Name the property used in the following- -2-3-3-4-1-2-2-3-3-4-2-3-1-2-

Property of Multiplication.The distributive property of multiplication is a(b+c)=ab+ac.Here, a = 2/3, b = 3/4 and c = 1/2Verify distributive property in ( 2/ ...

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Standard VIII

Mathematics

Distributive Property of Rational Numbers

Name the prop...

Question

Name the property used in the following: $(\frac{- 2}{3}) \times [(\frac{3}{4}) + (\frac{- 1}{2})] = [(\frac{- 2}{3}) \times (\frac{3}{4})] + [(\frac{- 2}{3}) \times (\frac{- 1}{2})]$

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Solution

Property of Multiplication.
The distributive property of multiplication is $a (b + c) = a b + a c$ .
Here, $a = \frac{- 2}{3}, b = \frac{3}{4}$ and $c = \frac{- 1}{2}$
Verify distributive property in $(\frac{- 2}{3}) \times [(\frac{3}{4}) + (\frac{- 1}{2})] = [(\frac{- 2}{3}) \times (\frac{3}{4})] + [(\frac{- 2}{3}) \times (\frac{- 1}{2})]$ as follow:

$LHS = (\frac{- 2}{3}) \times [(\frac{3}{4}) + (\frac{- 1}{2})] \begin{matrix} \Rightarrow (\frac{- 2}{3}) \times [(\frac{3}{4}) + (\frac{- 1}{2})] = \frac{- 2}{3} \times [(\frac{3 \times 1}{4 \times 1}) + (\frac{- 1 \times 2}{2 \times 2})] \\ \Rightarrow (\frac{- 2}{3}) \times [(\frac{3}{4}) + (\frac{- 1}{2})] = \frac{- 2}{3} \times [\frac{3}{4} - \frac{2}{4}] \\ \Rightarrow (\frac{- 2}{3}) \times [(\frac{3}{4}) + (\frac{- 1}{2})] = \frac{- 2}{3} \times \frac{1}{4} \\ \Rightarrow (\frac{- 2}{3}) \times [(\frac{3}{4}) + (\frac{- 1}{2})] = \frac{- 1}{6} \end{matrix}$
And
$RHS = [(\frac{- 2}{3}) \times (\frac{3}{4})] + [(\frac{- 2}{3}) \times (\frac{- 1}{2})] \begin{matrix} \Rightarrow [(\frac{- 2}{3}) \times (\frac{3}{4})] + [(\frac{- 2}{3}) \times (\frac{- 1}{2})] = \frac{- 1}{2} + \frac{1}{3} \\ \Rightarrow [(\frac{- 2}{3}) \times (\frac{3}{4})] + [(\frac{- 2}{3}) \times (\frac{- 1}{2})] = \frac{- 1 \times 3}{2 \times 3} + \frac{1 \times 2}{3 \times 2} \\ \Rightarrow [(\frac{- 2}{3}) \times (\frac{3}{4})] + [(\frac{- 2}{3}) \times (\frac{- 1}{2})] = \frac{- 3}{6} + \frac{2}{6} \\ \Rightarrow [(\frac{- 2}{3}) \times (\frac{3}{4})] + [(\frac{- 2}{3}) \times (\frac{- 1}{2})] = \frac{- 3 + 2}{6} \\ \Rightarrow [(\frac{- 2}{3}) \times (\frac{3}{4})] + [(\frac{- 2}{3}) \times (\frac{- 1}{2})] = \frac{- 1}{6} \end{matrix}$
Therefore, $LHS = RHS$
Hence, the property utilized in $(\frac{- 2}{3}) \times [(\frac{3}{4}) + (\frac{- 1}{2})] = [(\frac{- 2}{3}) \times (\frac{3}{4})] + [(\frac{- 2}{3}) \times (\frac{- 1}{2})]$ is distributive property of multiplication

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Name the property used in the following: -23×34+-12=-23×34+-23×-12

Name the property used in the following: $(\frac{- 2}{3}) \times [(\frac{3}{4}) + (\frac{- 1}{2})] = [(\frac{- 2}{3}) \times (\frac{3}{4})] + [(\frac{- 2}{3}) \times (\frac{- 1}{2})]$