We're asked to find the difference, if we have negative 45 minus 66. To find this difference,
write the difference as a sum, and then find the sum. We can write this difference as
a sum, because, subtracting an integer is
the same as adding the opposite.
So subtracting b, is the same as adding negative b. And therefore subtracting 66
is the same as adding negative 66. Which
means we can write negative 45 minus 66 as
negative 45 plus negative 66. And now we use the formula rules for adding integers
to find this sum, and also show this sum on the number line.
Because we have a negative plus a
negative, we use the rules for adding
two integers, with the same sign. So step
one, we add the absolute values of the
integers. So let's first find the absolute
value of both integers so we'll find the
absolute value of negative 45, and the
absolute value of negative 66.
The absolute value of a number is a numbers distance from zero. Distance is always positive.
The absolute value of negative 45 is positive 45. The absolute value of negative 66 is positive 66.
So now we add the absolute values. So 45 plus 66, adding, 5 plus 6 is 11, perform an exchange, 1 plus 4 plus 6 is 11.
The sum of the absolute values is 111
But for the sign of addition sum, we
use the common sign because we have
a negative plus a negative that means the
sum is negative, -111...
Now let's also show this sum on the  number line, to model negative 45
We start at 0, and move left 45 units to
negative 45....
and then from here because we're adding negative 66... We move left another 66 units from negative 45.
So if we move left 66 units,
it takes us to negative 111
Negative 45 plus negative 66, or negative 45 minus 66 ,equals negative 111
I hope you found this helpful!
