Evaluating expressions with & without parentheses
Sal evaluates an expression with and without parentheses. Created by Sal Khan.
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- In the example equation:
(10 × 4) + (4 ÷ 2)
You must solve the parenthesis first (Moving left to right)
(10 × 4 = 40) + (4 ÷ 2)
40 + (4 ÷ 2 = 2)
40 + 2 = 42
In this other example parentheses inside of parentheses:
((10 × (4 ÷ 2)) × 2) + 2
You solve the most nested parentheses first.
((10 × (4 ÷ 2 = 2)) × 2) + 2
((10 × 2 = 20) × 2) + 2
(20 × 2 = 40) + 2
40 + 2 = 42
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- A negative plus a negative will always equal a negative because you are taking a value less than zero and "applying more negativity to it" For example, you are already underground, and adding a negative distance means you will be digging even deeper underground.
However, a negative times a negative will become positive.(4 votes)
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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.