Transcript for:
Language of Algebra

hello class today we're going to learn about the language of algebra so today you get to be the translators and what you're going to be translating is from the english language to the math language so together we're going to go over what it is you need to know a few important keywords and we'll do some exercises together and you'll get to do a few exercises on your own the first thing we're going to talk about today are just the most common keywords that you need to know based on the most common math operations the four most popular operations which are addition subtraction multiplication and the last one is if you said division you said the right thing all right so those are the four most uh popular math operations and the thing is they're not always going to be listed to you like this you're not going to always be told to add or subtract there are sometimes important keywords that you have to look for in your book there's a table on that table there are important keywords that we need to know well you'll notice in the addition few keywords that are showing up there are sum plus added to in the subtraction we want to look for difference minus subtract less than for multiplication there's um product times multiply etc and for division you want to look for words such as quotient divide per now um there are four keywords that i want you to always pay close attention to and those four keywords kind of fallen under the same umbrella they're part of the same family and they are words that represent those four operations but the ones that i'm talking about in particular are the words some because sum represents addition subtraction would be the word difference for multiplication you would look for the word product and the last one for division you would look for the word quotient now those are four very popular um keywords that we have to pay close attention to when we see them but what i'd like you to do is to start getting in the habit of doing this when you see the word sum don't just put a plus sign my recommendation for you is to put parentheses and inside put a plus sign and i'll show you why when we start to do a few exercises together the word difference put parentheses and a minus sign for the word product put also parentheses and let's do the dot to represent the product all right and the last one for the quotient we're going to go ahead and put parentheses and we will use the division bar in this case to represent the quotient so whatever goes on top of it that would be our numerator and whatever's on the bottom that would be the denominator all right so now let's go ahead and do a few exercises together and what i'd like you to do is take a moment to read the first statement and try to spot out the keywords you can go ahead and underline them so we have a number increased by five so a number if we don't know what it is what do we use to represent if you said x you said the right thing so the number we don't know what it is so we're going to put an x increased by that's also one of our keywords that represents addition so increased by means we're going to be adding and 5 of course represents itself which represents the number 5. so if we are to pretty much write that as an expression that would be a number rx plus that represents increased by and the number five so the answer would be x plus five all right now let's take a look at the second statement we have twice a number minus four so once again um if we highlight the keywords we've got twice and twice which means if you said two times you got the right thing twice is a different way of saying two times something so that would be two times a number there goes again and that represents our unknown so that's our x minus is our subtraction and four again is the number four so if we want to write that as a final expression this would read as two times a number so two times a number that's our two x minus four so our final expression is two x minus four now the last one we have seven of course that's the number seven the key word here is divided by a number again our number is the unknown so that's the x so now to translate all of this we can write it as 7 divided by x but we can also write it as um as a fraction we can use it the division bar to represent the division so you can leave it like this or you might want to do it as a division bar and that would be 7 divided by the number so be 7 over x you're more likely to see it written as a fraction because that's more of the form that we tend to use to represent division now there are a few things in math we have to watch out for when it comes to subtraction because as you know subtraction is not commutative so the order does matter for example if we do three minus one we get two but if we do one minus three then we're not going to get the same answer we end up with a negative two so we have to watch out for those key words that represent subtraction so some of those words that i would like you to pay attention to are less than subtracted from and the last one is taken from so those are what i'd like to say the popular words or our keywords that you have to watch out for because when you see those um three key words what's gonna happen is we're gonna have to write the expression backwards again so watch out for them less than subtracted from taken from so those will allow us to write the expression backwards so with that in mind we're going to go ahead and do a few more exercises together to see how we treat those um keywords when they are written written sorry in an expression all right now let's go ahead and do a few exercises together so the first one we have five taken from a number so again if we notice here the keyword is taken from and taken from is one of those words that we had talked about earlier that we use to represent subtraction but it's the one where when we see it we have to construct the expression backwards so for example if i am to take something from you okay in order for me to do that you have to have something first so that i could take something from you hopefully that made sense so if i have five and we have a five that would that's taken from a number don't you agree that we have to have the number first so that we can take the 5 from it so with that in mind even though we see 5 first it has to go in the end because it's the 5 that's being taken from the number so 5 taken from x so the expression would be written as x minus five that's the answer for that one now the next one we have a number less than two so once again the number as we mentioned earlier represents our x less than is our keyword here that represents subtraction so a number less than two i'll give you a few moments to write it down on your paper all right so now a number that's our x less than is one of those keywords that we have to write backwards two so the answer is two minus x so that's how we translate a number less than two all right the next exercise five less a number again i'll give you a few moments for that one all right here we notice the word less so it's missing it's then right but it really doesn't need it um so we have five less a number in this case if it's not less than you don't have to write the expression backwards so in this in this particular example we'll start off with the five the less subtracts um sorry the less represents subtraction so b minus and the number is our x so the answer will be 5 minus x so watch out for that if you have less you will treat it differently than you will less than so less than we construct it backwards less you would write it in the same way as you are reading the expression okay we'll leave the challenging one till the end here so again um i would like you to take a few moments to try that one on your own four subtract it from twice a number so look for the keywords subtracted from is one of them we talked earlier about twice we have the number that represents x and the four which of course represents the number four so as we had mentioned subtracted from is one of those keywords that have we have to write backwards twice meaning if you said two times good job and the number is x so 4 is what we would have to write last so we are subtracting 4 from something so 4 needs to go in the end and what is it that we are subtracting it from we are subtracting the 4 from twice a number so as we had said earlier twice means 2 times something so that's 2 times x so 4 is being subtracted from twice the number but as we know we don't need to show the multiplication because 2 times x is the same as 2x so the final answer would be 2x minus 4. i listed four examples here on the board and let's first underline the main keywords starting with the first one the sum of five and a number so here's one of our main keywords the product of a number and eight there is another keyword twice the difference of a number and seven and the last one twice the number decreased by 10. so those are pretty much our main keywords um within each expression even though there are a lot more keywords within each statement but i want to want us to focus on those now for now and if you mentioned earlier we had if you remember earlier i had mentioned that we have the words some product difference and quotient i said those fall within the same family under the same umbrella and if you notice when we use those keywords what other word do you see that they all have in common in each of those statements so we have here the sum of okay if you noticed of that's good but also there's another word and that's the word end and and because even when we try to use that word as that statement we say the sum of this and that the difference of this and that the product of this and that so the word and has to be used in that statement um to have it grammatically correct let's just put it that way but in our case we are going to use that word to our advantage and the way that works is that if you remember i said when you see any of those keywords the moment you read it put parentheses and the operation symbol that goes with it so the sum let's go ahead and put right away parentheses and plus now when we have the sum there it's going to be of two things this and that so whatever we see before the word and goes before the plus sign whatever goes after the word and goes after the plus sign so the sum of 5 so that's the 5 and represented by our sum the addition and the number is x now since there's nothing there now you're free to remove the parentheses if you wish so you can leave the answer as five plus x and that's how that works and now the next exercise the product of a number and eight so product as we had mentioned before is multiplication so parentheses and the multiplication symbol now the word and is being represented by the multiplication symbol that we use so whatever is before and goes before multiplication sign and whatever is after end goes after it so the product of a number that's the x and eight so that's times eight now we wouldn't want to leave it that way it doesn't look nice right we can clean it up a little bit so we can fix it up and instead of saying x times 8 we can write that as 8 x without the parentheses and that would be our final answer for that one here's the next exercise it says twice the difference of a number and seven so go ahead and take a few moments to try to set this one up on your own you can also pause if you want a longer time so let's go ahead and try to work this one together so twice as we had said means two times the difference that represents subtraction the number is the unknown and of course the seven that represents itself so here that's where you're really going to appreciate the parentheses that i talked to you about because here we're saying two times the difference so when we say twice twice translates to two times so you don't want to put two times and a minus sign what you want to do is use the parentheses with the minus sign to represent the difference so that's two times the difference the entire difference so that's what how it reads twice the difference of two things and those two things are the number and the 7. so that's how we translate this um statement so again here you will need to leave the parentheses because there is something outside of it but you wouldn't need to put the multiplication symbol so you can write it as two parentheses x minus seven and leave that as your final answer now the last one over here it says twice the number decreased by six here are we i know twice is not a word but are we doubling are we multiplying the whole difference or are we only multiplying a part of it here it says twice the number so it's not the entire difference even though decreased by is subtraction it's twice the number so that's two times only the x and then this is being decreased by the number six so that's why when you see those words that i had mentioned earlier sum product difference quotient get into the habit of putting the parentheses there if you don't need it in the end you simply take it out because you'll see how you can easily make a mistake if you were supposed to put it and you didn't here it's decreased by is not one of those popular keywords that we had mentioned so here we're only doubling the number but not the six so we can leave it as 2x minus 6 and that would be the final answer for this expression the last thing we're going to look at is how to set up equations so we've already translated learned the important keywords when it comes to setting up expressions but there's just one last part that we need to look at which is how to set up equations so we want to refer to this table to look for the keywords that represent the equal sign because as you know in the equation an equal sign is definitely necessary so those are important keywords that when we see them in the statement they translate to the equal sign as we are doing our translation all right now let's go ahead and do a few more exercises together and focusing on setting up equations so with the first example that i have up here we have three times a number added to four is 16. so out of those words in this statement which word do you think represents the equal sign and if you answer the word is you are absolutely correct so what we can do is set up the equal sign which um and then this way we know that anything that we see before is is going to go to the left of it and where anything that goes after it goes to the right of it now definitely the right side is much shorter so we can go ahead and finish that one off so is 16 means equals 16. now let's focus on the left side of the equal sign and treat that just as a normal expression as we have done in the previous exercises so three times a number added to four three times a number that would be our 3x so that's three times x add it to four again added would be our addition sign so that's the plus three x plus four is 16. now we're not going to solve any of those equations we're simply going to be setting them up if we are to solve it then we would solve it following the same directions as you would when you have to solve any linear equation but now we're just gonna set them up the next exercise is the sum of a negative five and a number is equal to eight so if you want to pause this a bit longer to give you a few moments to set up set it up on your own you may go ahead and do so so let's go ahead and do it up together the sum watch out for that words so the sum this is our sum of two things right something and something and remember the plus sign we're going to treat that as our and so the sum of what negative five and the number so that's negative 5 plus x is equal to this right here represents the equal sign so we could have started off with the equal sign or we could have just started with it left to right and translating as we went along so you've got a couple of options on how you want to go about setting up your equations and or i should say translating your equations so is equal to 8. now once again because there's nothing outside of your parentheses if you want to go ahead and take them out feel free to do so so the sum of two things the negative 5 and the x is equal to that's our equal sign the number eight good now the last exercise is twice a number less than four gives us ten so if you want to pause go ahead and do so once again to try to set it up on your own but we are going to go ahead and work on it so twice two times as we had mentioned before a number that's our unknown that's our x less than what do you remember about less than if you said that's one of the words we have to write backwards and the expression backwards then you're absolutely correct um gives us or you could just focus on gifts that's where the equal sign is going to be replaced so if we want to start with the gifts part and it gives us part we can do that gives us what 10 then we can put the 10 on the right side and get that over with and now focus on the first part of our equation which is twice a number less than 4 so we can start backwards so twice a number that's 2x 2 times x is twice a number less than 4. so the final answer will be 4 minus 2x equals 10 and that's how we can that's what we get as our final equation for each of those statements all right now that wraps up our session on translations so now we are able to translate expressions we are able to translate equations so make sure that you get very familiar with those keywords that we talked about and also the other keywords that are mentioned in the tables that were introduced to you in this video and um there's a link for it for the handout that you need make sure you use it uh to take the to take in the notes as you are watching the video and also there are exercises on it that you need to make sure that you complete to give you more practice and that's where you can become the best translator from the english to math language so thank you so much for watching the video