For the following values of x, y and z. Verify the distributive property of rational numbers: [4 MARKS]
$x \times (y + z) = x \times y + x \times z$
i) $x = - 3, y = \frac{9}{2}, z = \frac{- 7}{9}$

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Solution

Concept : 1 Mark
Calculation : 2 Marks
Conclusion : 1 Mark

$L H S = x \times (y + z)$
$= - 3 \times (\frac{9}{2} + \frac{- 7}{9})$
$= - 3 \times (\frac{81 - 14}{18})$
$= - 3 \times \frac{67}{18}$
$= \frac{- 67}{6} . . . . . . . . . (i)$
$R H S = x \times y + x \times z$
$= (- 3 \times \frac{9}{2}) + (- 3 \times \frac{- 7}{9})$

$= \frac{- 27}{2} + \frac{7}{3}$
$= \frac{- 81 + 14}{6}$
$= \frac{- 67}{6} . . . . . . . . . (i i)$

From (i) and (ii) LHS = RHS.
Hence verified.

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Similar questions

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

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

x = \frac{2}{3}, y = \frac{- 3}{7}, z = \frac{1}{2}

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

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

z = \frac{- 7}{9}

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

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

z = \frac{- 7}{9}

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

x = \frac{7}{4}, y = \frac{- 11}{3}, z = \frac{1}{2}

Verify the property: $x \times (y \times z) = (x \times y) \times z b y t a k i n g :$

(i) $x = \frac{- 7}{3}, y = \frac{12}{5}, z = \frac{4}{9}$

(ii) $x = 0, y = \frac{- 3}{5}, z = \frac{- 9}{4}$

(iii) $x = \frac{1}{2}, y = \frac{5}{- 4}, z = \frac{- 7}{5}$

(iv) $x = \frac{5}{7}, y = \frac{- 12}{13}, z = \frac{- 7}{18}$

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