How to Divide a Whole Number by a Decimal | Math with Mr. J

[Music] Welcome to Math with Mr. J. In this video, I'm going to cover how to divide a whole number by a decimal. We'll go through two example problems together and then I'll give you two practice problems that you can try on your own. Let's jump into number one where we have 76 / 810. 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. 8/10 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. Our divisor for number one is 8/10. 8/10 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 8/10 by 10. 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 / 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 / 8. 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 / 8. How many whole groups of eight in 76? 9. 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 9 * 8 72 subtract 76 - 72 gives us four. Then we bring down and then repeat. So we go back to divide. Now we have 40 / 8. How many whole groups of 8 and 40? Well, five. That gets us to 40 exactly. multiply 5 * 8 40 subtract 40 - 40 is zero. We went all the way over to the furthest place to the right. We have a cleancut 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 cleancut 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 / 16 hundreds. Let's set this problem up. So we have 22 that's our dividend the number we are dividing and then 16 hundreds is our divisor the number we are dividing by is the divisor a whole number 16 hundreds 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 16 hundreds two places to the left to make that a whole 16. The power of 10 that we multiplied by was 100. 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 2,200 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 / 16. How many whole groups of 16 and two? Well, we can't do that. So, we need to use 22. 22 / 16. How many whole groups of 16 in 22? 1. 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 * 16 is 16. Subtract 22 - 16. Let's borrow. It's a one there. and we have 12 - 6 which is 6 and then 1 - 1 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 / 16. How many whole groups of 16 in 60? Well 16 * 3 is 48. 16 * 4 is 64. 4 is too many. It's going to be three. multiply 3 * 16 48. Now we subtract. So 60 minus 48 0 - 8 well we need to borrow here. 10 - 8 is 2. And then 5 - 4 is 1. So 60 - 48 = 12. 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 * 10 as our reference point. So our starting point 16 * 10 is 160. That's kind of close to 120. So we can adjust based on that. Let's try 16 * 8 and see how close to 120 we get. 16 * 8. So 8 * 6 48. 8 * 1 is 8 + 4 is 12. 128. So, eight groups of 16. That's too many. Let's try 7. 16 * 7. 7 * 6 42. 7 * 1 7 + 4 is 11. 112. So, it's going to be seven groups of 16. Let's put our 7 up here. Multiply 7 * 16 112 subtract 120 minus 112. Let's start with 0 - 2. We need to borrow. So that's 10 - 2, which is 8. And then we have 1 - 1 is 0. And then another 1 - 1, which is zero. So we end up with 8. 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 8. We do not want to write 137 remainder 8. 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 / 16. How many whole groups of 16 in 80? Well, 16 * 5 hits 80 exactly, so it's going to be 5. 5 * 16 is 80. 80 - 80 is 0. 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 510. So, there's how we divide whole numbers by decimals. Let's move on to a couple of practice problems that you can try on your own. Here are your practice problems. I'll give you four minutes and then we will go over the answers. Go ahead and start. [Music] [Music] [Music] [Music] [Music] [Music] Okay, so that was four minutes. Let's go over the answers. Here are our answers. For number one, we have 9 / 410. That equals 22 and 510th. And then for number two, 14 / 3500s equals 40. So there you have it. There's how to divide a whole number by a decimal. I hope that helped. Thanks so much for watching. Until next time, peace.