welcome to math with Mr J [Music] in this video I'm going to cover division involving decimals this is going to be a complete guide to dividing decimals I'll cover dividing decimals by whole numbers whole numbers by decimals decimals by decimals and dividing by mixed decimals we'll start with dividing decimals by whole numbers and we will go from there now decimals and division show up all throughout math and really throughout life as well so being able to work with decimals and solve division problems involving decimals will be beneficial no matter what class level of math or goal you are working towards whatever your situation may be this should be helpful in better understanding how to divide decimals let's jump into number one where we have 73 and 8 10 divided by three the first thing that we need to do is set this problem up up that way we can go through the division process 73 and 8 10 is the dividend the number we are dividing so it goes under the division bar 73 and 8 10 divided by three three is the divisor the number we are dividing by it goes on the outside of the division bar now whenever we have a division problem that involves decimals we always need to check is the divisor a whole number if yes bring the decimal straight up into the answer so for number one our divisor is three that's a whole number so we bring the decimal straight up into the answer now we go through the division process the same process we use when we divide whole numbers so divide multiply subtract bring down repeat we start with divide so we have 7 divided by three how many whole groups of three in seven well two that gets us to six now we multiply two times three is six subtract 7 minus six is one and then we bring down now we have 13 and we repeat so we go back to divide 13 divided by three how many whole groups of three in thirteen 4 that gets us to 12. now we multiply 4 times 3 equals 12. subtract 13 minus 12 is 1 and then we bring down the eight now we have 18 and we repeat so we go back to divide 18 divided by three so how many whole groups of three in eighteen six that equals eighteen exactly multiply 6 times 3 18 subtract and we get zero so we went all the way over to the furthest place to the right which was the tenths place for number one and we have a clean cut zero here that tells us that we are done our final answer 24 and six tenths for number two we will see what happens when we do not get that clean cut zero and we need to extend the problem until we do let's move on to number two where we have 46 and 62 hundredths divided by fifteen let's start by setting this problem up 46 and 62 hundredths divided by 15. is the divisor a whole number yes 15 is a whole number that means we bring the decimal straight up into the answer and now we go through the division process so we start with divide we have 4 divided by 15. how many whole groups of 15 and 4 well we can't do that so we need to use the 6 as well and take a look at 46 we have 46 divided by 15. how many whole groups of 15 in 46 well 3 that gets us to 45. make sure that 3 goes above the 6 in 46 not above the 4. since we used both of those digits and we had 46 divided by 15 that 3 needs to go above the 6. now we multiply 3 times 15 is 45 subtract 46 minus 45 is 1. and then bring down now we have 16 and we repeat so back to divide 16 divided by 15. how many whole groups of 15 in 16 1 now we multiply 1 times 15 is 15 subtract 16 minus 15 is 1. bring down the 2 and now we have 12. so repeat and we go back to divide 12 divided by 15. how many whole groups of 15 in 12 well we can't do that so we need a zero here and now we multiply 0 times 15 is 0. subtract 12 minus zero is twelve so we went all the way over to the furthest place to the right the hundredths place but we have a 12 at the end we do not have a clean cut zero yet that 12 does not mean remainder 12 like when we work with whole numbers this answer is in decimal form so we need to keep it that way what we need to do is extend the problem until we do get a clean cut zero and that will mean the problem is done and we have our final answer we can do this by using placeholder zeros that we can bring down so let's use a placeholder 0 in the thousandths place that we can bring down and continue this problem in order to work towards that final answer now remember zeros to the right of a decimal do not change the value of that decimal of that number so we are able to use this strategy let's bring this zero down and continue the problem so now we have 120 and we repeat so we go back to divide we have 120 divided by 15. how many whole groups of 15 in 120 well eight and that hits 120 exactly now we Multiply eight times fifteen is 120 subtract 120 minus 120 is zero so now we have that clean cut zero and we are done with this problem we have our final answer three and one hundred eight thousandths so there's how we divide decimals by whole numbers let's move on to dividing whole numbers by decimals here are our examples of dividing whole numbers by decimals let's jump into number one where we have 76 divided by eight tenths the first thing that we need to do is set this problem up that way we can go through the division process 76 is the dividend the number we are dividing it goes under the division bar eight tenths is the divisor the number we are dividing by it goes on the outside of the division bar now whenever we have a division problem that involves decimals we always need to check is the divisor a whole number our divisor for number one is eight tenths eight tenths is not a whole number that means we need to make it a whole number let's move the decimal once to the right to make that a whole eight now technically speaking we need to multiply the divisor by a power of 10 in order to make it a whole number for example number one we multiplied eight tenths by ten that shifted the digits one place to the left therefore giving us a whole eight but we made that process a little simpler to Think Through by just thinking of this as moving the decimal to make the divisor whole now whatever we do to the outside the divisor we must do to the inside the dividend so if we multiplied the outside by 10 we need to multiply the inside by 10 as well to keep this problem balanced so let's move the decimal once to the right on the inside now 76 is a whole number so the decimal comes after 76 and any other whole number let's move it once to the right fill this with a zero and we multiplied our dividend by 10 as well now that we have our whole divisor let's rewrite this equivalent problem to the side so we have 760 divided by 8. now our divisor is whole so we can go through the division process so divide multiply subtract bring down repeat let's start with divide so we have 7 divided by eight how many whole groups of eight in seven well we can't do that so we need to use the six and take a look at 76. 76 divided by eight how many whole groups of eight in seventy six nine that gets us to 72 and that 9 needs to go above the six not above the seven because we used 76 there now we multiply nine times eight seventy-two subtract 76 minus 72 gives us four then we bring down and then repeat so we go back to divide now we have 40 divided by 8. how many whole groups of eight and forty well five that gets us to 40 exactly multiply five times eight forty subtract 40 minus forty is zero we went all the way over to the furthest place to the right we have a clean cut zero at the end here so we are done our final answer 95. now for number one we have a whole number answer we went all the way over to the furthest place to the right in our dividend as far as bringing digits down and we have a clean cut zero at the end so we do not have a decimal part of our answer again we have a whole number answer in number two we will see what happens when we do have a decimal part of our answer let's move on to number two where we have 22 divided by sixteen hundredths let's set this problem up so we have 22 that's our dividend the number we are dividing and then sixteen hundredths is our divisor the number we are dividing by is the divisor a whole number sixteen hundredths is not a whole number so let's make it a whole number by moving this decimal twice to the right and that's going to be a whole 16 now now technically we shifted the digits of Sixteen hundredths two places to the left to make that a whole 16. the power of 10 that we multiplied by was one hundred now since we multiplied the divisor by 100 we need to multiply the dividend by 100. let's move that decimal twice so the decimal comes after 22. once twice fill those gaps with zeros and we have our equivalent problem that we can rewrite and solve so we have two thousand two hundred for our dividend divided by 16. so now our divisor is whole and we can go through our process start with divide so we have 2 divided by 16. how many whole groups of 16 and 2 well we can't do that so we need to use 22 22 divided by 16. how many whole groups of 16 and 22 one that one needs to go above the 22 not that first two since we used both of those digits and took a look at 22. now we multiply 1 times 16 is 16. subtract 22 minus 16. let's borrow it's a one there and we have 12 minus 6 which is six and then one minus one is zero now we can bring down this zero and we have 60. so we need to repeat and we go back to divide 60 divided by 16. how many whole groups of 16 in 60 well 16 times 3 is 48 16 times 4 is 64. four is too many it's going to be three multiply three times sixteen forty eight now we subtract so sixty minus 48 0 minus eight well we need to borrow here 10 minus eight is two and then five minus four is one so sixty minus 48 equals twelve let's bring down that next zero now we repeat so we go back to divide we have 120 divided by 16. how many whole groups of 16 in 120 now you may not know how many whole groups of 16 are in 120 using mental math so we can estimate and check in order to find out so I'm going to come to the side and use 16 times 10 as our reference point so our starting point 16 times 10 is 160. that's kind of close to 120 so we can adjust based on that let's try 16 times 8 and see how close to 120 we get 16 times 8. so 8 times 6 48 8 times 1 is 8 plus 4 is 12. 128 so 8 groups of 16 that's too many let's try seven sixteen times seven times six forty-two seven times one seven plus four is eleven one hundred twelve so it's going to be seven groups of 16. let's put our 7 up here multiply 7 times 16 112 subtract 120 minus one hundred twelve let's start with zero minus two we need to borrow so that's 10 minus 2 which is 8 and then we have 1 minus 1 is 0 and then another one minus one which is zero so we end up with eight now we went all the way over to the furthest place to the right within our dividend so we do not have anything else to bring down but we do not have a clean cut zero at the end we have an eight we do not want to write 137 remainder eight we are working with decimals so we want everything within our problem to be in decimal form including our answer so we need to continue this problem until we do get a clean cut zero so what we can do we can include the decimal in our dividend and then bring it straight up into our answer now we need something to bring down in order to continue this problem so what we can do we can use placeholder zeros to bring down remember zeros to the right of a decimal or decimal digits do not change the value of that number so we are able to use this strategy in order to continue the problem let's bring this zero down and continue the problem now we have 80 and we can repeat so we go back to divide 80 divided by 16. how many whole groups of 16 in 80 well 16 times 5 hits 80 exactly so it's going to be 5. 5 times 16 is 80. 80 minus 80. is zero so we went all the way over to the right now we have that clean cut zero so we are done our final answer 137 and 5 10. so there's how we divide whole numbers by decimals let's move on to dividing decimals by decimals here are our examples of dividing decimals by decimals let's jump into number one where we have 2 and 66 hundredths divided by seven tenths the first thing that we need to do is set this problem up that way we can go through the division process 2 and 66 hundredths is the dividend the number we are dividing it goes under the division bar 7 10 is the divisor the number we are dividing by it goes on the outside of the division bar now whenever we have a division problem that involves decimals we always need to check is the divisor a whole number well seven tenths is our divisor that's not a whole number so we need to make it a whole number we can do this by moving the decimal once to the right that will give us a whole seven now technically we multiply our divisor by a power of 10. in the case of number one that power of 10 was 10 so we multiplied 7 10 by 10. this shifts the digits of our divisor to the left and gives us a whole number we made this process simpler to Think Through by just thinking of this as moving the decimal to make the divisor whole now whatever we do to the outside the divisor we must do to the inside the dividend in order to keep this problem balanced and equivalent so we need to multiply the dividend by 10 as well let's move this decimal once to the right now we can rewrite our new equivalent problem with the whole divisor so we have 26 and 6 10. for our dividend and then 7 for our divisor so is our divisor now a whole number yes so we can bring our decimal straight up into our answer and now go through the division process so divide multiply subtract bring down repeat let's start with divide so we have 2 divided by 7. how many whole groups of seven in two well we can't do that so we need to use the six and take a look at 26 we have 26 divided by 7. how many whole groups of 7 in 26 well 3 that gets us to 21. let's put the three above the 6 in 26 not above the two it needs to go above the six since we did 26 divided by 7. now we multiply three times seven is twenty one subtract 26 minus 21 gives us 5. bring down now we have 56 and we repeat so we go back to divide we have 56 divided by 7. how many whole groups of 7 in 56 well eight that hits 56 exactly multiply 8 times 7. 56 subtract 56 minus 56 is zero we went all the way over to the right within our dividend as far as bringing digits down and we have a clean cut zero at the end so we are done our final answer 3 and 8 10. let's move on to number two where we have 88 and 4 10 divided by 34 hundredths let's set this problem up we have 88 and four tenths divided by 34 hundredths is the divisor a whole number no 34 hundredths is not a whole number so let's make it a whole number let's move the decimal once and then twice so now we have a whole 34. now technically we multiplied that divisor by 100 that was the power of 10 that we multiplied the divisor by so those digits shifted two places to the left in order to give us a whole number now whatever we do to the outside the divisor we must do to the inside the dividend so let's multiply 88 and 4 10 by 100 as well once twice to the right we can fill this Gap with a zero now we can rewrite our equivalent problem with the whole divisor so we have eight thousand eight hundred forty for our dividend and then 34 for our divisor now we're ready to go through the division process let's start with divide so we have 8 divided by 34. how many whole groups of 34 in eight well we can't do that so we need to take a look at the next date as well and use 88 so we have 88 divided by 34. how many whole groups of 34 in 88 well 2 that gets us to 68 so put the 2 Above This 8 not the other eight because again we used the 88 so the two needs to go above that 8 and then we multiply 2 times 34 68 subtract 88 minus 68 well 8 minus 8 is 0 and then 8 minus 6 is 2. so we get 20. bring down and we have 204 now we repeat so we go back to divide we have 204 divided by 34. how many whole groups of 34 in 204 now for this we are going to estimate and check in order to figure out how many whole groups of 34 are in 204 so let's come to the side here and I'm going to use 34 times 10 as a reference point so a starting point something to go off of 34 times 10 is 340. now 204 is quite a bit lower than 340. so if we know 34 times 10 equals 340 we can base our estimate off of that so for example let's try 34 times 7 and see how close to 204 we get so 34 times 7. 4 times 7 28 7 times 3 is 21 plus 2 23. so 238 so 7 was too many so let's scale that back and try 34 times 6. 34 times 6. 6 times 4 24 6 times 3 is 18 plus 2 is 20. so we get 204 exactly so it's going to be six now we multiply 6 times 34 204 subtract 204 minus 204 is zero now that 0 does not mean we are done we need to go all the way over within our dividend and bring down all the digits we still have this zero to bring down so now we have 0 divided by 34. how many whole groups of 34 in zero well zero multiply 0 times 34 0 subtract 0 minus zero is zero now we went all the way over to the furthest place to the right within our dividend we have a clean cut zero so we are done 260 is our final answer for number two so there's how we divide decimals by decimals let's move on to dividing by mixed decimals here are our examples of dividing by mixed decimals let's jump into number one where we have 3 and 22 hundredths divided by one and four tenths now the first thing that we need to do we need to set this problem up that way we can go through the division process 3 and 22 hundredths is the dividend the number we are dividing it goes under the division bar one and four tenths is the divisor the number we are dividing by it goes on the outside of the division bar now we have our division problem set up but before we go through the division process we have a division problem that involves decimals so we always need to check is the divisor a whole number 1 and 4 10 is not a whole number that means we need to make it a whole number we do this by multiplying the divisor by a power of 10. this will shift the digits to the left and make the divisor whole now we can make that very simple and just think of this as moving the decimal to make the divisor whole for example let's move this decimal one place to the right so it goes after the four and we have a whole 14. now whatever we do to the outside the divisor we must do to the inside the dividend so let's move this decimal once to the right as well now again technically we multiplied the divisor and dividend by a power of 10 to shift the digits to the left and make the divisor whole for example we multiplied the divisor by 10 for number one in order to make it whole that shifted the digits one place to the left and again gave us that whole divisor we then needed to multiply the dividend by 10 as well we made this process simpler to Think Through by just thinking of this as moving the decimal to make the divisor whole whatever we do to the divisor we must do to the dividend making the divisor whole places the decimal for us in our answer and since our divisor is now whole we can go through our division process the same process we use with whole numbers so divide multiply subtract bring down repeat now we need to rewrite our new equivalent problem with the whole divisor so our dividend is 32 and two tenths divided by 14. now as far as our new equivalent problem is the divisor a whole number yes so we can bring the decimal straight up into our answer now let's go through the division process starting with divide so we have 3 divided by 14. how many whole groups of 14 in 3 well we can't do that so we need to use the 2 and look at 32. how many whole groups of 14 in 32 well 2 that gets us to 28 so the 2 needs to go above the 2 and 32 not the 3 since we used both the 3 and the two now multiply 2 times 14 28. subtract 2 minus eight well we need to borrow so we have 12 minus 8 which is 4 and then 2 minus two is zero so 32 minus 28 equals four then we bring down that gives us 42 and we repeat so we go back to divide we have 42 divided by 14. how many whole groups of 14 in 42 well 3. that hits 42 exactly multiply 3 times 14 2 subtract 42 minus 42 is 0. we went all the way over to the right within our dividend as far as bringing digits down and we have a clean cut 0 at the end so we are done our final answer 2 and 3 10. let's move on to number two where we have 46 and 5 10 divided by 6 and 2 tenths let's set this problem up 46 and five tenths is the dividend the number we are dividing six and two tenths is the divisor the number we are dividing by now that we are set up we need to check is the divisor a whole number six and two tenths is not a whole number so let's make it a whole number let's move the decimal once to the right so now we have a whole 62. technically we multiplied our divisor by ten that was the power of 10 we multiplied the divisor by now whatever we do to the outside the divisor we must do to the inside the dividend so let's move this decimal once to the right as well and again technically we are multiplying our divisor and dividend by 10. now we have a whole divisor so we can rewrite our equivalent problem we have 465 divided by 62. now that we have our Rewritten equivalent problem with a whole divisor we can go through the division process starting with divide so we have 4 divided by 62. how many whole groups of 62 in four well we can't do that so we need to use the 6 and take a look at 46. how many whole groups of 62 in 46 well we can't do that either so we need to use the 5 and take a look at 465. how many whole groups of 62 in 465 we're going to need to estimate and check in order to figure this out because I don't know how many whole groups of 62 are in 465. so let's come to the side and again estimate and check I'll use 62 times 10 as a reference a starting point we know 62 times 10 is 620. that gives us something to go off of we can base our first estimate off of 620 and go from there 465 is less than 620 but it's kind of close so let's back up from 10 and try 62 times 8 and see how close we get so let's multiply 62 times 8 and again see how close we get we are estimating and checking eight times two sixteen eight times six forty eight plus one 49. so we get 496 which is too much so we need to back it up let's try 7. 62 times seven seven times two fourteen seven times six forty-two plus one 43. so 434 it's going to be seven whole groups of 62. so put the 7 above the 5 since we used 465. now multiply 7 times 62 400 34. subtract 5 minus 4 is 1 6 minus 3 is 3 4 minus four is zero so we get 31. so 465 minus 434 equals 31. now we are at the bring down step but there's nothing else to bring down and we don't want to write 7 remainder 31. we are working with decimals so we want to keep everything in decimal form even the answer so we need to continue this problem so what we can do we can place the decimal in our dividend a decimal comes after a whole number so after 465 then we can write a zero in the tenths place now we're able to bring that zero down and continue the problem that zero to the right of a decimal does not change the value of the problem we still have 465 live so we are able to do this once we place the decimal and write the zero we can bring the decimal straight up into the answer and bring the zero down we have 310 and we repeat so we go back to divide 310 divided by 62. how many whole groups of 62 in 310 well 310 is exactly half of 620 so it's going to be five but let's come to the bottom and make sure let's do 62 times five five times two is ten five times six is thirty plus one is Thirty-One so five whole groups of 62 hits 310 exactly so let's put our 5 up here and we can extend this division bar multiply 5 times 62 310 subtract we get that clean cut zero we went all the way over within our dividend and we have a clean cut zero at the end so we are done seven and five tenths is our final answer so there you have it there's a complete guide to dividing decimals I hope that helped thanks so much for watching until next time peace