Which property of multiplication is illustrated by-43- -65-87 - -43-65 - -43-87

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Standard VI

Mathematics

Distributivity

Which propert...

Question

Which property of multiplication is illustrated by:
$\frac{- 4}{3} \times (\frac{- 6}{5} + \frac{8}{7}) = (\frac{- 4}{3} + \frac{- 6}{5}) + (\frac{- 4}{3} + \frac{8}{7})$

Commutative property

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Associative property

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None of these

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Distributive property

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Solution

The correct option is D Distributive property
We know that distributive property of multiplication with respect to addition is defined as:

For any real number $a, b, c,$

$a \times (b + c) = a \times b + a \times c$

Let us take $a = \frac{- 4}{3}, b = \frac{- 6}{5} and c = \frac{8}{7}$ and apply the distributive property stated above:

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

Hence, it is the distributive proverty of multiplication.

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Similar questions

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

$Name the multiplication property of rational numbers shown below: (i) \frac{3}{5} \times \frac{- 8}{9} = \frac{- 8}{9} \times \frac{3}{5} (i i) \frac{- 3}{4} \times (\frac{5}{7} \times \frac{- 8}{15}) = (\frac{- 3}{5} \times \frac{5}{7}) \times \frac{- 8}{15} (i i i) \frac{4}{5} \times (\frac{3}{- 8} + \frac{- 4}{7}) = \frac{4}{5} \times \frac{3}{- 8} + \frac{4}{5} \times \frac{- 4}{7} (i v) \frac{- 7}{5} \times \frac{5}{- 7} = 1 (v) \frac{8}{- 9} \times 1 = 1 \times \frac{8}{- 9} = \frac{8}{- 9} (v i) \frac{- 3}{4} \times 0 = 0$

Q. Find the value of:

(1) 3⁶
(2) 6³
(3) 2⁶
(4) 1⁸
(5) 5⁴
(6) 4³
(7) 10⁵
(8) 10⁷
(9) 7⁴
(10) 8²

Q. Which property of multiplication is illustrated by :

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

Q. Name the property of multiplication illustrated by

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

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Which property of multiplication is illustrated by: −43×(−65+87)=(−43+−65)+(−43+87)

Which property of multiplication is illustrated by:
$\frac{- 4}{3} \times (\frac{- 6}{5} + \frac{8}{7}) = (\frac{- 4}{3} + \frac{- 6}{5}) + (\frac{- 4}{3} + \frac{8}{7})$