1.

Verify the property x + y = y + x of rational numbers by taking x = -2/3, y = -5/6.

Answer»

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


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