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# Evaluating expressions with & without parentheses

Sal evaluates an expression with and without parentheses. Created by Sal Khan.

Video transcript

What I wanna do is think about whether
this expression right over here, would evaluate the same way, whether
or not we had parenthesis. So to think about that, let's first think
about how it would evaluate if we had the
parenthesis. So if we have the parenthesis, we want to
do what's ever in the parenthesis 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 parenthesis 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, 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 a negative, another 3, you're gonna get to
negative 19, so clearly, clearly, you get very,
very different values depending on whether or not you
have parentheses.