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(male narrator) In this video,
we're going to take a closer look
at the first step in order of operations--the parentheses.
There can be several different types of parentheses
in a problem.
The innermost parentheses are often curved,
but if we have to put parentheses around those,
we'll usually draw square parentheses around those.
And finally, we can even do
bracket parentheses around those.
While this can seem confusing, what we will remember is
to always do the inner parentheses...
first.
And then once those are simplified,
we will continue working
simplifying the parentheses around those.
Let's do an example where we can see
several types of parentheses working together.
In this problem, we see several sets of parentheses:
the square ones and the curved ones.
We will start with the innermost parentheses,
which are both sets of curved parentheses:
4 plus 2 is 6, minus 5 squared, divided by 2, plus 3, is 5.
Next, you notice there still is
a square parentheses to focus on,
and inside that parentheses, the exponents must come next.
Now, we have 6 minus 5 squared, which is 25; divided by 5.
Continuing to work inside the parentheses,
we must do the division next.
So now, we have 6 minus 25; divided by 5, which is just 5.
Finally, finishing the problem by doing the subtraction,
6 minus 5 is 1.
So as you see, we start with the innermost parentheses
and work our way to the outer parentheses.
Let's do another example where we can see that work out.
This problem has several parentheses in it.
You'll notice a curved parentheses...
a bracket parentheses, a square parentheses,
and a curved parentheses.
We will start with the innermost parentheses:
the curved parentheses.
So now, we have 7 times; 2 squared; plus 2; times 20;
divided by 4; plus 6, which is 10;
and that completes the curved parentheses.
For our next step,
we will again look at the innermost parentheses:
the division in the square parentheses.
We will do that next.
So we have 7 times 2 squared; plus 2; times 20;
divided by 10, which is 2;
and that completes the square parentheses.
Continuing to work out,
now we'll simplify the bracket parentheses.
Order of operations tells us to do the exponent first,
so we will start with that: 7 times 2 squared, which is 4;
plus 2; times 2; close the bracket.
Continuing to work in the parentheses,
multiplication must be done next.
So we have 7 times 4, plus 2, times 2, is 4.
Now, we can simplify that parentheses
by simply doing that addition, giving us 7 times 8.
Finally, 7 times 8 finishes the problem, which is 56.
By starting with the innermost parentheses
and working our way out to the outer parentheses,
we can simplify an expression correctly
following the order of operations.