Verify the property x + y = y + x of rational numbers by taking
(a) x = 1/2, y = 1/2
(b) x = -2/3, y = -5/6
(c) x = -3/7, y = 20/21
(D) x = -2/5, y = -9/10

Solution:

Rational numbers are closed under addition

(a) x = 1/2, y = 1/2

x + y = 1/2 + 1/2 = 2/2 = 1

y + x = 1/2 + 1/2 = 2/2 = 1

(b) x = -2/3, y = -5/6

x + y = -2/3 - 5/6 = -4/6 - 5/6 = -9/6 = -3/2

y + x = -5/6 - 2/3 = - 5/6 -4/6 = -9/6 = -3/2

(c) x = -3/7, y = 20/21

x + y = -3/7 + 20/21=-9/21 + 20/21 = 11/21

y + x = 20/21 - 3/7 = 20/21 - 9/21 = 11/21

(d) x = -2/5, y = -9/10

x + y = -2/5 - 9/10 = -4/10 - 9/10 = -13/10

y + x = -9/10 - 2/5 = -9/10 - 4/10 = -13/10

✦ Try This: Verify the property x × y = y × x of rational numbers by taking
(a) x = 1/2, y = 1/2
(B) x = -2/3, y = -5/6
(C) x = -3/7, y = 20/21
(D) x = -2/5, y = -9/10

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

---

NCERT Exemplar Class 8 Maths Chapter 1 Problem 105

Verify the property x + y = y + x of rational numbers by taking (a) x = 1/2, y = 1/2, (b) x = -2/3, y = -5/6, (c) x = -3/7, y = 20/21, (D) x = -2/5, y = -9/10

Summary:

Rational numbers are closed under addition

---

☛ Related Questions:

• Simplify each of the following by using suitable property. Also name the property. (a) [1/2 × 1/4] + . . . .
• Tell which property allows you to compute 1/5 × [5/6 × 7/9] as [1/5 × 5/6] × 7/9
• Verify the property x × y = y × x of rational numbers by using (a) x = 7, y = 1/2 (b) x = 2/3, y = 9 . . . .