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Decimals Add, Sub, Multiply, divide

Added Nov 09, 2016 •

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hi I'm Rob welcome to Math Antics in this lesson we're going to learn about decimal arithmetic but before we get started if you don't already know how to do multi digit arithmetic with regular whole numbers be sure to watch our videos that are those subjects first that's really important because I'm just going to show you how you can modify the procedures that we already learned in those videos so that they work for decimal so if you don't know how to do those procedures already this video won't make very much sense specifically you should make sure you watch the videos about multi digit addition subtraction multiplication and long division if you know how to do the problems in those videos in decimal arithmetic won't be too hard that's because the is 4 decimal arithmetic are basically the same as they are for whole numbers but there's a few important differences that you need to know about and that's what I'm going to show you in this video are you ready let's start with an easy one multi digit addition when adding multi-digit whole numbers the key was to stack the numbers up so that the ones place digits line up in a which ensured that all the other number places lined up in columns to then you just add up the digits in each column starting with the ones place and working to the left Will adding multi digit decimal numbers works the same way the main difference is that instead of lining up the ones place digits when we stack the numbers we line up the smoke points instead but wait a minute I mean isn't that the same thing as lining up the ones place digits yes it is and that's because the is our reference Mark that always goes between the ones place and the tenths place so lining up the decimal points is the same thing as lining up the places it make sure all the number places lineup in columns you've probably noticed that decimal numbers can have different numbers of decimal digits example 10.8 has only one decimal digit but 5.34 has two decimal digits and what that means is that when you line up the points of the two decimal numbers they might not form a nice column on the right Edge sum of the digits might be missing but that's no problem remember if there's not a digit in a particular number place you can just put a zero there to help you keep track of things now that these numbers are lined up by their decimal points we can add call One by call but instead of starting with the ones place like we always did with whole numbers we start with whatever number Place column is the furthest to the right in this case that's the hundreds place so we'll start there so we add the digits in each column hearing or regrouping as needed and we get one six one for so we're done right wrong there's one last really important step remember we're doing decimal addition so we can't just forget about set decimal point we need to bring a copy of it straight down into our answer line so we keep the same reference point for number places now we can see that the answer is really 16.14  that's not so hard as it and I've got more good news decimal subtraction works the same way you start by lining up the desk points of the two numbers remember that the order of the numbers matters in subtraction so be sure that the number you're taking away is on the but then starting with whatever call what is furthest to the right you subtract the digits call him by, borrowing if you need to after that you just bring down a copy of the decimal point and you have your answer okay so decimal addition and subtraction are pretty easy let's move on to something a little harder decimal multiplication as you know multi-digit multiplication ocean is more complicated because there's so many multiplication steps but the good news is that decimal numbers don't really make the procedure much harder than it is with whole that's because there's a clever way that we can make decimal multiplication look exactly like the multi digit multiplication with whole numbers that you already know how to do the key is to pretend that the decimal points are not really there hold on a minute I mean I like pretending as much as you do but if we just pretend that the Four Points aren't even there we aren't going to get the right answer are we well know but the only thing that will be wrong with the answer is that the decimal point won't be in the spot so we'll need to fix that at the end I know it sounds a little confusing so here's an example that should help you understand I knew you would say that let's say that you need to multiply 3.65 by 2.4 and that seems a little tricky but what if we just pretend that the decimal point turn off there for now another words what if we pretended that the numbers were 365 and 24 you already know how to do that problem you just follow the that we learn in multi-digit multiplication part 2 and you'll get the answer 8760 but that's the answer to 365 what time is 24.65 * 2.4 so it's time to stop pretending to get the correct answer for the decimal problem we've got first and what's going on with those decimal points and why we just pretended they weren't there the truth is when we pretended that the decimal points weren't there what we were really doing pretending that they had been shifted until both of our numbers became whole numbers remember the numbers 365 and 24 technically do had appoints the right there next to the ones place we just don't need to show them since there aren't any decimal digits so by ignoring the decimal points what we were really doing is mentally Shifting the decimal points to the right we shifted the top decimal point 2 places to the right and we shifted the bottom decimal point one place to the right what doing that change the numbers it made the top number 100 times bigger than the decimal version and it made the bottom number 10 times bigger that's because every time you shift the decimal point one number place to the right it's like multiplying by a factor of 10 and that means the answer we got is way too it's too big by three factors of 10 because the decimal points in our problem got shifted a total of three places to the right two on the top and on the bottom so the fix that we're going to have to shift the decimal point in our answer the same amount in the opposite direction in other words we need to move the no point in our answer three places to the left which will make it smaller by three factors of 10 so starting right here where the decimal point would be answer was 8760 we shipped it three places to the left and we end up with 8.760 or just ate 76 and that is the answer to 3.65 * 2.4 that's a cool trick huh it means that you can do decimal multiplication just like regular multi-digit multiplication you start by setting up your multiplication problem exactly like you would at the decimal points were invisible but don't just because you'll need them at the end to figure out how many places to ship the decimal point in the answer then keep ignoring the decimal points what you follow them application procedure once you have an answer count of how many places the decimal points are shifted in the problem you're working don't forget it's the full shift of both the top and bottom decimal points and then shut the decimal point in your answer to the left that same number of places so decimal multiplication turns out to be not too bad after all but what about decimal division that's got to be hard right well multi digit division is is a little hard but luckily decimals don't really make it very much harder in fact it's only when there's a decimal divisor that the procedure is a little different if you just have a decimal dividend and the divisor is a whole number it's really simple that's because you can just do the long division procedure that we learned in the long division videos and the decimal point doesn't affect it at all you just need to make sure that you bring a copy of the decimal point up into the answer line when you're done so if you have vision problem 12.64 / 4 you would follow the division procedure as at the decimal point was not even there and you'll get three once an answer why but then you need to bring a copy of the decimal point straight up into the final answer making it 3.16 all there is to it if it's only the dividend that's a decimal number but what if both the divisor and the dividend are decimals like what if you have to do 6.45 by 1.5 well the first step is Don't Panic as you'll see this isn't much harder it turns out there's a very simple trick that we can use to make its or divisor is not a decimal we can just shift the decimal point in the divisor to the right and tell it's a whole number but if we do that then we also need to shift the decimal in the dividend the same amount to the right so when this case if we want to shift the decimal point are the visor one place to the right so that it's 15 we can do that as long as we also ship the decimal point in the dividend by the same amount which will turn it into 54.5 and here's the really cool part if we do this new division problem 64.5 divided by 15 will get exactly the I'm answer we would have if we did the problem 6.45 / 1.5 that only works because we shifted the decimal point in the divisor and the dividend by the same amount in the same direction and you'll realize why that works if you remember equivalent fractions think about the fraction 1/2 that's the same as 1/2 right okay but what if I multiplied both the top and bottom number by 10 that would give me 10 / 20 which is equivalent to 1/2 even though it uses different top and bottom numbers both represent the value 1/2 there what fractions that's what we did in our decimal division problem when we shifted the decimal point in both the divisor and the dividend by one place we multiplied each number by 10 and since fractions and division are basically the same we made equivalent division problems but now one Tim has a whole number divisor pretty cool huh that means if we solve 64.5 divided by 15 we get the answer for .3 which exactly the same answer we get if we did 6.45 / 1.5 and you can use that trick to avoid ever having to divide with will the visor even if the dividend is a whole number for example if you have the problem 148 / 1.6 you can ship the decimal both the divisor and the dividend one place to the right remember there's always a decimal point even in a whole number it's just that when you shift it to the right you need what is 0 in the place that it shifts past that gives you the equivalent division problem 1480 / 16 and since these division albums are equivalent you'll get the same answer for both  alright so that's how you can modify all the traditional arithmetic procedures to work with decimal numbers give me a little tricky at first since there's a few extra steps that you have to keep track of when the numbers are decimals but if you practice a lot and check your answers with a calculator you'll get it remember you can always re watch this video if you need to along with the other videos about multi-digit arithmetic as always thanks for watching Math Antics and I'll see you in learn more at mathantics.com

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Decimals Add, Sub, Multiply, divide

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