Find the additive inverse of - 7 10 .

Additive inverse of a number A B is the number - A B such that, A B + - A B = 0 Additive inverse for a rational number is the same number with the opposite sign. Also, adding its additive inverse to a number results in zero. Since the opposite sign of - 7 10 is 7 10 . Therefore, Additive inverse of - 7 10 is 7 10 , as - 7 10 + 7 10 = 0 .

What should be added to 1 2 + 1 3 + 1 5 to get 3 ?

1 2 + 1 3 + 1 5 = 15 30 + 10 30 + 6 30 = 31 30 (L.C.M of 2 , 3 , 5 = 30 ) Consider the number to be added as x . According to the question, 1 2 + 1 3 + 1 5 + x = 3 ⇒ x = 3 - ( 15 × 1 15 × 2 + 10 × 1 10 × 3 + 6 × 1 6 × 5 ) ⇒ x = 3 - ( 15 × 1 + 10 × 1 + 6 × 1 ) 30 ⇒ x = 3 × 30 1 × 30 - 31 30 ⇒ x = 90 30 - 31 30 ⇒ x = 59 30 Hence, the required number = 59 30

From a rope 11 m long, two pieces of lengths 2 3 5 m and 3 3 10 m are cut off. What is the length of remaining rope?

Given, total length of a rope is 11 m And, length of first piece cut off from rope = 2 3 5 m Length of second piece cut off from rope = 3 3 10 m Total length cut off from rope = Length of first piece cut off from rope + Length of second piece cut off from rope = 2 3 5 m + 3 3 10 m = 13 5 + 33 10 m LCM of 5 and 10 = 10 So, 13 5 + 33 10 m = 13 × 2 5 × 2 + 33 10 m = 26 + 33 10 m = 59 10 m Length of remaining rope = Total length of rope - Total length cut off from rope = 11 - 59 10 m = 110 - 59 10 m = 51 10 m = 5 1 10 m Hence, the length of remaining rope = 5 1 10 m .

The sum of two rational numbers is - 8 . If one of the numbers is - 15 7 , find the other.

Consider the unknown number to be x . Putting the question into the equation form, we get - 15 7 + x = - 8 ⇒ x = - 8 - - 15 7 ⇒ x = - 8 × 7 1 × 7 + 15 × 1 7 × 1 ⇒ x = - 56 7 + 15 7 ⇒ x = - 56 + 15 7 ⇒ x = - 41 7 So, the other number is - 41 7 .

Add the following rational numbers: - 5 7 and 3 7

Given, - 5 7 and 3 7 Hence, adding the numbers, we get: - 5 7 + 3 7 = - 5 + 3 7 = - 2 7 (Since denominators are same, we will just add the numerators and write the fraction keeping the denominator same.) Hence, the addition of the given rational numbers gives - 2 7 .

The sum of two numbers is - 1 3 . If one of the numbers is - 12 3 , find the other.

Given, Sum of two numbers = - 1 3 One of the number = - 12 3 Consider the unknown number be x . According to the question: - 12 3 + x = - 1 3 ⇒ x = - 1 3 - - 12 3 ⇒ x = - 1 + 12 3 ⇒ x = 11 3 Hence, the other rational number is 11 3 .

What should be added to - 7 8 to get 5 9 ?

Consider the number to be added to be x Putting the question into the equation form, we get - 7 8 + x = 5 9 ⇒ x = 5 9 - - 7 8 ⇒ x = 5 9 + 7 8 ⇒ x = 5 × 8 9 × 8 + 7 × 9 8 × 9 ⇒ x = 40 72 + 63 72 ⇒ x = 40 + 63 72 ⇒ x = 103 72 So, the other number is 103 72 .

What number should be subtracted from - 5 3 to get 5 6 ?

Consider the number to be subtracted to be x Putting the question into the equation form, we get - 5 3 - x = 5 6 ⇒ - x = 5 6 + 5 3 ⇒ - x = 5 6 + 5 × 2 3 × 2 ⇒ - x = 5 6 + 10 6 ⇒ - x = 5 + 10 6 ⇒ - x = 15 6 ⇒ x = - 15 6 ⇒ x = - 5 2 Hence, the number to be subtracted = - 5 2 .

What number should be subtracted from 3 7 to get 5 4 ?

Consider the number to be subtracted to be x . Putting the question into the equation form, we get 3 7 - x = 5 4 ⇒ - x = 5 4 - 3 7 ⇒ - x = 5 × 7 4 × 7 - 3 × 4 7 × 4 ⇒ - x = 35 28 - 12 28 ⇒ - x = 35 - 12 28 = 23 28 ⇒ x = - 23 28 Hence, the required number = - 23 28