# Verify the Property: X × (Y + Z) = X × Y + X × Z by Taking: X = − 3 4 , Y = − 5 2 , Z = 7 6 - Mathematics

Sum

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

$x = \frac{- 3}{4}, y = \frac{- 5}{2}, z = \frac{7}{6}$

#### Solution

$\text{We have to verify that} x \times (y + z) = x \times y + x \times z .$
$x = \frac{- 3}{4}, y = \frac{- 5}{2}, z = \frac{7}{6}$
$x \times (y + z) = \frac{- 3}{4} \times (\frac{- 5}{2} + \frac{7}{6}) = \frac{- 3}{4} \times \frac{- 15 + 7}{6} = \frac{- 3}{4} \times \frac{- 8}{6} = 1$
$x \times y + x \times z = \frac{- 3}{4} \times \frac{- 5}{2} + \frac{- 3}{4} \times \frac{7}{6}$
$= \frac{15}{8} + \frac{- 7}{8}$
$= \frac{15 - 7}{8}$
$= 1$
$\therefore \frac{- 3}{4} \times (\frac{- 5}{2} + \frac{7}{6}) = \frac{- 3}{4} \times \frac{- 5}{2} + \frac{- 3}{4} \times \frac{7}{6}$
$\text{Hence verified .}$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 1 Rational Numbers
Exercise 1.6 | Q 3.4 | Page 32