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# One-step addition & subtraction equations: fractions & decimals

CCSS.Math:

## Video transcript

let's give ourselves some practice solving equations so let's say we had the equation 1/3 plus a is equal to 5/3 what is the a that makes this equation true if I had 1/3 plus this a what a what does a need to be in order for 1/3 to that in order for 1/3 plus that to be equal to 5/3 so there's a bunch of different ways of doing this and this is one of the fun things about equations is there's now exactly one right way to do it but let's think about what at least I think might be the simplest way and before I worked or anything you should always try to pause the video and do it on your own so what I like to think about is well can I can I can I have just my a on one side of the equation since it's already on the left-hand side let's see if I can keep it on the left-hand side but get rid of this 1/3 somehow well the easiest way I can think of getting rid of this 1/3 is to subtract 1/3 from the left hand side of the equation now I can't just do that from the left hand side of the equation if 1/3 plus a is equal to 5/3 and if I just subtract 1/3 from the left hand side then they're not going to be equal any more then this thing is going to be 1/3 less while this thing isn't going to change so then this thing on the Left would become less than 5/3 so in order to hold the Equality whatever I do on the left hand side I have to do on the right hand side as well so I have to subtract 1/3 from both sides and if I do that then on the left hand side 1/3 minus 1/3 that's the whole reason why I subtracted 1/3 was to get rid of the 1/3 and I am left with a is equal to 5/3 minus 1/3 5/3 minus 1/3 minus 1/3 and what is that going to be equal to I have five of something in this case I have 5/3 and I'm going to subtract a 1/3 so I'm going to have be left with 4/3 so I could write a a is equal to 4/3 and you could check to make sure that works 1/3 plus 4/3 is indeed equal to 5/3 let's do another one of these so let's say that we have the equation K minus 8 is equal to eleven point eight so once again I want to solve for K I want to have just two K on the left hand side I don't want this so I don't want this subtracting this 8 right over here so in order to get rid of this 8 let's add 8 on the left hand side and of course if I do it on the left hand side I have to do it on the right hand side as well so we're going to add 8 to both sides the left hand side you are subtracting 8 and then you're adding 8 that's just going to cancel out and you're just going to be left with K and on the right hand side 11.8 plus 8 well 11 plus 8 is 19 so it's going to be 19 point eight and we're done and once again what's neat about equations you can always check to see if you get the right answer nineteen point eight minus eight is eleven point eight let's do another one this is too much fun all right so let's say that I had 5 thirteenth's is equal to t minus 6 13 all right this is interesting because now I have my variable on the right-hand side well let's just leave it there let's just see if we could solve for t by getting rid of everything else on the right-hand side and like we've done in the past if I want to I'm subtracting 6 over 13 so why don't I just add it why don't I just add 6 over 13 I can't just do that on the right hand side then the two sides won't be equal anymore so I got to do it on the left hand side if I want to hold the equality so what happens so what happens on the left hand side I have let me give myself a little bit more space I have 5 13 plus 6 13 plus 6/13 are equal to or equal to well I was subtracting 6 13 so now I add 6 13 s well those are just going to add to 0-6 13 s minus 6 13 s is just 0 so you're left with T so T is equal to this if I have 5 13 Sen I add to that 6 13 well I'm going to have 11 13 so this is going to be 11 13 is equal to T or I could write that the other way around I could write T is equal to 1113