Express each of the following as a rational number of the form pq-i -83-14-116-38-3ii 67-1-79-1921-127iii 152-98-113-6-76iv -74-0-95-1910-1114v -74-53-12-56-2

(i) #160; 83+ 14+ 116+38 3= 6424+ 624+ 4424+924 7224=( 64)+( 6)+( 44)+9+( 72)24= 64 6 44+9 7224= 17724= 598(ii) #160;67+1+ 79+1921+ 127=5463+6363+ 4963+5763 ...

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Byju's Answer

Standard VI

Mathematics

Associative Property

Express each ...

Question

Express each of the following as a rational number of the form $\frac{p}{q} :$
(i) $\frac{- 8}{3} + \frac{- 1}{4} + \frac{- 11}{6} + \frac{3}{8} - 3$
(ii) $\frac{6}{7} + 1 + \frac{- 7}{9} + \frac{19}{21} + \frac{- 12}{7}$
(iii) $\frac{15}{2} + \frac{9}{8} + \frac{- 11}{3} + 6 + \frac{- 7}{6}$
(iv) $\frac{- 7}{4} + 0 + \frac{- 9}{5} + \frac{19}{10} + \frac{11}{14}$
(v) $\frac{- 7}{4} + \frac{5}{3} + \frac{- 1}{2} + \frac{- 5}{6} + 2$

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Solution

$(i) \frac{- 8}{3} + \frac{- 1}{4} + \frac{- 11}{6} + \frac{3}{8} - 3 = \frac{- 64}{24} + \frac{- 6}{24} + \frac{- 44}{24} + \frac{9}{24} - \frac{72}{24} = \frac{(- 64) + (- 6) + (- 44) + 9 + (- 72)}{24} = \frac{- 64 - 6 - 44 + 9 - 72}{24} = \frac{- 177}{24} = \frac{- 59}{8} (ii) \frac{6}{7} + 1 + \frac{- 7}{9} + \frac{19}{21} + \frac{- 12}{7} = \frac{54}{63} + \frac{63}{63} + \frac{- 49}{63} + \frac{57}{63} + \frac{- 108}{63} = \frac{54 + 63 + (- 49) + 57 + (- 108)}{63} = \frac{54 + 63 - 49 + 57 - 108}{63} = \frac{17}{63} (iii) \frac{15}{2} + \frac{9}{8} + \frac{- 11}{3} + 6 + \frac{- 7}{6} = \frac{180}{24} + \frac{27}{24} + \frac{- 88}{24} + \frac{144}{24} + \frac{- 28}{24} = \frac{180 + 27 + (- 88) + 144 + (- 28)}{24} = \frac{180 + 27 - 88 + 144 - 28}{24} = \frac{235}{24} (iv) \frac{- 7}{4} + 0 + \frac{- 9}{5} + \frac{19}{10} + \frac{11}{14} = \frac{- 245}{140} + \frac{- 252}{140} + \frac{266}{140} + \frac{110}{140} = \frac{(- 245) + (- 252) + 266 + 110}{140} = \frac{- 245 - 252 + 266 + 110}{140} = \frac{- 121}{140} (v) \frac{- 7}{4} + \frac{5}{3} + \frac{- 1}{2} + \frac{- 5}{6} + 2 = \frac{- 21}{12} + \frac{20}{12} + \frac{- 6}{12} + \frac{- 10}{12} + \frac{24}{12} = \frac{(- 21) + 20 + (- 6) + (- 10) + 24}{12} = \frac{- 21 + 20 - 6 - 10 + 24}{12} = \frac{7}{12}$

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