Question

Fill in the blanks to make the following statements true:
(i) (–5) + (– 8) = (– 8) + (............)
(ii) –53 + ............ = –53
(iii) 17 + ............ = 0
(iv) [13 + (– 12)] + (............) = 13 + [(–12) + (–7)]
(v) (– 4) + [15 + (–3)] = [– 4 + 15] + ............
NCERT Class 7th Mathematics Chapter 1 Integers

Answer 1

(–5) + (– 8) = (– 8) + (-5)
–53 + 0 = –53
17 + (-17) = 0
 [13 + (– 12)] + (-7) = 13 + [(–12) + (–7)]
(– 4) + [15 + (–3)] = [– 4 + 15] + (-3)

Answer 2

The answer to the given blanks are provided below:

(i) The correct answer in the blank is -5.

=> The property of integers that apply here is the commutative property.

=> (–5) + (– 8) = (– 8) + (-5)

∴ -13 = -13

∴ LHS = RHS

(ii) The correct answer to the given blank is 0 (zero).

=> It shows the identity property for the addition of integers.

=> –53 + 0 = –53

∴ Therefore, the value doesn't change.

(iii) The correct response to the given blank is -17.

=> It shoes the additive inverse property of the integers where the sum is zero.

=> 17 + (-17) = 0

∴ Therefore we get zero from the sum of numbers that are the additive inverse of each other.

(iv) The correct answer to the given blank is -7.

=> It shows the associative property of integers where interchanging the sequence of numbers gives an equal answer.

=> [13 + (– 12)] + (-7) = 13 + [(–12) + (–7)]

=> -6 = -6

∴LHS = RHS

∴ Hence, we get equal answer on both the sides.

(v) The correct answer to the given blank is -3.

=> This shows the associative property of the integers.

=> (– 4) + [15 + (–3)] = [– 4 + 15] + (-3)

=> +8 = +8

∴ LHS = RHS

∴ Hence, proved that integers exhibit associative property in addition.