Which property can be defined for the expression:
$9 + (12 + 15) = 12 + (9 + 15)$

commutative property of addition

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associative property of addition

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commutative property of multiplication

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associative property of multiplication

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Solution

The correct option is B associative property of addition
$9 + (12 + 15) = 9 + 27 = 36$
Also, $12 + (9 + 15) = 12 + 24 = 36$

$∴ 9 + (12 + 15) = 12 + (9 + 15)$

Here, The associative property of addition says that changing the grouping of the addends does not change the sum.

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

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Class:	$3 - 6$	$6 - 9$	$9 - 12$	$12 - 15$	$15 - 18$	$18 - 21$	$21 - 24$
Frequency:	$2$	$5$	$10$	$23$	$21$	$12$	$3$

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