Question

Without simplifying the given expression state whether the given expression is an integer or not:
$68\times 12+\left[\right(-3)\times 68]+68.$
Also, find the additive inverse of the sum obtained.

Answer 1

Here, both $68\times 12$ and $(-3)\times 68$ are integers by the virtue of closure property of multiplication.
So, $68\times 12+\left[\right(-3)\times 68]+68$ is also an integer by the virtue of closure property of addition.

Now, let's simplify the given expression using distributive property:
$68\times 12+\left[\right(-3)\times 68]+68$
$=68\times (12-3+1)$
$=68\times \left[\right(12-3)+1]$
$=68\times [9+1]$
$=68\times 10$
$=680$
So, the additive inverse of $680$ is $-680.$