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Current time:0:00Total duration:4:29

Topic A: Addition and subtraction of integers and rational numbers

Video transcript

79% - 79.1 - 58 and one-tenth and I encourage you to pause this video and try to try to compute this expression on your own well the thing that jumps out at you is that these are in different these are in different formats this is a percentage of different representations as a percentage this is a decimal this is a mixed number and so it makes sense of it it's probably a good idea to get them all in the same format and it seems like we could get all of these into a decimal format pretty easily so let's go that way so 79% that literally means 79 per hundred as if you wanted to write as a fraction would be 79 over 100 but if you wanted to write as a decimal it's 79 hundredths which could be zero or we would write it down as zero point seven nine now 779 point one is already written as a as a decimal so we'll just write again so - seventy nine point one and then 58 and 1/10 well 1/10 is the same thing as point one so you could view this as 58 well it and literally as 1/10 so it's minus 58 and 1/10 or you could view this as 58 point one so now they're all in the same format let's actually do the computation now the first thing that jumps out at you is you have a fairly small number here small positive number it's it's it's less than 1 and you're subtracting fairly large numbers right over here so your whole answer is going to be negative and to make sense of this a little bit what I'm going to do is I'm going to factor out a negative sign and that'll make the computation at least in my brain it's going to make it a little bit easier so if we factor out a negative sign this becomes so we're going to factor it out actually let me just do it this way so we could if we factor out a negative sign then this will become negative this would be positive and this is this would be positive and just to verify this imagine this distributing this negative sign or if this was a negative one negative one times this is positive negative one times this is negative negative one times this is negative so these these two expressions are the exact same thing and the reason why I did that is now we'll do the more natural thing if we will add these two numbers we'll get a positive number a larger positive number then what we're going to subtract from it right over here so we could kind of use our traditional methods and we can't forget about this negative out here so let's first do that let's add seventy nine point one plus fifty eight point one so seventy nine point one plus fifty eight point one so 1/10 plus 1/10 is two tenths 9 Plus 8 is 17 so that's seven ones and one 10 so one 10 plus 7 tens is going to give us two eight tens plus five tens gets us to 13 tens or 130 so we have one hundred thirty seven point two is this part right over here so one hundred let me write this down so we have one hundred thirty seven point two and then from that we can adding a negative zero point seven nine as the equivalent of subtracting zero point seven nine so let's do that let's subtract zero point seven nine making a point to align our decimal points so that we're subtracting the right place from the right place and now let's do our subtraction so right now we're subtracting 9 from nothing we could write a zero right over here but we still face an issue in the hundreds place we're also subtracting a 7/10 from two tenths so that we're going to have to regroup a little bit in the numerator in order to subtract or lose at least in order to subtract using the the most traditional technique so let's take a tenth from the two so it's only one tenth now and give it to the hundreds so one tenth is ten hundredths so we could subtract that ten hundredths minus nine hundredths is one hundredth now in the tenths place we don't have enough up here so let's take one from the ones place so that becomes a six one is 10 tens so now we have eleven 11 10 11 10 11 minus seven is for better decimal place six minus zero is six and then we got our 13 all right just like that so when I computed all of this inside the parenthesis so outside the parenthesis I still have the negative sign when I computed all of this inside the parenthesis I got 136 0.41 and then we can't forget about the negative sign out here so this whole thing computes to negative 136 point four or one