Question

[(- 27) + (- 52)] +

_____

=

_____

+ [(- 52) + 100]

.

Accepted Answer

Let the number in the blank in the LHS be $100$ .

The associative property of the addition of integers states that, if there are three integers $a, b$ and $c$ , then $(a + b) + c = a + (b + c)$ is true.

This means that we can add the integers in any order.

Applying the associative property of the addition of integers on the given statement, we obtain, $[(- 27) + (- 52)] + 100 = (- 27) + [(- 52) + 100]$ .

This indicates that when the number in the first blank be $100$ and that in the second blank is $27$ , the given statement is satisfied and also, the statement satisfies the associative property of the addition of integers.

Note that without applying the associative property of the addition of integers also, the given statement can be satisfied with many other pairs of integers also.

For example, when the number in the blanks in the LHS and RHS be $- 1$ and $- 128$ , respectively, we obtain:

LHS $= [(- 27) + (- 52)] + (- 1)$

$= (- 79) + (- 1) = - 80$

And, RHS $= - 128 + [(- 52) + 100]$

$= - 128 + 48 = - 80$

Hence, LHS $=$ RHS.

Many other combinations are also possible.

EXERCISE 1.2

Jayashree Vipin Mathematics Solutions for EXERCISE 1.2

Questions from EXERCISE 1.2 with Hints & Solutions

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