Which of the following represents associative property?

-3 + 4 = 4 +(-3)

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2×(3+4) = (2×3)+(2×4)

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6 - 8 = (-8) + 6

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3 + ((-4)+5) = (3 +(-4)) + 5

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Solution

The correct option is D
3 + ((-4)+5) = (3 +(-4)) + 5

Commutative property: a + b = b + a
(-3) + 4 = 4 +(-3) is commutative property.
6 + (-8) = (-8) + 6 is commutative property.
Distributive property: a × (b + c) = (a × b) + (a × c)
2 × (3 + 4) = (2×3) + (2 × 4) is distributive property.

Associative property: a + (b + c) = (a + b) + c
3 +((-4) + 5)=(3+(-4)) + 5 is associative property.

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Similar questions

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})

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

Q. Name the property under multiplication used in each of the following:
(i)

\frac{2}{3} \times \frac{4}{5} = \frac{4}{5} \times \frac{2}{3}

(ii)

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

(iii)

(\frac{- 17}{28}) \times (\frac{- 28}{17}) = 1

(iv)

\frac{1}{5} \times (\frac{7}{8} \times \frac{4}{3}) = (\frac{1}{5} \times \frac{7}{8}) \times \frac{4}{3}

(v)

\frac{2}{7} \times (\frac{9}{10} + \frac{2}{5}) = \frac{2}{7} \times \frac{9}{10} + \frac{2}{7} \times \frac{2}{5}

Solve the following:
(a) $5 x + 8 = 23$ (b) $2 y - 4 = - 8$ (c) $2 (t + 1) + 15 = 3$ (d) $- y + 46 = 32$ (e) $2 x + 3 = 3$

\frac{1}{2} + \frac{2}{4} + \frac{3}{8} + \frac{4}{16} + \frac{5}{32} + \dots =

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