In this video,
we will evaluate expressions with parentheses.
Sometimes it can be a little challenging
to interpret the operation of an expression,
because there are so many ways
to write equivalent expressions.
Just remember if there's a single number
inside the parentheses, this just
represents the value of the number itself.
And when an operation is being performed,
the operator will be given,
except for the case when we have implied multiplication.
We have implied multiplication here,
because we have a number inside parentheses,
next to a second number inside parentheses,
and therefore this is implied multiplication.
This expression is equivalent to
negative eight times negative two.
And because a negative times a negative is positive,
negative eight times negative two is equal to a positive 16.
And there are also many other ways to write this product.
We can leave the eight outside the parentheses,
and then put the negative two inside parentheses.
This also means negative eight times negative two.
We can also include a multiplication sign
as we did here, with or without parentheses.
So we could write negative eight times negative two,
or negative eight times negative two
with no parentheses.
We can also use different symbols for multiplication.
But all these expressions are equivalent.
Looking at the next expression,
notice how we have a division sign here
before the negative two in parentheses.
This just means negative eight divided by negative two.
A negative divided by a negative is equal to a positive,
this quotient is positive four.
Again, the reason we have the parentheses here
is just to clarify that we're dividing by a negative two.
Without the parentheses, the quotient is not as clear,
we would have negative divided by negative two,
and having the division sign right next to the negative sign
does tend to be a little more confusing.
But it does mean the same thing, and is equivalent.
And because a fraction bar means division,
we can right an equivalent quotient
as negative eight divided by negative two.
Again, with the negative eight and/or
the negative two in parentheses.
All these expressions are equivalent
and mean negative eight divided by negative two.
Next we have a minus sign in front
of the negative two in parentheses,
which means we have the expression
negative eight minus negative two,
and again the parentheses are used here
to clarify what we're subtracting.
If we did not have parentheses,
the expression would be negative eight minus negative two,
which is not incorrect, but using the parentheses,
it's more clear that we are subtracting negative two.
And subtractive negative two is equivalent
to adding positive two, so this is equivalent
to negative eight plus two, which equals negative six.
Negative eight minus negative two is equal to negative six.
Next, notice how we have a plus sign
in front of the parentheses, which means
you are adding negative two.
Our expression is negative eight plus negative two,
which is equal to negative 10.
Again, the parentheses are used
to clarify that we are adding negative two.
If we did not have the parentheses,
we would have negative eight plus negative two,
which looks like this, which is equivalent,
but just not as clear when parentheses are included.
For the last two examples, notice how
we have a difference inside the parentheses.
When following the order of operations,
we know we need to simplify inside the parentheses first.
So for both of these last two expressions,
we begin by determining negative five minus two.
Well negative five minus to is equivalent to
negative five plus negative two,
which is equal to negative seven.
So this first expression simplifies to
negative eight, then in parentheses
we have negative seven.
And again, this is implied multiplication.
This means negative eight times negative seven,
which is equal to positive 56.
Looking at our last expression,
we already know that negative five minus two
is equal to negative seven.
The expression simplifies to
negative eight minus negative seven.
Because of the minus sign here,
we know we subtract negative seven from negative eight.
Well negative eight minus negative seven
is equivalent to negative eight plus positive seven,
which is equal to negative one.
I hope you found this helpful.