5. Fill in the missing numbers using the properties of integers.

a. 21 + ____ = 0.
b. ____ + 12 = 0.
c. -5 x ____ = 1

d. (-12) + 3 = 3 + (____)

6. Rahil travels 56 km due north from a point P to the point Q. He then goes 45 km towards south along the same road. If the distance towards north is taken as a positive integer, then how will the point P be represented? How far is Rahil from the starting point?

The missing numbers are -21 for part a, -12 for part b, -1/5 for part c, and -12 for part d. Rahil ends up 11 km north from his starting point P after traveling 56 km north and then 45 km south. Point P can be represented as 0 in this context.
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Answered by Anonymous | 2025-07-04

To solve the questions related to the properties of integers, we need to use basic principles such as the additive inverse and the multiplicative identity.

Fill in the missing numbers using the properties of integers:

(a) 21 + ____ = 0
To make the sum zero, you need to add the additive inverse of 21, which is -21. Therefore, the missing number is -21.
(b) ____ + 12 = 0
Here, you need the additive inverse of 12, which is -12. So, the missing number is -12.
(c) − 5 × ____ = 1
There is no integer (and actually no real number) that when multiplied by -5 gives you 1, as 1 is the multiplicative identity. This indicates the missing number is not possible with the given condition as it requires the reciprocal which is -1/5 in rational numbers.
(d) ( − 12 ) + 3 = 3 + ( ____ )
This uses the commutative property of addition, which means the terms on either side should remain equal regardless of their order. The missing number here is -12 since the expression ( − 12 ) + 3 equals 3 + ( − 12 ) .

Rahil travels 56 km due north from point P to point Q. He then goes 45 km towards south along the same road. If the distance towards north is taken as a positive integer:


Point P is the starting point, and its distance is represented as 0 km north.

First, Rahil travels 56 km north: His position relative to point P is +56 km.

Then he travels 45 km south: Net displacement from P is 56 − 45 = 11 km north.


Thus, Rahil is 11 km north of his starting point, P.

Answered by LucasMatthewHarris | 2025-07-06