Rearrange suitably and find the sum in each of the following-vi 18-512-27-712-97-516

Given : nbsp;18+512+27+712+97+ 516 ∴18+512+27+712+97+ 516 =(18+ 516)+(27+97)+(512+712) =(1× 28× 2+ 516)+(2+97)+(5+712) =(2 516)+(117)+(1212) = 316+117+1 = 3× ...

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Standard VII

Mathematics

Operations on Rational Numbers using PEMDAS Rule

Rearrange sui...

Question

Rearrange suitably and find the sum in each of the following:

vi) $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$

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Solution

Given : $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$

$∴ \frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$
$= (\frac{1}{8} + \frac{- 5}{16}) + (\frac{2}{7} + \frac{9}{7}) + (\frac{5}{12} + \frac{7}{12})$
$= (\frac{1 \times 2}{8 \times 2} + \frac{- 5}{16}) + (\frac{2 + 9}{7}) + (\frac{5 + 7}{12})$
$= (\frac{2 - 5}{16}) + (\frac{11}{7}) + (\frac{12}{12})$
$= \frac{- 3}{16} + \frac{11}{7} + 1$
$= \frac{- 3 \times 7}{16 \times 7} + \frac{11 \times 16}{7 \times 16} + \frac{112}{112}$
$= \frac{- 21}{112} + \frac{176}{112} + \frac{112}{112}$
$= \frac{- 21 + 176 + 112}{112}$
$= \frac{267}{112}$

Hence, $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16} = \frac{267}{112}$

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Similar questions

Re-arrange suitably and find the sum in each of the following :

(i) $\frac{11}{12} + \frac{- 17}{3} + \frac{11}{2} + \frac{- 25}{2}$

(ii) $\frac{- 6}{7} + \frac{- 5}{6} + \frac{- 4}{9} + \frac{- 15}{7}$

(iii) $\frac{3}{5} + \frac{7}{3} + \frac{9}{5} + \frac{- 13}{15} + \frac{- 7}{3}$

(iv) $\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13}$

(v) $\frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5}$

(vi) $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Fill in the blanks.

(i) $(\frac{- 3}{17}) + (\frac{- 12}{5}) = (\frac{- 12}{5}) + (. . . . .)$

(ii) $- 9 + \frac{- 21}{8} = (. . . . . .) + (- 9)$

(iii) $(\frac{- 8}{13} + \frac{3}{7}) + (\frac{- 13}{4}) = (. . . . . .) + [\frac{3}{7} + (\frac{- 13}{4})]$

(iv) $- 12 + (\frac{7}{12} + \frac{- 9}{11}) = (- 12 + \frac{7}{12}) + (. . . . .)$

(v) $\frac{19}{- 5} + (\frac{- 3}{11} + \frac{- 7}{8}) = {\frac{19}{- 5} + (. . . . .)} + \frac{- 7}{8}$

(vi) $\frac{- 16}{7} + . . . . . = . . . . . . + \frac{- 16}{7} = \frac{- 16}{7}$

Verify each of the following :

(i) $\frac{3}{7} \times \frac{- 5}{9} = \frac{- 5}{9} \times \frac{3}{7}$

(ii) $\frac{- 8}{7} \times \frac{13}{9} = \frac{13}{9} \times \frac{- 8}{7}$

(iii) $\frac{- 12}{5} \times \frac{7}{- 36} = \frac{7}{- 36} \times \frac{- 12}{5}$

(iv) $- 8 \times \frac{- 13}{12} = \frac{- 13}{12} \times (- 8)$

Verify the following

(i) $\frac{- 12}{5} + \frac{2}{7} = \frac{2}{7} + \frac{- 12}{5}$

(ii) $\frac{- 5}{8} + \frac{- 9}{13} = \frac{- 9}{13} + \frac{- 5}{8}$

(iii) $3 + \frac{- 7}{12} = \frac{- 7}{12} + 3$

(iv) $\frac{2}{- 7} + \frac{12}{- 35} = \frac{12}{- 35} + \frac{2}{- 7}$

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Operations on Rational Numbers using PEMDAS Rule

Standard VII Mathematics

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Rearrange suitably and find the sum in each of the following: vi) 18+512+27+712+97+−516

Given : 18+512+27+712+97+−516 ∴18+512+27+712+97+−516 =(18+−516)+(27+97)+(512+712) =(1×28×2+−516)+(2+97)+(5+712) =(2−516)+(117)+(1212) =−316+117+1 =−3×716×7+11×167×16+112112 =−21112+176112+112112 =−21+176+112112 =267112 Hence, 18+512+27+712+97+−516=267112

Rearrange suitably and find the sum in each of the following:

vi) $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$