Find the reciprocal of 11 - 12 .

Rational numbers are those numbers that can be represented in the form of p q , where q ≠ 0 . If x is any non-zero rational number, then its reciprocal is denoted by x - 1 which is equal to 1 x . Given, 11 - 12 To get the reciprocal of a given rational number, simply interchange the integers in the numerator and the denominator. ⇒ - 12 11 Hence, this is the required answer.

Find the reciprocal of - 2 - 19 .

Rational numbers are those numbers that can be represented in the form of p q , where q ≠ 0 . If x is any non-zero rational number, then its reciprocal is denoted by x - 1 which is equal to 1 x . Given, - 2 - 19 To get the reciprocal of a given rational number, simply interchange the integers in the numerator and the denominator. ⇒ - 19 - 2 Hence, this is the required answer.

Verify that x - y - 1 ≠ x - 1 - y - 1 by taking x = - 2 7 & y = 4 7

Rational numbers are those numbers that can be represented in the form of p q , where q ≠ 0 . Given, x = - 2 7 & y = 4 7 ⇒ x - y - 1 = - 2 7 - 4 7 - 1 ⇒ x - y - 1 = - 6 7 - 1 = - 7 6 And ⇒ x - 1 - y - 1 = - 2 7 - 1 - 4 7 - 1 ⇒ x - 1 - y - 1 = - 7 2 - 7 4 = - 21 4 We can see that x - y - 1 ≠ x - 1 - y - 1 . Hence, verified.

Verify that x + y - 1 ≠ x - 1 + y - 1 by taking x = 5 9 & y = - 4 3 .

Rational numbers are those numbers that can be represented in the form of p q , where q ≠ 0 . Given, x = 5 9 & y = - 4 3 ⇒ x + y - 1 = 5 9 + - 4 3 - 1 ⇒ x + y - 1 = 5 - 12 9 - 1 = - 7 9 - 1 = - 9 7 And ⇒ x - 1 + y - 1 = 5 9 - 1 + - 4 3 - 1 ⇒ x - 1 + y - 1 = 9 5 + - 3 4 = 36 - 15 20 = 21 20 We can see that x - y - 1 ≠ x - 1 - y - 1 . Hence, verified.

Verify that x × y - 1 = x - 1 × y - 1 by taking x = - 2 3 & y = - 3 4

Rational numbers are those numbers that can be represented in the form of p q , where q ≠ 0 . Given, x = - 2 3 & y = - 3 4 ⇒ x × y - 1 = - 2 3 × - 3 4 - 1 ⇒ x × y - 1 = - 1 1 × - 1 2 - 1 = 1 2 - 1 = 2 And ⇒ x - 1 × y - 1 = - 2 3 - 1 × - 3 4 - 1 ⇒ x - 1 × y - 1 = - 3 2 × - 4 3 = - 1 1 × - 2 1 = 2 We can see that x × y - 1 = x - 1 × y - 1 . Hence, verified.