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Verify the Property: X × (Y × Z) = (X × Y) × Z by Taking: X = 1 2 , Y = 5 − 4 , Z = − 7 5 - Mathematics

Sum

Verify the property: x × (y × z) = (x × y) × z by taking:

\[x = \frac{1}{2}, y = \frac{5}{- 4}, z = \frac{- 7}{5}\]
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Solution

\[\text{We have to verify that} x \times (y \times z) = (x \times y) \times z . \]
\[x = \frac{1}{2}, y = \frac{5}{- 4}, z = \frac{- 7}{4}\]
\[x \times (y \times z) = \frac{1}{2} \times (\frac{5}{- 4} \times \frac{- 7}{4}) = \frac{1}{2} \times \frac{35}{16} = \frac{35}{32}\]
\[(x \times y) \times z = (\frac{1}{2} \times \frac{5}{- 4}) \times \frac{- 7}{4} = \frac{5}{- 8} \times \frac{- 7}{4} = \frac{35}{32}\]
\[ \therefore \frac{1}{2} \times (\frac{5}{- 4} \times \frac{- 7}{4}) = (\frac{1}{2} \times \frac{5}{- 4}) \times \frac{- 7}{4}\]
\[\text{Hence verified .} \]

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APPEARS IN

RD Sharma Class 8 Maths
Chapter 1 Rational Numbers
Exercise 1.6 | Q 2.3 | Page 31
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