Question 110iiVerifty the property x - y-z - x - y - x - z of rational numbers by takingx - -1-2- y - 2-3 and z - 3-4

Given, x = 1/2, y = 2/3 and z = 3/4 Now LHS = x × (y + z) = 1/2× ( 2/3 + 3/4 ) = 1/2× ( 8+9/12 ) = 1/2×17/12 = 17/24 and RHS = x × y + x × z = 1/2×2/3 + ...

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Standard VIII

Mathematics

Distributive Property of Rational Numbers

Question 110i...

Question

Question 110(ii)
Verifty the property $x \times (y + z) = x \times y + x \times z$ of rational numbers by taking
$x = \frac{- 1}{2}, y = \frac{2}{3}$ and $z = \frac{3}{4}$

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Solution

Given, $x = \frac{- 1}{2}, y = \frac{2}{3}$ and $z = \frac{3}{4}$
Now LHS $= x \times (y + z) = \frac{- 1}{2} \times (\frac{2}{3} + \frac{3}{4}) = \frac{- 1}{2} \times (\frac{8 + 9}{12}) = \frac{- 1}{2} \times \frac{17}{12} = \frac{- 17}{24}$
and RHS $= x \times y + x \times z = \frac{- 1}{2} \times \frac{2}{3} + (\frac{- 1}{2}) \times \frac{3}{4} = \frac{- 1}{3} - \frac{3}{8} = \frac{- 8 - 9}{24} = \frac{- 17}{24}$
$∴$ LHS = RHS $\Rightarrow x \times (y + z) = x \times y + x \times z$
Hence verified.

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Similar questions

Q. Question 110(ii)
Verifty the property

x \times (y + z) = x \times y + x \times z

of rational numbers by taking

x = \frac{- 1}{2}, y = \frac{2}{3}

and

z = \frac{3}{4}

Q. Question 110(i)
Verifty the property

x \times (y + z) = x \times y + x \times z

of rational numbers by taking

x = \frac{- 1}{2}, y = \frac{3}{4}

and

z = \frac{1}{4}

Q. Question 110(i)
Verifty the property

x \times (y + z) = x \times y + x \times z

of rational numbers by taking

x = \frac{- 1}{2}, y = \frac{3}{4}

and

z = \frac{1}{4}

Q. Question 110(iii)
Verifty the property

x \times (y + z) = x \times y + x \times z

of rational numbers by taking

x = \frac{- 2}{3}, y = \frac{- 4}{6}

and

z = \frac{- 7}{9}

Question 110(iv)
Verifty the property $x \times (y + z) = x \times y + x \times z$ of rational numbers by taking
$x = \frac{- 1}{5}, y = \frac{2}{15}$ and $z = \frac{- 3}{10}$

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Distributive Property of Rational Numbers

Standard VIII Mathematics

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Question 110(ii) Verifty the property x×(y+z)=x×y+x×z of rational numbers by taking x=−12,y=23 and z=34

Given, x=−12,y=23 and z=34 Now LHS =x×(y+z)=−12×(23+34)=−12×(8+912)=−12×1712=−1724 and RHS =x×y+x×z=−12×23+(−12)×34=−13−38=−8−924=−1724 ∴ LHS = RHS ⇒x×(y+z)=x×y+x×z Hence verified.

Question 110(ii)
Verifty the property $x \times (y + z) = x \times y + x \times z$ of rational numbers by taking
$x = \frac{- 1}{2}, y = \frac{2}{3}$ and $z = \frac{3}{4}$