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# Evaluating expressions with & without parentheses

Video transcript

What I want to do is think about
whether this expression right over here would evaluate
the same way whether or not we had parentheses. So to think about
that, let's first think about how
it would evaluate if we add the parentheses. So if we add the
parentheses, we want to do what's ever in
the parentheses first. And so here we have 8 minus
3, which is equal to 5. So this simplifies to 5
times 5 times 8 minus 3. And now we want to
do the multiplication before we do subtraction. This goes back to
order of operations. You do your multiplication
and division first. Well, you do your
parentheses first. Then if you have multiplication,
division, addition, and subtraction
all in a row, you want to do your multiplication
and your division first. So here we're going to
multiply 5 times 8 to get 40, and then we're going to
subtract 3 to get 37. Now, let's think about
what this would evaluate to if we did not
have the parentheses. So it would be 8 minus
3 times 8 minus 3. So we just have to
remind ourselves about the order of operations. The convention is to do
your multiplication first. So you're actually going to
multiply the 3 times the 8 before you subtract
it from this 8 and then before you
subtract this 3. So we took away the parentheses,
but the order of operations say, hey, do this
multiplication first. We could even put a parentheses
here to emphasize that. So this will become
8 minus 8 minus 24. Let me write it this way. 8 minus 24 minus 3. 8 minus 24 minus 3. Now, 8 minus 24 is negative 16. You subtract another 3, you're
going to get to negative 19. So clearly, you get very,
very different values depending on whether or
not you have parentheses.