Writing expressions with parentheses | 6th grade | Khan Academy

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.

Five times the difference of x and two. The difference of x and two we could write as x minus, 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 5 and the x first and then subtract 2.

But that's not what's going on in the sentence. It's 5 times, not x, but the difference of x and 2. So what you need to do is put parentheses here to make sure that you take the difference of x and 2 first and then multiply that by 5.

Now, with that in mind, let's tackle this example right over here: 10 times the sum of y and 3. Well, once again, if you just wrote 10 times the sum of y and 3, 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 3. So that's where the parentheses are really important to make sure that we take the sum of y and 3 first and then multiply that by 10.