Find the additive inverse of the following: - 16 13

Given, The rational number is - 16 13 . Now, we know that if the sum of two rational number is 0 , then the two numbers are additive inverse of each other. Therefore, for every rational number a b , there is a number - a b . So, the additive inverse of - 16 13 is 16 13 . Hence, the required additive inverse is 16 13 .

Find the additive inverse of the following: 8 - 29

Given, The rational number is 8 - 29 . ⇒ - 8 29 Now, we know that if the sum of two rational number is 0 , then the two numbers are additive inverse of each other. Therefore, for every rational number a b , there is a number - a b . So, the additive inverse of - 8 29 is 8 29 . Hence, the required additive inverse is 8 29 .

Arrange and simplify : 1 2 + - 3 5 + 3 2

Rational numbers are numbers that can be represented in the form of p q , where q ≠ 0 . Given rational numbers are 1 2 + - 3 5 + 3 2 . The denominators of the given rational numbers are 2 , 2 & 5 . L.C.M. of denominators 2 & 5 i s 10 . ⇒ 1 2 + - 3 5 + 3 2 ⇒ 1 × 5 10 + - 3 × 2 10 + 3 × 5 10 ⇒ 5 10 + - 6 10 + 15 10 ⇒ 5 - 6 + 15 10 ⇒ 20 - 6 10 ⇒ 14 10 = 7 5 = 1 2 5 Hence, the required answer is 1 2 5 .

Arrange and simplify : 28 17 + 35 17 + - 16 17 + - 23 17

Rational numbers are numbers that can be represented in the form of p q , where q ≠ 0 . Given rational numbers are 28 17 + 35 17 + - 16 17 + - 23 17 . The denominators of the given rational numbers are 17 , 17 , 17 , 17 . L.C.M. of denominators is 17 . ⇒ 28 17 + 35 17 + - 16 17 + - 23 17 ⇒ 28 + 35 - 16 - 23 17 ⇒ 63 - 39 17 ⇒ 24 17 = 1 7 17 Hence, the required answer is 1 7 17 .

Arrange and simplify : 2 3 + - 3 5 + 1 6 + - 8 15

Rational numbers are numbers that can be represented in the form of p q , where q ≠ 0 . Given rational numbers are 2 3 + - 3 5 + 1 6 + - 8 15 . The denominators of the given rational numbers are 3 , 5 , 6 & 15 . L.C.M. of denominators 3 , 5 , 6 & 15 i s 30 . ⇒ 2 3 + - 3 5 + 1 6 + - 8 15 ⇒ 2 × 10 30 + - 3 × 6 30 + 3 × 5 30 + - 8 × 2 30 ⇒ 20 30 + - 18 30 + 15 30 + - 16 30 ⇒ 20 + 15 - 18 - 16 30 ⇒ 35 - 34 30 = 1 30 Hence, the required answer is 1 30 .

Arrange and simplify : 3 5 + 5 3 + - 11 5 + - 2 3

Rational numbers are numbers that can be represented in the form of p q , where q ≠ 0 . Given rational numbers are 3 5 + 5 3 + - 11 5 + - 2 3 . The denominators of the given rational numbers are 3 & 5 . L.C.M. of denominators 3 & 5 i s 15 . ⇒ 3 5 + 5 3 + - 11 5 + - 2 3 ⇒ 3 × 3 15 + 5 × 5 15 + - 11 × 3 15 + - 2 × 5 15 ⇒ 9 15 + 25 15 + - 33 15 + - 10 15 ⇒ 9 + 25 - 33 - 10 15 ⇒ 34 - 43 15 ⇒ - 9 15 = - 3 5 Hence, the required answer is - 3 5 .

Arrange and simplify : 4 3 + 3 5 + - 2 3 + - 11 5

Rational numbers are numbers that can be represented in the form of p q , where q ≠ 0 . Given rational numbers are 4 3 + 3 5 + - 2 3 + - 11 5 . The denominators of the given rational numbers are 3 & 5 . L.C.M. of denominators 3 & 5 i s 15 . ⇒ 4 3 + 3 5 + - 2 3 + - 11 5 ⇒ 4 × 5 15 + 3 × 3 15 + - 2 × 5 15 + - 11 × 3 15 ⇒ 20 15 + 9 15 + - 10 15 + - 33 15 ⇒ 20 + 9 - 10 - 33 15 ⇒ 29 - 43 15 ⇒ - 14 15 Hence, the required answer is - 14 15 .

Arrange and simplify : 4 9 + 5 3 + - 4 5 + 7 9 + - 2 9 + 9 5

Rational numbers are numbers that can be represented in the form of p q , where q ≠ 0 . Given rational numbers are 4 9 + 5 3 + - 4 5 + 7 9 + - 2 9 + 9 5 . The denominators of the given rational numbers are 3 , 5 & 9 . L.C.M. of denominators 3 , 5 & 9 i s 45 . ⇒ 4 9 + 5 3 + - 4 5 + 7 9 + - 2 9 + 9 5 ⇒ 4 × 5 45 + 5 × 15 45 + - 4 × 9 45 + 7 × 5 45 + - 2 × 5 45 + 9 × 9 45 ⇒ 20 45 + 75 45 + - 36 45 + 35 45 + - 10 45 + 81 45 ⇒ 20 + 75 + 35 + 81 - 36 - 10 45 ⇒ 211 - 46 45 ⇒ 165 45 = 33 9 = 3 6 9 Hence, the required answer is 3 6 9 .