} Therefore, \frac{- 8 \times 3}{19 \times 3} + \frac{- 4}{57} = \frac{- 24 - 4}{57} = \frac{- 28}{57}$

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