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# Combining like terms with rational coefficients

CCSS.Math:

## Video transcript

what I want to do in this video is get some practice simplifying expressions and have some hairier numbers involved and these numbers are kind of hairy and like always try to pause this video and see if you can simplify this expression before I take a stab at it alright I'm assuming you have attempted it now let's look at it we have negative five point five five minus eight point five five C plus four point three five C so the first thing I want to do is can I combine these C terms and I definitely can this is if you we can add negative eight point five five C to four point three five C first and then that would be let's see that would be negative eight point five five plus four point three five I'm just adding the coefficients times C and of course we still have that negative five point five five out front negative five point five five and I'll just put a plus there now how do we calculate negative eight point five five plus four point three five well there's a couple of ways to think about it or visualize it one way is to say well this is the same thing as the negative of eight point five five minus four point three five and eight point five five minus four point three five let's see eight minus four is going to be the negative 8 minus 4 is 4 5500 so minus 35 hundreds is 20 hundreds so I could write four point two zero which is really just the same thing as four point two so all of this all of this can be replaced with a negative four point two so my entire expression has simplified to negative five point five five instead of saying plus negative four point two C I can just write it as minus 4.2 4.2 C and we're done we can't simplify this anymore we can't add this term that doesn't involve the variable to this term that does involve the variables so this is about as simple as we're going to get so let's do another example so here I have these I have some some more hairy numbers involve these are all expressed as fractions and so let's you have 2/5 M minus 4/5 minus 3/5 M so how can I simplify well I could I can add all the M term together so let me just change the order I could rewrite this as 2/5 M minus 3/5 M minus 4/5 all I did is I change the order and we can see that I have these two M terms I can add those two together so this is going to be 2/5 minus 3/5 times M and then I have the minus 4/5 still on the right hand side now what's 2/5 minus 3/5 well that's going to be negative 1/5 it's going to be negative 1/5 so I have negative 1/5 M minus 4/5 minus 4/5 and once again I'm done I can't simplify it anymore I can't add this term that involves M somehow to this to this negative 4/5 so we are done here let's do let's do one more let's do one more example so here this is interesting I have a have a parentheses and all the rest and like always pause the video see if you can simplify this alright let's work through it together now the first thing that I want to do is let's distribute this to so that we just have three terms that are just being added and subtracted so if we distribute this 2 we're going to get 2 times 1/5 M is 2/5 M let me make sure you see that M M is right here 2 times negative 2/5 is negative 4/5 and then I have plus 3/5 now how can we simplify this more well I have these two terms here that don't involve the variable those are just numbers I can add them to each other so if negative 4/5 plus 3/5 so what's negative 4 plus 3 that's going to be negative 1 so this is going to be negative 1/5 what we have in yellow here and I still have I still have the two over 5m 2/5 M minus 1/5 and we're done we've simplify that as much as we can