[Division, 1960s]

[Music] Hello, Linda. I see Bob is having some trouble with division. He's not using what he knows about place value, I see. And he's not using his division and multiplication facts very well either. Even though he has worked the same problem several times, he keeps getting different answers. Bob, I think you need some brushing up on division. Let's start our brushing up right from the beginning with very simple ideas. Here's an easy example. 12 / 3. As you know, there are two ways of indicating division. But we'll use this way of showing it. Of course, you know what the answer is? Four. But what does 12 / 3= 4 really mean? We can illustrate one meaning this way. Here are 12 squares. Let's divide them into equal groups with three squares in each group. There are four groups. By dividing we found how many groups of three there are in 12. This time let's divide the squares so that there are three equal groups. Now there are four squares in each group. This time by dividing we found how many there are in each equal group. So you see you divide to find how many equal groups or how many in each equal group. Now let's review what the terms in division are called. The number to be divided is the dividend. The number you divide by is the divisor. And the answer is the quotient. The quotient tells us how many equal numbers or add ends the size of the divisor must be added together to equal the dividend. Now Bob, do you remember how to check division? In even division, the quotient times the divisor should equal the dividend. As you can see, division is just the opposite of multiplication. Now suppose a dividend can't be divided evenly by a divisor. Let's try 163 divided by 5. Let's remember place value, ones, tens, and hundreds. First of all, Bob, you have to remember that 163 is really one 100, six tens, and three 1's. Since you do not have enough 100s to make a group of five, you must think of the 100 as tens. And so you have 16 tens. Bob, do you see? Now, how many equal groups of five tens can we make from 16 10? You can't divide 16 evenly by five. Do you know what to do, Bob? All right, then, Linda. To remember that there are three groups of five 10 in 16 10. You have to think of the next number lower than 16 that can be divided by five. That number is 15. Had you forgotten that division fact? Well, Bob, there's an easy way to remember a division fact if you forget it. When you're trying to think 15 / 5 equals what? And you can't remember. Think of this. 15 equals what * 5? Your multiplication facts tell you that 3 * 5 = 15. Because you know this fact, you know that 15 / 5 = 3. So you see the multiplication facts will help you find the answers in division. Now go on with the example. Bob, notice that the three is in the 10 place. That's because it answers the question, in 16 10, how many equal groups of five tens are there? Three of them and one 10 left over. Go on, Bob. Now we bring down the three ones in this new dividend. 13 1's. How many groups of five ones can we find? And notice that Bob is putting the two in the ones place. 13 1's equal two groups of five ones with three ones left over. Do you remember what this three is called? That's right, the remainder. 163 / 5 = 32. Remainder 3. Now Bob to check this example of uneven division we multiply the divisor 5 by the quotient 32 then we add the remainder three to the product. Now you can see that multiplication is opposite division. In division, we change a number into groups of equal add-ins. In multiplication, we combine equal add- ends. Now, Bob, let's try an example with a two place divisor. 65 / 13. And let's remember place value. Now, let's divide into how many groups of 13 10 can six 10 be divided? None. So we think of the dividend as 65 1's. Now to divide 65 1's into groups of 13, Bob is thinking in 60s, how many groups of 10 1's will there be? Six, of course. But six is just a trial quotient. To see if six is the true quotient, Bob multiplies 13 by 6 in his head. He knows a quick way of doing this. He thinks of 13 as 1 10 + 3 1's. 6 * 1 10 = 6 10. 6 * 3 1's = 18 1's which equals 1 10 + 8 1's. Now Bob adds both products. 6 10 + 1 10 are 7 10 plus 8 1's equals 78. 6 * 13 = 78. But 78 is larger than the dividend 65. So 6 is not the true quotient. That's right. Try five. 5 * 13 = 65. Since 65 is our dividend, 5 is our true quotient. 5 13s or five groups of 13 1's equal 65 1's. Very good. Now, let's look at the problem that's been giving you trouble. 1,658 divided by 24. Here's what this problem is about. The school band is going to give a concert next month in the school auditorium which holds 1,658 people. Linda and Bob are on the ticket committee and they want to divide the 1,658 tickets to be sold equally among the 24 rooms of their school. How many tickets should each room get? Bob, can you work the problem now? Remember place value. Try out your trial quotients until you find the true quotient. You're forgetting place value. That's better. Be careful of your division facts. Very good. If you give 69 tickets to each of the 24 rooms to sell, you will have two tickets left over. You and Linda can sell those two extra tickets, can't you? Linda, do you want to check the answer? That's right. Multiply together the quotient 69 and the divisor 24. and add the remainder too. Yes, it checks. Very well done, Linda. Now Bob and Linda can get their work done. But what about you? Does your division need brushing up? Why not start now? [Music]