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# Translating expressions with parentheses

CCSS.Math:

## Video transcript

what I hope to do in this video is give ourselves some practice interpreting statements and writing them as mathematical expressions possibly using parentheses so let's get started and for any of these statements if you get so inspired and encourage you to get so inspired pause the video and see if you can write them as mathematical expressions so this first one says seven hundred minus 19 divided in half so we could say we another way to think about divided in half is divided by two so we could write this as seven hundred and nine minus 19 and we're going to do that first so that's why I put the parentheses around it divided by 2 or divided in half that's one way that we could write this now the next one and once again pause it if you get inspired and I encourage you to three times the sum of 56 and seven so it's going to be 3 times the sum of 56 and seven so the sum of 56 and seven we want to take that first so it's going to be 56 plus seven that's the sum of 56 and seven and then we want to do three times that we want to do three times this sum so we could write it we could write it like that another way we could write it when you're dealing with parenthesis and you're going to see this more and more as you get into more and more fancy algebra I guess you could say but what I'm about to show you is it so fancy is you don't have to write the multiplication sign here you could just write three and then open parenthesis 56 plus seven 56 56 plus seven and this too is 3 times the sum of 56 and seven and you want to be very careful because you might be tempted to maybe do it without the parentheses so you might be tempted to do something like this 3 times 3 times 56 56 plus seven but this one isn't obviously 3 times the sum of 56 and seven in fact the standard way to interpret this is that you would do the multiplication first you would do three times 56 and then add 7 which is going to give you a different all you and you could try it out then if you were to add the 56 and the seven first so to make sure that you do the 56 and the seven first you want to put this parenthesis around it so let's keep going the sum of three times 56 and seven so we're going to take the sum of two things so we're going to take the sum of two things the first thing that we're going to take the sum of is three times 56 so three times 56 and a seven and then let me do that in a different color and seven and seven so this right over here is the sum of three times 56 and seven now it's always good to write the parenthesis it makes it a little bit cleaner a little bit more obvious that look I'm going to take the three times 56 I'm going to do that first and then I'm going to add seven but based on what I just told you the standard way if you were someone were to just write three times 56 plus 7 plus already three times 56 if someone order just write this three times 56 plus seven this actually can still be interpreted as the sum of three times 56 and seven because as I just said the standard the convention so to speak is to do your multiplication first order of operations which you may or may not but if you're not familiar you will be familiar with it soon is to do the multiplication first and then add the seven and then do the addition but just to make it clear it doesn't hurt to put the parenthesis there three times 56 plus seven now we have 43 minus the sum of 16 and 11 so 43 minus so we're going to have 43 minus minus the sum of 16 and 11 so minus the sum of 16 and 11 so from 43 we're going to take the sum of 16 and 11 and so once again the parenthesis make it clear that we're going to take the sum of 16 and 11 and we're going to take that from 43 parenthesis are very very very important here because if we just did 4343 minus 16 minus 16 plus 11 the standard way of interpreting this would be 43 minus 16 and then adding 11 which would give you a different value than 43 minus the sum of 16 and 11 so once again the parentheses are very very very important here to emphasize that you're going to add the 16 and 11 first and then subtract that sum from 43 this is fun let's keep going ten times the quotient of 104 and eight so we're going to do 10 times something 10 times the quotient of 104 and eight and so the quotient of 104 and 8 we can write like this 104 divided by divided by 8 or based on what we told you a little earlier you could write this as 10 times the quotient the quotient of 104 and 8 or 104 divided by divided by 8 now let's just do this last one four times as large so four four times as large as the expression as the expression 175 minus 58 so I'm going to do four times as large as something so I'm going to multiply something times four and I'm going to multiply as large as the expression 175 minus 58 175 minus 58 and once again I could write it as four times four times as large as the expression let me do that in that purple color as the expression 175 minus 175 minus 58 either way and once again if you were to do it like this if you weren't right if you were it didn't write the parentheses then it wouldn't be the same thing because if the parentheses weren't here then you would want to do the 4 times 175 first and then subtract the 58 which isn't what this statement is telling us and this last one I think brings up an interesting thing for us to think about because if someone were to walk up walk up to you on the street and they were to show you ups what's going on with my computer and they were to show you two different expressions is well the first expression said said - let's write it this way actually I'm not going to speak them out I'm just going to going to write it down I'm just going to write some some crazy number here some crazy some crazy numbers here so that's one expression that someone were to write and let's say another one is this one and I'm intentionally but I put the commas in the wrong place on let me make sure I get this right all right this one hundred eighty three thousand five hundred seventy six this is thirty seven thousand three hundred ninety nine so that's one expression and then another expression is this and I'm intentionally not reading it out well I'll read it out a little bit thirty-seven thousand three hundred and ninety nine if someone said quick which expression is larger and you might be tempted or you might not be tempted but you might be tempted oh let me calculate this thing gee I'm gonna have to write this thing down or use a calculator or something or whatever else to add one hundred eighty three five one hundred eighty three thousand five hundred 676 was thirty-seven thousand three hundred ninety nine and then have to multiply that by two and figure out what that number is equal to and then I would have to take one hundred eighty three thousand five hundred seventy-six plus thirty seven thousand three hundred ninety nine figure out what that is multiply that by seven and figure out what that's going to be that's that's hard that's going to take not hard it's just going to take you some time you might make some careless mistakes but the big realization to say well which one is larger well I don't have to even calculate these things because this is two times this this craziness right over here this thing that's going to be two hundred something thousand and this is seven times that thing that is going to be two hundred and something thousand so seven times that thing is going to be larger than two times that thing and so one way to you know before you dive deep and start computing things it's always good to take a step back and say hey look can I look at kind of how the expressions are formed the structure of these Russians and say look this is this is two times this thing and this is seven times this thing well the seven is going to be this one right over here is going to be is going to be a larger expression anyway hopefully you enjoyed that as much as I did