Verify the property: x × (y + z) = x × y + x × z by taking: $$x = \dfrac{-3}{4}, y = \dfrac{-5}{2}, z = \dfrac{7}{6}$$

Asked by Aaryan | 1 year ago |  55

##### Solution :-

By using the property

x × (y + z) = x × y + x × z

$$\dfrac{-3}{4} × (\dfrac{-5}{2} + \dfrac{7}{6}) = \dfrac{-3}{4} × \dfrac{-5}{2} + \dfrac{-3}{4} × \dfrac{7}{6}$$

$$\dfrac{-3}{4} × \dfrac{((-5×3) + (7×1))}{6}$$

$$= \dfrac{(-3×-5)}{(4×2) }+ \dfrac{(-3×7)}{(4×6)}$$

$$\dfrac{-3}{4} ×\dfrac{ (-15+7)}{6} = \dfrac{15}{8} – \dfrac{21}{24}$$

$$\dfrac{-3}{4} × \dfrac{-8}{6} = \dfrac{(15×3 – 21×1)}{24}$$

$$\dfrac{ -3}{4} × \dfrac{-4}{3} = \dfrac{(45-21)}{24}$$

$$1 = \dfrac{24}{24}$$

= 1

Hence, the property is verified.

Answered by Sakshi | 1 year ago

### Related Questions

#### By what number should 1365 be divided to get 31 as quotient and 32 as remainder?

By what number should 1365 be divided to get 31 as quotient and 32 as remainder?

#### Which of the following statement is true / false?

Which of the following statement is true / false?

(i) $$\dfrac{ 2 }{ 3} – \dfrac{4 }{ 5}$$ is not a rational number.

(ii) $$\dfrac{ -5 }{ 7}$$ is the additive inverse of $$\dfrac{ 5 }{ 7}$$

(iii) 0 is the additive inverse of its own.

(iv) Commutative property holds for subtraction of rational numbers.

(v) Associative property does not hold for subtraction of rational numbers.

(vi) 0 is the identity element for subtraction of rational numbers.

#### If x = 4 / 9, y = – 7 / 12 and z = – 2 / 3, then verify that x – (y – z) ≠ (x – y) – z

If x = $$\dfrac{4 }{ 9}$$, y =$$\dfrac{-7 }{ 12}$$ and z = $$\dfrac{-2 }{ 3}$$, then verify that x – (y – z) ≠ (x – y) – z

If x = $$\dfrac{ – 4 }{ 7}$$ and y = $$\dfrac{2 }{ 5}$$, then verify that x – y ≠ y – x
Subtract the sum of $$\dfrac{ – 5 }{ 7} and\dfrac{ – 8 }{ 3}$$ from the sum of $$\dfrac{5 }{ 2} and \dfrac{– 11 }{ 12}$$