About this video
The video turns the phrases '5 times the difference of x and 2' and '10 times the sum of y and 3' into algebraic expressions. Writing 5 · x − 2 is wrong because order of operations would multiply 5 and x first, so parentheses are needed: 5(x − 2) and 10(y + 3). In algebra, a dot is used for multiplication so it isn't confused with x.
You'll be able to
- translate phrases like 'the difference of x and 2' and 'the sum of y and 3' into algebra.
- use parentheses so the sum or difference is worked out before multiplying.
- explain why a dot is used for multiplication in algebra.
Key words
- difference
- The result of subtracting one number from another; 'the difference of x and 2' is x − 2.
- sum
- The result of adding numbers; 'the sum of y and 3' is y + 3.
- parentheses
- Brackets ( ) that show which part of an expression to work out first.
- order of operations
- The rules for which calculations to do first; multiplication comes before addition and subtraction unless brackets say otherwise.
Transcript
- [Narrator] We have two different statements written in English that I would like you to pause this video and try to write as an algebraic expression. All right, now let's work on this first one. So you might be tempted to say, all right, I have five. So let me just write a five, times and I'll write a dot because when we're dealing with algebra, if you write a traditional multiplication sign, it can get confused with an X.
So five times the difference of X and two. The difference of X and two, we could write as X minus two, but this expression has a problem because whoever's interpreting it, if they're following order of operations, which they should, that would mean that they would multiply the five and the X first and then subtract two.
But that's not what's going on in the sentence. It's five times, not X, but the difference of X and two. So what you need to do is put parentheses here to make sure that you take the difference of X and two first, and then multiply that by five. Now, with that in mind, let's tackle this example right over here, 10 times the sum of Y and three.
Well, once again, if you just wrote 10 times the sum of Y and three, you'll run into the same problem. someone would interpret this as, hey, maybe I should multiply 10 and Y first, because that's what order of operations would tell me to do, but that's not what we want.
We want 10 times, not just Y, but the sum of Y and three. So that's where the parentheses are really important to make sure that we take the sum of Y and three first and then multiply that by 10.
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