Verify the property x-y- z-x- y- z of rational numbers by usinga x-1- y-12- z-14b x-23- y-37- z-12

(a) #160; #160; #160; #160; x ×( y × z) = 1 ×( 12×14) = 1 ×( 18) = 18 ( x × y) × z = ( 1 × 12) ×14 = ...

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Standard VIII

Mathematics

Associative Property of Rational Numbers

Verify the pr...

Question

Verify the property $x \times (y \times z) = (x \times y) \times z$ of rational numbers by using
(a) $x = 1, y = \frac{- 1}{2}, z = \frac{1}{4}$
(b) $x = \frac{2}{3}, y = \frac{- 3}{7}, z = \frac{1}{2}$

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Solution

(a) $x \times (y \times z)$
$= 1 \times (\frac{- 1}{2} \times \frac{1}{4})$
$= 1 \times (\frac{- 1}{8})$
$= \frac{- 1}{8}$
$(x \times y) \times z$
$= (1 \times \frac{- 1}{2}) \times \frac{1}{4}$
$= \frac{- 1}{2} \times \frac{1}{4}$
$= \frac{- 1}{8}$
So $x \times (y \times z) = (x \times y) z$
$(b) x \times (y \times z) = \frac{2}{3} \times (\frac{- 3}{7} \times \frac{1}{2})$
$= \frac{2}{3} \times \frac{- 3}{14}$
$= \frac{- 6}{42}$
$(x \times y) \times z = (\frac{2}{3} \times \frac{- 3}{7})$
$= \frac{- 6}{21} \times \frac{1}{2} = \frac{- 6}{42}$
$= \frac{- 6}{2}$
So, $x \times (y + z) = (x \times y) \times z$

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Similar questions

Question 109(ii)
Verify the property $x \times (y \times z) = (x \times y) \times z$ of rational numbers by using
$x = \frac{2}{3}, y = \frac{- 3}{7}$ and $z = \frac{1}{2}$
and what is the name of this property?

Verify associativity of addition of rational numbers i.e., $(x + y) + z = x + (y + z)$

when:

(i) $x = \frac{1}{2}, y = \frac{2}{3}, z = - \frac{1}{5}$

(ii) $x = \frac{- 2}{5}, y = \frac{4}{3}, z = \frac{- 7}{10}$

(iii) $x = \frac{- 7}{11}, y = \frac{2}{- 5}, z = \frac{- 3}{22}$

(iv) $x = - 2, y = \frac{3}{5}, z = \frac{- 4}{3}$

Q. Verify the property

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

of rational numbers by using

x = 0, y = \frac{1}{2}

and

z = \frac{1}{4}

and what is the name of this property?

Q. For the following values of x, y and z. Verify the distributive property of rational numbers: [4 MARKS]

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

x = - 3, y = \frac{9}{2}, z = \frac{- 7}{9}

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}

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Verify the property x×(y×z)=(x×y)×z of rational numbers by using(a)x=1,y=−12,z=14(b)x=23,y=−37,z=12

(a) x×(y×z)=1×(−12×14)=1×(−18)=−18(x×y)×z=(1×−12)×14=−12×14=−18So x×(y×z)=(x×y)z(b)x×(y×z)=23×(−37×12)=23×−314=−642(x×y)×z=(23×−37)=−621×12=−642=−62So, x×(y+z)=(x×y)×z

Verify the property $x \times (y \times z) = (x \times y) \times z$ of rational numbers by using
(a) $x = 1, y = \frac{- 1}{2}, z = \frac{1}{4}$
(b) $x = \frac{2}{3}, y = \frac{- 3}{7}, z = \frac{1}{2}$