Verify that - ( - x ) is the same x for x = 11 15 .

Given, x = 11 15 Since - x = - 11 15 Thus, - - x = - - 11 15 = 11 15 = x ∴ - - x = x Hence, - - x is the same x for x = 11 15 .

Verify that - ( - x ) is the same x for x = 11 15 .

Given, x = 11 15 Since - x = - 11 15 Thus, - - x = - - 11 15 = 11 15 = x ∴ - - x = x Hence, - - x is the same x for x = 11 15 .

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 numbers is - 4 3 . If one of the numbers is - 5 , find the other.

Consider the unknown number to be x Putting the question into the equation form, we get: - 5 + x = - 4 3 ⇒ x = - 4 3 - ( - 5 ) ⇒ x = - 4 3 + 5 1 ⇒ x = - 4 3 + 5 × 3 1 × 3 ⇒ x = - 4 + 15 3 ⇒ x = 11 3 So, the other number is 11 3 .

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 .

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 should be added to - 5 11 to get 26 33 ?

Consider the number to be added to be x Putting the question into the equation form, we get - 5 11 + x = 26 33 ⇒ x = 26 33 - - 5 11 ⇒ x = 26 33 - - 5 11 We need to find the L.C.M. of the denominators to make the denominators same. L.C.M of 33 , 11 is 33 . ⇒ x = 26 × 1 33 × 1 - - 5 × 3 11 × 3 ⇒ x = 26 - ( - 15 ) 33 ⇒ x = 41 33 So, the other number is 41 33 .

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 should be added to 2 3 + 3 5 to get - 2 15 ?

Consider the number to be added as x . Putting the question into the equation form, we get 2 3 + 3 5 + x = - 2 15 ⇒ x = - 2 15 - 2 3 + 3 5 ⇒ x = - 2 15 - 2 × 5 3 × 5 + 3 × 3 5 × 3 ⇒ x = - 2 15 - 10 15 + 9 15 ⇒ x = - 2 15 - 10 + 9 15 ⇒ x = - 2 15 - 19 15 ⇒ x = - 2 - 19 15 ⇒ x = - 21 15 ⇒ x = - 7 5 Hence, the required number = - 7 5