Coronet Dividing 2

each friend to have three is how many friends will get three pennies. They'll take a first they subtract one group or subset of three. Now they subtract another subset of three and another and now the last subset of three. So there are four subsets of three. The answer was found by subtraction. Another name for what we've done is division. We divided the set of 12 into four subsets of three. But a faster way of dividing is to remember and use our division facts. 12 members in one set separated into subsets of three. Four subsets. This is the division fact that shows this 12 / 3 = 4. Now let's find the answer to another question. If you've ever played the game of ring toss, you know each Jim, Fred, and Grace have 12 rings altogether. If they divide the set of 12 rings among themselves, how many does each player get? They'll have to divide the rings into one, two, three subsets. They're thinking how many rings will there be in each subset. This is one way to divide the set. A ring for Grace, one for Fred, one for Jim himself. Then a second ring for Grace, for Fred, for Jim, and so forth until the rings have been divided into three subsets or groups. But we can use an easier and faster way of dividing. We'll use our division facts. We started with 12 members in a set and separated the set into three subsets. These were equivalent. Four members in each. The division fact is 12 / 3 equals 4. So we've now seen that 12 / 3 could really be asking two questions. How many subsets of three in 12? The answer is four. How many in each of three equivalent subsets? The answer is again four. The answer to both questions is the same. 12 / 3 = 4. Let's check this division problem on the number line. We can ask how many threes in 12. Remember how we subtracted the subsets from 12? On the number line, we also start with 12. As in subtraction, we move to the left three spaces. Then three more spaces. Three more. And we see that there are four threes in 12. So 12 / 3 equal. We've checked our division fact on the number line. We can also check our division by doing multiplication on the number line. How many * 3 = 12. We see that 4 * 3 = 12. So we see that division is the opposite or the inverse of multiplication. 12 / 3 = 4 and 4 * 3 = 12. So for each division fact, there's a multiplication fact that goes with it. We also know from multiplication that multiplication facts come in pairs. The law of order helps us remember that if 4 * 3 = 12, then 3 * 4 = 12. If 3 * 4 = 12, then how many fours in 12? The answer is 3. 12 / 4 = 3. This is the division fact that goes with the multiplication fact. 3 * 4 = 12. So we see that we now have four number facts. They make up a number family. We know that in a multiplication fact, these are the factors and this the product. In a division fact, this is the product and these are the factors. There are many more division facts here is 6 / 2. Now what about this 4 / 1? We can ask how many ones in four. Let's use the number line for this problem. We'll start at four and move one space at a time to the left. 1 1 2 1's 3 1's 4 1's. We see that 4 / 1 equals 4. Let's divide 7 by 1. 7 1's in seven. We see that in division any number divided by one equals that number. So we can divide numbers by one. Can we divide a number by zero? Let's take 7 / 0. Remembering that division is the inverse of multiplication. Let's ask what number * 0 equ= 7. In multiplication, there is no number time 0 that equals 7. So there is no inverse. We cannot divide seven or any number by zero. Now let's use our number line to try to divide 7 by 0. We know that to divide we move spaces to the left. But to divide by zero would mean moving zero spaces to the left. But zero spaces are no spaces. If we cannot move any spaces, we cannot divide by zero. Now let's think about zero with our set of 12 rings. If we divide the set among three people, each person would get four rings. 12 / 3 equals 4. What if we had only three rings? Each of three persons would get just one ring. 3 / 3 equals 1. Suppose we had no rings, zero rings. Each of three persons would get zero rings. So 0 divided by 3 equals 0. In division 0 divided by any number is zero. We have seen that in division a problem like 12 / 3 could really be asking two questions. How many subsets of three in the set of 12? Or how many in each subset if we separate the set of 12 into three sets? If we how many in each subset, our answer tells us the number of subsets. Four. If we know how many equivalent subsets, the answer tells us how many in each subset, four. So, we can solve our division problems by knowing our division facts. Nancy and Jack can also use multiplication facts to help solve their division problems. They know that division is the inverse of multiplication. A problem like 12 / 3 asks what number* 3= 12. So when we know our division facts, when we remember that division is the opposite or inverse of multiplication and when we can check division on the number line, we will be using division to help solve our mathematics problems. [Music]