1.

Verify the property x + y = y + x of rational numbers by taking x = -2/5, y = – 9/10.

Answer»

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

∴ -9/6 = -9/6

Hence x + y = y + x


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