Verify the property: x × (y + z) = x × y + x × z by taking: $$x = \dfrac{-3}{7}, y = \dfrac{12}{13}, z = \dfrac{-5}{6}$$

Asked by Aaryan | 1 year ago |  67

##### Solution :-

By using the property

x × (y + z) = x × y + x × z

$$\dfrac{ -3}{7} × (\dfrac{ 12}{13}+ \dfrac{ -5}{6}) = \dfrac{ -3}{7} × \dfrac{ 12}{13} + \dfrac{ -3}{7} × -\dfrac{ -5}{6}$$

$$\dfrac{ -3}{7} × \dfrac{((12×6) + (-5×13))}{78}$$

$$= \dfrac{(-3×12)}{(7×13)} + \dfrac{(-3×-5)}{(7×6)}$$

$$\dfrac{ -3}{7}× \dfrac{(72-65)}{78} = \dfrac{-36}{91} + \dfrac{ 15}{42}$$

$$\dfrac{ -3}{7} ×\dfrac{ 7}{78}= \dfrac{(-36×6 + 15×13)}{546}$$

$$\dfrac{ -1}{26} = \dfrac{(196-216)}{546}$$

= $$\dfrac{ -21}{546}$$

=$$\dfrac{ -1}{26}$$

Hence, the property is verified.

Answered by Sakshi | 1 year ago

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