We have 45×37×1516×( 149)=( 4× 35× 7)×(15× ( 14)16× 9) = 1235×( 3524)=( 12× ( 34)35× 24)=12 We can also solve it as 45×37×1516×( 149)=( 45×1516)×[37×( 149 ...

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Byju's Answer

Standard VI

Mathematics

Closure Property

Find -45×37×1...

Question

$F i n d \frac{- 4}{5} \times \frac{3}{7} \times \frac{15}{16} \times (\frac{- 14}{9})$

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Solution

$W e h a v e \frac{- 4}{5} \times \frac{3}{7} \times \frac{15}{16} \times (\frac{- 14}{9}) = (- \frac{4 \times 3}{5 \times 7}) \times (\frac{15 \times (- 14)}{16 \times 9})$

$= \frac{- 12}{35} \times (\frac{- 35}{24}) = (\frac{- 12 \times (- 34)}{35 \times 24}) = \frac{1}{2}$

We can also solve it as

$\frac{- 4}{5} \times \frac{3}{7} \times \frac{15}{16} \times (\frac{- 14}{9}) = (\frac{- 4}{5} \times \frac{15}{16}) \times [\frac{3}{7} \times (\frac{- 14}{9})]$ (Using commutativity and associativity)

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

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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)

We have −45×37×1516×(−149)=(−4×35×7)×(15×(−14)16×9) =−1235×(−3524)=(−12×(−34)35×24)=12 We can also solve it as −45×37×1516×(−149)=(−45×1516)×[37×(−149)] (Using commutativity and associativity) =−34×(−23)=12

$F i n d \frac{- 4}{5} \times \frac{3}{7} \times \frac{15}{16} \times (\frac{- 14}{9})$