Evaluating expressions with & without parentheses
About this video
The video evaluates the same numbers with and without parentheses. With parentheses, (8 - 3) x 8 - 3 becomes 5 x 8 - 3 = 40 - 3 = 37. Without parentheses, 8 - 3 x 8 - 3 means multiplying 3 x 8 first, so it becomes 8 - 24 - 3 = -19, showing that parentheses can change the value a lot.
You'll be able to
- evaluate an expression by doing the parentheses first, then multiplication, then subtraction.
- use the order of operations when there are no parentheses.
- explain how parentheses change the value of an expression.
Key words
- parentheses
- Brackets ( ) showing which part of an expression to work out first.
- order of operations
- The agreed rule: parentheses first, then multiplication and division, then addition and subtraction.
- evaluate
- To work out the value of an expression.
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.
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