Verify each of the following - i 3-7-5-9 - -5-9-3-7 ii -8-7-13-9 - 13-9-8-7 iii -12-5-7-36 - 7-36-12-5 iv -8 -13-12 - -13-12- -8

(i) L.H.S. = 3/7× 5/9 = 3 × ( 5)/7 × 9 = 15/63 R.H.S. = 5/9×3/7 = 5 × 3/9 × 7 = 15/63 ∴3/7× 5/9 = 5/9×3/7 (ii) L.H.S. = 8/7×13/9= 8 × 13/7 × 9 = 104/63 ...

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Standard VII

Mathematics

Multiplication and Division of Rational Numbers

Verify each o...

Question

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

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Solution

(i) $L . H . S . = \frac{3}{7} \times \frac{- 5}{9}$

$= \frac{3 \times (- 5)}{7 \times 9} = \frac{- 15}{63}$

$R . H . S . = \frac{- 5}{9} \times \frac{3}{7} = \frac{- 5 \times 3}{9 \times 7} = \frac{- 15}{63}$

$∴ \frac{3}{7} \times \frac{- 5}{9} = \frac{- 5}{9} \times \frac{3}{7}$

(ii) $L . H . S . = \frac{- 8}{7} \times \frac{13}{9} = \frac{- 8 \times 13}{7 \times 9} = \frac{- 104}{63}$

$R . H . S . = \frac{13}{9} \times \frac{- 8}{7} = \frac{13 \times (- 8)}{9 \times 7} = \frac{- 104}{63}$

$∴ \frac{- 8}{7} \times \frac{13}{9} = \frac{13}{9} \times \frac{- 8}{7}$

(iii) $L . H . S . = \frac{- 12}{5} \times \frac{7}{- 36} = \frac{- 12 \times 7}{5 \times (- 36)}$

$= \frac{- 84}{- 180} = \frac{84}{180} = \frac{84 \div 12}{180 \div 12} = \frac{7}{15}$

$R . H . S . = \frac{7}{- 36} = \frac{- 12}{5} = \frac{7 \times (- 12)}{- 36 \times 5} = \frac{- 84}{- 180}$

$= \frac{84}{180} = \frac{84 \div 12}{180 \div 12} = \frac{7}{15}$

$∴ \frac{- 12}{5} \times \frac{7}{- 36} = \frac{7}{- 36} \times \frac{- 12}{5}$

(iv) $L . H . S . = - 8 \times \frac{- 13}{12} = \frac{- 8 \times (- 13)}{12}$

$= \frac{104}{12} = \frac{104 \div 4}{12 \div 4} = \frac{26}{3}$

$R . H . S . = \frac{- 13}{12} \times \frac{- 13 \times (- 8)}{12} = \frac{104}{12}$

$= \frac{104 \div 4}{12 \div 4} = \frac{26}{3}$

$∴ - 8 \times \frac{13}{12} = \frac{- 13}{12} \times - 8$

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Similar questions

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) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

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

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

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

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

Verify each of the following :

(i) $(\frac{5}{7} \times \frac{12}{13}) \times \frac{7}{18} = \frac{5}{7} \times (\frac{12}{13} \times \frac{7}{18})$
(ii) $\frac{- 13}{24} \times (\frac{- 12}{5} \times \frac{35}{36}) = (\frac{- 13}{24} \times \frac{- 12}{5}) \times \frac{35}{36}$
(iii) $(\frac{- 9}{5} \times \frac{- 10}{3}) \times \frac{21}{- 4} = \frac{- 9}{5} \times (\frac{- 10}{3} \times \frac{21}{- 4})$

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

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