Division: dividing by a single whole number

[One speaker] 

[Any necessary descriptions.]

Narrator: In this video we’re going to discuss the algorithm, or the pattern that we use to do division. Around the world different people use different algorithms to do division. If you use a different pattern that you’re comfortable with, go ahead and use that. Let’s start with the number three hundred and sixty-four divided by seven. So we want to divide three hundred and sixty-four into seven equals pieces. We start by creating a box. This is just used to help us organize our problem. Under the box we put three hundred and sixty-four, on the outside of the box we put the divisor, seven. In this case we start with the first number on the left, a three. We have to ask ourselves, does seven go into three? Or in other words, how many sevens make up a three? And the answer is zero. Now, we can put the zero here or we can just leave it off, usually that’s the case. Since seven does not go into three we look at the next number over. Now we’re looking at the whole number, thirty-six. How many times does seven go into thirty-six? Or what times seven is close to thirty-six? Well, seven times five is thirty-five, and that’s close to thirty-six, and it’s still less than thirty-six. So let’s put a five here in the tens column. Seven times five is thirty-five, multiply the two together, and now subtract. Six minus five is one, three minus three is zero, since it’s a zero we can just leave it blank. Next, we carry down the number in the next column to the right, which is four. Now we have fourteen. So, our new number we are looking at is fourteen. How many times does seven go into fourteen? The answer is two, because seven times two is fourteen. We put a two here, and now we multiply again. Two times seven is fourteen, subtract, equals zero. Because we have zero, we know that we’re done, and our answer is fifty-two. So, three hundred sixty-four divided by seven is fifty-two. So let’s exam for a minute just why this works. So, three hundred sixty-four divided by seven. So, in reality, when we’re talking about this column right here, we’re talking about the tens column, this is the tens column. When we multiply a five times seven, this is actually fifty because it’s in the tens column, this represents fifty, and fifty times seven is the same as three hundred and fifty. So now, when we’re subtracting we’re actually subtracting three hundred and sixty-four minus three hundred and fifty, because fives tens times seven equals three hundred and fifty, is the closest that we can get to three hundred and sixty-four as far as the tens place is concerned. If we instead tried a six here, in the tens column, well this would be sixty times seven, and sixty times seven is four hundred and twenty. Now this is too big because four hundred and twenty is bigger than three hundred and sixty-four. It doesn’t work because we are trying to find the closest number that is less than the number that we started with. So let’s go back to five. Five times seven, or fifty times seven, is three hundred and fifty. Now when we subtract we already know that fifty goes into three hundred and sixty-four. So now we want to know how much is left over. So that’s why we subtract. Notice how we’ve come to the exact same point that we came to over here. In the first example I told you to just bring down the four, this new example is doing the exact same thing, I’m just showing you why you can bring down the four because under the four is really a zero. So when we subtract, we can subtract and the four minus zero is four. So it’s the same just bringing down the four, and then thirty-six minus thirty-five is one. The fourteen means there’s still fourteen left over that still needs to be divided by seven. So now fourteen divided by seven is two, because two times seven is fourteen, and because two times seven is exactly fourteen, we don’t have anything left over, so we don’t have any other remainders, and we don’t have to worry about numbers after the decimal point. Let’s look at another example. We will divide nine hundred eighty-four by eight. Nine hundred eighty-four divided by, that’s what this little sign means, eight. Now, we start with the column farthest to the left, so this hundreds column. How many times does eight go into nine? Well, one time. One time eight is eight. Nine minus eight is one, so we have one left over, bring down the next number to the right. So now let’s consider eighteen. How many times does eight go into eighteen? Well, eight times two is sixteen, sixteen is less than eighteen, but very close to it, so let’s do two. Two times eight is sixteen, subtract, and we’re left with two. Now, bring down the next number to the right, we have twenty-four. Eight times three is twenty-four. So we have an exact number there at the end again. Three times eight is twenty-four, when we subtract it’s zero. So it’s zero leftover. So our answer to nine hundred eighty-four divided by eight is one hundred twenty-three.

[end of video.]