Translation Terminology Writing

Transcription

>>Hi this is Julie Harland and I'm your math gal. Please visit my website at yourmathgal.com where you could search for any of my videos organized by topic. We'll be translating verbal expressions into algebraic expressions so there's some terms we need to know. The first one is sum. When you see the sum that refers to addition so when you see this word sum it means we're going to be adding. Okay, sum is the same thing as adding. So we read this, the sum of a number and 6 makes sense, if you have a sum you've got two things. So the two things we have, so you've got a number and 6. Usually it's separated by that word and, okay? So what do we call the number? Well let's just use a variable. I'm gonna use n for a number. So we could write n, that's one part of the sum and 6 is the other part of the sum. So that's how we would write the sum of a number and 6. What about the difference of a number and 2? Difference refers to subtraction so when you see the word difference it means we are subtracting. And again notice this is of a number and 2. The two parts are separated by that word and so whatever comes first you'll put before the minus sign and what comes after the word and is what you would subtract. That's how you would differentiate what comes first and what comes second. So again, let's just use n again to represent the number, it has to be a variable, and 2. So n minus 2 is how we would write the difference of a number in 2. Alright next one, the product of a number and 5, product means multiplication so when you see the word product you have to associate that with multiplying. We've got a number and 5 so how would we write a number and 5 multiplied together? Well you could say n times 5, right? Often you would write this as 5 times n. And the most simplified way of writing it is you know when you have a dot between it and you have a variable and a number you can just put it together and write it as 5n. Now you could also put a parenthesis around the n or a parenthesis around the 5 or a parenthesis around both of them. There's more than these three ways to show a product but 5 n is probably the simplest way of writing this answer so that would be the product of a number and 5. The last one will be the quotient or ratio. Both of those words represent subtraction. Both quotient and ratio mean division but we usually don't write the division sign when we are doing algebra so a more common way of writing this answer, again we're separating a number and 4 so those are the two things, you could of course say the number is n, n divided by 4 and it doesn't matter whether it says quotient or ratio, both of them mean the same thing. That represents division so whatever comes first goes before the division sign so we have a number and 4, those are the two things. I forgot to circle it up here, here we go. So the more common way of writing this is as a fraction so we say the quotient of a number divided by, we use the fraction bar, and 4. So this is the way we usually want to write our answers when we are doing algebra so when we're working with variables. So we've got the sum of a number and 6 and plus 6. The difference of a number and 2, n minus 2. The product of a number and 5 is 5n. It looks funny to put n5. We always put the coefficient, the number part, in front of the variable. And the last is the quotient or the ratio of a number and 4. The way we write that is n over 4 so whatever comes first you put in the numerator and what comes second, and 4, that's what goes in the denominator. Alright there are a lot of ways of expressing subtraction and there's a lot of little nuances here. Let's look at these, 6 more than a number, that refers to addition cause we're doing more than something so we're going to add it so if it says 6 more than a number, think of 6 more than your age. Well you have to know your age and then you would add 6 to it. So in this case 6 more than a number means you start with the number so we have a number and then we're gonna do 6 more than that so we're going to add 6 to it. Now the question is could you write 6 plus n? Certainly because n plus 6 does happen to be the same thing as 6 plus n. But these next three are subtraction and it's gonna make a difference what comes first before the minus sign and what comes after the minus sign. So look at this first one, 7 less than a number. So one technique is thinking about how you would answer this question, 7 less than my age, how would you get that answer? You would take your age and then you would subtract 7 from it. So instead of starting with an age we're gonna start with a number, okay, and then we're gonna subtract 7 from it. So this is tricky. It's not 7 minus n. What it's saying is 7 less than a number means you have to start with a number and then subtract 7 from it. Now look at this third one, it's not the same. It says 7, oops it is the same. I didn't mean to put less than. I meant to put 7 less a number. A little bit different. Seven less a number, well first of all most people don't talk that way but you might see this once in a while. Seven less a number means we start with 7 less a number means we take away that number. So this is 7 minus n, that's pretty tricky. What's the difference? It doesn't have that word less than. So again for this one 7 less than a number, if you're not sure how to do it, put in something you would know like your age and then do the same thing using a number as opposed to your age. Seven less a number, that's like saying 7 less 2. You mean you start with 7, subtract 2. And how about this last one, 9 decreased by a number. It means I've got to start with 9 and then I'm gonna decrease it so I have to take something away from it and I'm gonna take away the number, again I'll call it n. These are pretty tricky, the ones for subtraction. So you can see we have the word difference, which means subtraction but here's some other ways that subtraction might come up. You also might see minus or you might see subtracted from, decreased by, is here, etcetera, there's a few more that might pop up. By the way, these are all just expressions. They're not equations. We're not solving for anything. We're just writing an expression. Notice there's no verb. Six more than a number, 7 less than a number, etcetera. No verb. It's not going to be an equation. There's going to be no equal sign. We're simply writing an expression from English into mathematical symbols. Let's try doing some that are used for multiplication. Alright first one here, twice a number, what does that mean? Twice a number just means 2 times the number so we're gonna use n for the number, 2 times the number you would just write as 2n. Now this next one I'm putting two things together. It says 3 times a number, well what would that be? That would be 3n. Okay 3 times a number subtracted from 10. Okay, so what are you gonna start with? Three times the number or the number 10? Well you're subtracting from 10 so that means you've got to start off with 10 and then you're gonna subtract something from it and what are you gonna subtract? Three times a number, that would be 3n. So there are a couple examples where we've got multiplication in the mix and the second one also has the subtraction. Okay try these two on your own. Put the video on pause and see if you could write this as an expression. Go ahead and let the number be n. Okay so what do we have? Five added to the product of 9 and a number. So we're adding 5 to something so I have to do this part first. The product, remember, means multiplication and what are the two parts? I've got 9 and a number. So how do I write the product of 9 and a number? I do 9 times n which is 9n. And then it says I'm gonna add 5 to that so then I add 5. That's what you should get. Alright, excellent. Six less than the quotient of a number and 4 so 6 less than something means I'm gonna take away 6 from something. So I know I'm gonna subtract 6 from something, now I've gotta figure out what I'm subtracting it from. What am I subtracting 6 from? The quotient, okay remember what the quotient means, we write that as a fraction, fraction bar and we have the number and 4 so we'll put n in the numerator, cause that comes before the word and, so in the 4 in the denominator so we've got n over 4 minus 6. So now we've written 6 less of the quotient of the number and 4. [ Silence ] >>Please visit my website at yourmathgal.com where you can view all of my videos which are organized by topic.