Find -45-37-1516- -149

45×37×1516× ( 149 ) = 15×37×154× ( 149 ) = 15×31×154× ( 29 ) = 11×31×34× ( 29 ) = 94× ( 29 ) =( 1)× ( 2)4 =24=12 ...

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Byju's Answer

Standard VI

Mathematics

Importance of Brackets

Find -45×37...

Question

Find $\frac{- 4}{5} \times \frac{3}{7} \times \frac{15}{16} \times (\frac{- 14}{9})$

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Solution

Given $\frac{- 4}{5} \times \frac{3}{7} \times \frac{15}{16} \times (\frac{- 14}{9})$ [Since $- 4$ and $16$ gets cancelled by $4$ ]

$= \frac{- 1}{5} \times \frac{3}{7} \times \frac{15}{4} \times (\frac{- 14}{9})$ [ $- 14$ and $7$ gets cancelled by 7]

$= \frac{- 1}{5} \times \frac{3}{1} \times \frac{15}{4} \times (\frac{- 2}{9})$ [ $5$ and $15$ gets cancelled by $5$ ]

$= \frac{- 1}{1} \times \frac{3}{1} \times \frac{3}{4} \times (\frac{- 2}{9})$

$= \frac{- 9}{4} \times (\frac{- 2}{9})$ [ $- 9$ and $9$ gets cancelled by $9$ itself]

$= \frac{(- 1) \times (- 2)}{4}$

$= \frac{2}{4} = \frac{1}{2}$

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Similar questions

Q. 3, 20, 18, 16 : 5, 14, 9, 7 : : 6, 15, 12, 10 : ?

Name the property of multiplication illustrated by each of the following statements :

(i) $\frac{- 15}{8} \times \frac{- 12}{7} = \frac{- 12}{7} \times \frac{- 15}{8}$

(ii) $(\frac{- 2}{3} \times \frac{7}{9}) \times \frac{- 9}{5} = \frac{- 2}{3} \times (\frac{7}{9} \times \frac{- 9}{5})$

(iii) $\frac{- 3}{4} \times (\frac{- 3}{4} \times \frac{- 5}{6}) + (\frac{- 3}{4} \times \frac{7}{8})$

(iv) $\frac{- 16}{9} \times 1 = 1 \times \frac{- 16}{9} = \frac{- 16}{9}$

(v) $\frac{- 11}{15} \times \frac{15}{- 11} = \frac{15}{- 11} \times \frac{- 11}{15} = 1$

(vi) $\frac{- 7}{5} \times 0 = 0$

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) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

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

2, 3, 4, 14; 2, 3, 4, 16; 13, 14, 15, 9, ?

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Find −45×37×1516×(−149)

Given −45×37×1516×(−149) [Since −4 and 16 gets cancelled by 4]=−15×37×154×(−149) [−14 and 7 gets cancelled by 7]=−15×31×154×(−29) [5 and 15 gets cancelled by 5]=−11×31×34×(−29)=−94×(−29) [−9 and 9 gets cancelled by 9 itself]=(−1)×(−2)4=24=12

Find $\frac{- 4}{5} \times \frac{3}{7} \times \frac{15}{16} \times (\frac{- 14}{9})$