 # Verify the property x + y = y + x of rational numbers by taking

Question:

Verify the property x + y = y + x of rational numbers by taking

(a) x = ½, y = ½

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

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

(d) x = -2/5, y = – 9/10

Solution:

(a) x = ½, y = ½

In the question is given to verify the property = x + y = y + x

Where, x = ½, y = ½

Then, ½ + ½ = ½ + ½

LHS = ½ + ½

= (1 + 1)/2

= 2/2

= 1

RHS = ½ + ½

= (1 + 1)/2

= 2/2

= 1

By comparing LHS and RHS

LHS = RHS

∴ 1 = 1

Hence x + y = y + x

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

Solution:-

In the question is given to verify the property = x + y = y + x

Where, x = -2/3, y = -5/6

Then, -2/3 + (-5/6) = -5/6 + (-2/3)

LHS = -2/3 + (-5/6)

= -2/3 – 5/6

The LCM of the denominators 3 and 6 is 6

(-2/3) = [(-2×2)/ (3×2)] = (-4/6)

and (-5/6) = [(-5×1)/ (6×1)] = (-5/6)

Then,

= – 4/6 – 5/6

= (- 4 – 5)/ 6

= – 9/6

RHS = -5/6 + (-2/3)

= -5/6 – 2/3

The LCM of the denominators 6 and 3 is 6

(-5/6) = [(-5×1)/ (6×1)] = (-5/6)

and (-2/3) = [(-2×2)/ (3×2)] = (-4/6)

Then,

= – 5/6 – 4/6

= (- 5 – 4)/ 6

= – 9/6

By comparing LHS and RHS

LHS = RHS

∴ -9/6 = -9/6

Hence x + y = y + x

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

Solution:-

In the question is given to verify the property = x + y = y + x

Where, x = -3/7, y = 20/21

Then, -3/7 + 20/21 = 20/21 + (-3/7)

LHS = -3/7 + 20/21

The LCM of the denominators 7 and 21 is 21

(-3/7) = [(-3×3)/ (7×3)] = (-9/21)

and (20/21) = [(20×1)/ (21×1)] = (20/21)

Then,

= – 9/21 + 20/21

= (- 9 + 20)/ 21

= 11/21

RHS = 20/21 + (-3/7)

The LCM of the denominators 21 and 7 is 21

(20/21) = [(20×1)/ (21×1)] = (20/21)

and (-3/7) = [(-3×3)/ (7×3)] = (-9/21)

Then,

= 20/21 – 9/21

= (20 – 9)/ 21

= 11/21

By comparing LHS and RHS

LHS = RHS

∴ 11/21 = 11/21

Hence x + y = y + x

(d) x = -2/5, y = – 9/10

Solution:-

In the question is given to verify the property = x + y = y + x

Where, x = -2/5, y = -9/10

Then, -2/5 + (-9/10) = -9/10 + (-2/5)

LHS = -2/5 + (-9/10)

= -2/5 – 9/10

The LCM of the denominators 5 and 10 is 10

(-2/5) = [(-2×2)/ (5×2)] = (-4/10)

and (-9/10) = [(-9×1)/ (10×1)] = (-9/10)

Then,

= – 4/10 – 9/10

= (- 4 – 9)/ 10

= – 13/10

RHS = -9/10 + (-2/5)

= -9/10 – 2/5

The LCM of the denominators 10 and 5 is 10

(-9/10) = [(-9×1)/ (10×1)] = (-9/10)

and (-2/5) = [(-2×2)/ (5×2)] = (-4/10)

Then,

= – 9/10 – 4/10

= (- 9 – 4)/ 10

= – 13/10

By comparing LHS and RHS

LHS = RHS

∴ -13/10 = -13/10

Hence x + y = y + x