Verify the property x × (y + z) = x × y + x × z of rational numbers by taking
(a) x = -1/2, y = 3/4, z = 1/4
(b) x = -1/2, y = 2/3, z = 3/4
(c) x = -2/3, y = -4/6, z = -7/9
(d) x = -1/5, y = 2/15, z = -3/10

Solution:

(a) x = -1/2, y = 3/4, z = 1/4

x × (y + z) = -1/2 × (3/4 + 1/4) = -1/2 × 1 = -1/2 = LHS

x × y + x × z = -1/2 × 3/4 + -1/2 × 1/4 = -3/8 - 1/8= -4/8 = -1/2 = RHS

LHS = RHS

It is the distributive property

(b) x = -1/2, y = 2/3, z = 3/4

x × (y + z) = -1/2 × (2/3 + 3/4) = -½ (8/12 + 9/12) = -17/24 = LHS

x × y + x × z = -1/2 × 2/3 + -1/2×3/4 = -1/3 - 3/8 = -8/24 - 9/24 = -17/24 = RHS

LHS = RHS

It is the distributive property

(c) x = -2/3, y = -4/6, z = -7/9

x × (y + z) = -2/3 × (-4/6 - 7/9) = -2/3 × (-12-14)/18= -2/3×-26/18 = 26/27 = LHS

x × y + x × z = -2/3 × -4/6 + -2/3 × -7/9 = 8/18-14/27=(12+14)/27=26/27 = RHS

LHS = RHS

It is distributive property

(d) x = -1/5, y = 2/15, z = -3/10

x × (y + z) = -1/5 × (2/15 - 3/10) = 1/30 = LHS

x × y + x × z = -1/5 × 2/15 + -1/5 × -3/10 = 1/30 = RHS

LHS = RHS

It is distributive property

✦ Try This: Verify the property x × (y + z) = x × y + x × z of rational numbers by taking

(a) x = -1, y = 1/3, z = 1/4

(b) x = -1/2, y = 1/3 , z = 3/4

(c) x = -2/3, y = -1/6, z = -1/9

(d) x = -1/5, y = 1/5, z = -3/10

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 1

NCERT Exemplar Class 8 Maths Chapter 1 Problem 110

Verify the property x × (y + z) = x × y + x × z of rational numbers by taking (a) x = -1/2, y = 3/4, z = 1/4 (b) x = -1/2, y = 2/3, z = 3/4 (c) x = -2/3, y = -4/6, z = -7/9 (d) x = -1/5, y = 2/15, z = -3/10

Summary:

The distributive property x × (y + z) = x × y + x × z of rational numbers is verified (a) x = -1/2, y = 3/4, z = 1/4 (b) x = -1/2, y = 2/3, z = 3/4 (c) x = -2/3, y = -4/6, z = -7/9 (d) x = -1/5, y = 2/15, z = -3/10

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