[Music] welcome to math with Mr J [Music] in this video I'm going to cover how to divide a decimal by a decimal so let's jump into our two examples here and for number one we have 5 and 76 hundredths divided by three tenths so let's set our problem up 5 and 76 hundredths is our dividend so it goes underneath the division bar here it's the number that we are splitting or dividing up now three tenths is our divisor it's the outside number so now that we're set up we need to ask ourselves a very important question before we start this problem is the divisor a whole number and in this case that three-tenths there that is not a whole number we need to have a whole number on the outside there that divisor in order to go through our division process so we can do this by multiplying that divisor by a power of 10. and therefore creating a whole number divisor so we can do this by moving the decimal to the right once that will give us a whole 3 Right Moving the decimal to the right once will push the digits to the correct Place it'll push that 3 over to the ones place so moving the decimal once to the right where you can think of it as sliding the 3 over to the ones place we multiplied that outside number by 10. so if you do something to the outside number that divisor you have to do the same thing to the inside remember whatever you do to the outside you have to do to the inside so we moved the decimal once to the right and therefore shifted each digit one spot to the left let's do the same thing to the inside the dividend now we're ready to go as far as setting up our problem with a whole divisor so we have those arrows underneath there so let's rewrite our problem so it's a little more neat so we have three as our divisor and for our dividend we have 57 and six tenths so now is our divisor whole yes we can start our problem so once your divisor is whole you bring your decimal straight up and go through your division process so divide multiply subtract bring down and repeat so 5 divided by 3 how many whole groups of three out of five well one one times three is three subtract we get 2 bring down the 7. 27 divided by 3 is 9. 9 times 3 27 subtract we get zero bring down this 6 here and we end with 6 divided by three which is two two times three is six subtract and we get a clean cut zero here and a final answer of nineteen and two tenths so let's do another example here in order to get this down a little better and number two is going to be a little different and you'll see why here in a second so our dividend 86 and 4 10 is the number being divided or split up and that goes underneath the division bar so 86 and 4 10 divided by 12 hundredths so 12 hundredths is our divisor it goes on the outside now let's ask ourselves the important question is the divisor a whole number no so we need to make it a whole number in order to go through the process so let's multiply by a power of 10. let's multiply by 10 and now the decimal will be between the one and the two is that a whole number no so we need to multiply by 10 again so 10 times 10 we need to multiply that outside number by 100 in order to push the digits to the correct place values in order to make it a whole number so we need to move the decimal twice or multiply that 86 and 4 10 by 100 as well remember whatever you do to the outside you do to the inside so once twice and we can fill that with a placeholder zero there and our decimal goes at the end so now we actually have a whole dividend so our new problem is going to be 12 and on the inside our dividend is eight thousand six hundred forty and that decimal is at the end so we don't really need it when it comes to whole numbers but we can put it there in case we need to extend with zeros for remainder purposes so we'll see if we'll need that decimal as we go through this problem so let's go through our steps so 8 divided by 12 well we can't pull any whole groups of 12 out of eight so we need to go to 86. so how many whole groups of 12 out of 86 well 7 times 12 is 84 that's as close as we are going to get so 7 7 times 12 is 84 subtract we get 2 bring down the four so 24 divided by 12 how many whole groups of 12 out of 24 well 2 times 12 is 24 subtract we get 0. now do not stop here we did not go all the way over to the ones place here so our answer is not 72. we need to keep going because we still have numbers to bring down here so let's bring our zero down and we have 0 divided by 12. so how many whole groups of 12 out of zero well zero 0 times 12 is 0. subtract and we get zero so remember our decimals at the end there so it's just a whole number and our final answer is going to be 720. so there you have it there's how you divide a decimal by a decimal remember is the divisor a whole number if not we need to multiply it by a power of 10 in order to make it a whole number whatever you do to the outside you have to do to the inside so whatever you do to the divisor you have to do to the dividend then you can rewrite your problem go through the division process and that will bring you to the correct answer I hope that helped thanks so much for watching until next time peace foreign