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Mathematics

Name the property of multiplication illustrated by the following statement:

−23×(−56+78)=(−23×−56)+(−23×78)\dfrac{-2}{3} \times \left(\dfrac{-5}{6} + \dfrac{7}{8}\right) = \left(\dfrac{-2}{3} \times \dfrac{-5}{6}\right) + \left(\dfrac{-2}{3} \times \dfrac{7}{8}\right)

Rational Numbers

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Answer

Here a rational number has been multiplied by the sum of two rational numbers, which is the same as the sum of the two separate products.

If ab,cd and ef\dfrac{a}{b}, \dfrac{c}{d} \text{ and } \dfrac{e}{f} are any three rational numbers, then

ab×(cd+ef)=(ab×cd)+(ab×ef)\dfrac{a}{b} \times \left(\dfrac{c}{d} + \dfrac{e}{f}\right) = \left(\dfrac{a}{b} \times \dfrac{c}{d}\right) + \left(\dfrac{a}{b} \times \dfrac{e}{f}\right)

Hence, the given statement illustrates the distributive law of multiplication over addition.

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