Find 311-56-912-43-513-615

Consider, (311×56) (912×43)+(513×615) Solving it we get ⇒522 1+213 ⇒5 2222+213=213 1722 ⇒44 221286= 177286 ...

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Byju's Answer

Standard VIII

Mathematics

Commutative Property of Rational Numbers

Find 311×56...

Question

Find $(\frac{3}{11} \times \frac{5}{6}) - (\frac{9}{12} \times \frac{4}{3}) + (\frac{5}{13} \times \frac{6}{15})$

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Solution

Consider, $(\frac{3}{11} \times \frac{5}{6}) - (\frac{9}{12} \times \frac{4}{3}) + (\frac{5}{13} \times \frac{6}{15})$

Solving it we get
$\Rightarrow \frac{5}{22} - 1 + \frac{2}{13}$
$\Rightarrow \frac{5 - 22}{22} + \frac{2}{13} = \frac{2}{13} - \frac{17}{22}$
$\Rightarrow \frac{44 - 221}{286} = \frac{- 177}{286}$

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

Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

Find each of the following products :

(i) $\frac{3}{5} \times \frac{- 7}{8}$ (ii) $\frac{- 9}{2} \times \frac{5}{4}$ (iii) $\frac{- 6}{11} \times \frac{- 5}{3}$

(iv) $\frac{- 2}{3} \times \frac{6}{7}$ (v) $\frac{- 12}{5} \times \frac{10}{- 3}$ (vi) $\frac{25}{- 9} \times \frac{3}{- 10}$

(vii) $\frac{5}{- 18} \times \frac{- 9}{20}$ (viii) $\frac{- 13}{15} \times \frac{- 25}{26}$ (ix) $\frac{16}{- 21} \times \frac{14}{5}$

(x) $\frac{- 7}{6} \times 24$ (xi) $\frac{7}{24} \times (- 48)$ (xii) $\frac{- 13}{5} \times (- 10)$

Q. Write the following in set builder form:
(a)

1, 3, 5, 7, 9, 11, 13

(b)

3, 6, 9, 12, 15

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Find (311×56)−(912×43)+(513×615)

Consider, (311×56)−(912×43)+(513×615)Solving it we get⇒522−1+213⇒5−2222+213=213−1722⇒44−221286=−177286

Find $(\frac{3}{11} \times \frac{5}{6}) - (\frac{9}{12} \times \frac{4}{3}) + (\frac{5}{13} \times \frac{6}{15})$