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Pre-Algebra: Simplifying an Expression

Added Dec 14, 2020 •

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Follow the Rules of GEMDAS aka the Order of Operations to simplify an expression Distributing to eliminate grouping symbols Sorting terms by Like Terms in order to Combine Like Terms

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simplifying expressions simplifying an expression here we have the quantity 4K -7 and what you don't see this with the between this three is a multiplication we are Distributing this 3 -6 k + 2 even though these are outside the parentheses you might want to do this first remember gem dust you got to do the grouping first then we got exma we haven't gone to exponents yet we will get to this eventually multiplication or division Mall duplication or division then addition or subtraction so do what's in the group first then exponents multiplication division left to right and then addition subtraction left to right so if you look at this right here we have 14 - 7 we can't do any sing inside the group because these are not like terms in our prior example we had the identifying terms understanding that what terms are in like terms are will help you understand it's so 4K -7 these are not like this right here we got 3 - 6K + 2 even though the three and the two are constants you have this right here let's rewrite this so we can see the steps so far all I remember you wrote the same thing but you need to know when there is a parenthesis and a number next to it and nothing is connecting them you need to know it's connect multiplication so multiplication comes before the addition and subtraction left to right and this 3 is multiplied by this group so what we are actually doing is this tributing so simplifying is making the smaller we're Alicia Saint combine like terms make smaller looking simpler looking less terms get rid of as many things that are unnecessary so right here let's go to distribute to a 3 so we have 4K * 3 and then we got this - 7 * 3 and then let's rewrite everything else - 6K 8 + 2 so now there's no distribution but it's multiplication multiplication before addition or subtraction or subtraction addition cuz we're going left to right 4K x 3 we get 12K 7 * 3 that's 21 and that's a minus -21 men - 6K Plus right here we're going to combine like terms understanding which terms are alike so let's just separate them so we have this 12K that Rita 12 K - 2 1 - 6 k + 2 you have your Constance here these are numbers no variable connected to them and their variable terms these are two separate Kay's got a 12K here and a -6 K here how many case do you have total then you have -21 + 2 so what's Griffith -12 K - 6K -21 + a + 2 I just group them together like this was just combine or like terms 12 K - 6 we have 6K -21 + 2 so when the signs are different words acting just like here you could pretty much say the slip + 12 K - 6K when you line them the bigger absolute values on top at the sons of different you subtract notice this right here it's positive up top so then negative on the bottom or subtracting them and we keep the sign of the top turn so it's a positive then go 12 - 6 and it's positive topped the bigger absolute value is the 20 the two signs are different so we subtract we keep the sign of the top number 21 - 2 -21 + 2 is the same thing as 21 - 2 and then we get the negative sign so that when 1 - 219 and since this is a k and imagine these are 19 ones -19 ones and this is 6 cases we don't know what Kaiser but we got six and this is a straight of 19th and this is simplified 6K - 19 we cannot combine these because these are not like terms and there is your simplified expression and expression it's all your terms combined as simple as possible but because it's not equal to anything it is not an equation we can't saw for cable because because we don't have anything equal to it simplify an expression your answer is an expression you can only solve an equation you can simplify an expression let's do another one so let's what's the temperature six quantity 9 - 5 m -3 * -7 M - 2 following the rules of we do inside the parentheses first to listen to this first one 9 - 5m the terms are not alike we can't do anything inside look at this one -7 M - 2 inside this group again the terms are not alike can't do anything we can I combine these because that's an m and these are pretty much ones M's ones who can't combine if they're not alike but we got these two terms in front 666 parentheses mean it's 6 * -3 next to parentheses mean it's negative three times so we are Distributing these two terms in front into the group first so let's rewrite this showing that extra bit for clarity notice all I did was rewrite it I just wanted to show you that that means we're multiplying we're Distributing the six into this group and this group only for distributor -3 into this group and this group only so let's rewrite this let's go 6 X 9 cuz they were Distributing the six and then minus the six times. buy them and then let's go cheer -3 * -7 m and then negative 3 -2 * 2 let's look at this 6 X 9 so we distribute it out let's simplify now 6 * 954 6 * 5 m -30 m let me have this negative 3 times negative 7 m negative times negative times a positive 3 * 7 is 21 m and then this right here we got a negative negative three times too so -3 * 2 is -6x right on here minus a negative 6 minus a minus becomes a positive so that becomes a + 6 what could this negative times negative positive -3 * -7 M plus positive 21 M -3 times a negative to a positive 6 so we have 54 - 30 m + 21 m plus 6 see that we have like terms we have -30 m + 21 m + let's organize that so -3 m + 21 let me have 54 and a positive sign as separate their plus two separate the terms + 6 so combine like terms we have are like terms that we have Constance right here 54 + 6 that is 60 and then we have our emblems hear you got a -30 m + 21 M signs are different so we subtract to keep the sign of the bigger number to top top figure it out figure absolute value so that's -30 - 21 that is 9 -9 m + 6 simplifying expressions combining like terms getting rid of parentheses

Uploaded by W. Leung.

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