Brushing Up On Division

[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 4 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 diviser 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 / 5 let's remember place value ones T and hundreds first of all Bob you  have to remember that 163 is really 1 100 6 10 and 3 1's since you do not have enough 100s to  make a group of five you must think of the 100 as T and so you have 16 tens Bob do you see now  how many equal groups of five tens can we make from 16 tens you can't divide 16 evenly by five  do you know what to do Bob all right then Linda remember that there are three groups of  five 10 in 16 T 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 time * 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 tens how many equal groups  of five tens are there three of them and 11 10 left over go on Bob  now we bring down the three ones in this new dividend 13 ones how  many groups of five ones can we find and notice that Bob is  putting the two in the one's place 13 1es equal two groups of five 1es with three  ones left over do you remember what this three is called that's right the remainder  163 ID 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 addends in multiplication we combine equal addends now Bob let's  try an example with a two-place divide 65 / 13 and let's remember place value now let's  divide into how many groups of 13 T can 6 tens be divided none so we think of the dividend  as 65 1es now to divide 65 1es into groups of 13 Bob is thinking in 61's how many groups of  10 ones 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 110 + 3 1's 6 * 11 = 61 6 * 3 1's equal 18 1's which = 110 + 8 1's now Bob adds both products 61  + 1 10 are 7 10 + 8 1's = 78 6 * 13 equals 78 but 78 is larger than the dividend 65 so 6 is not  the true quotient that's right try five 5 * 13 equals 65 since 65 is our dividend five is our  true quotient 5 13s or five groups of 13 1es equal 65 1es very good now let's look at the  problem that's been giving you trouble 1,658 / 24 here is 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 cauti 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 then add the remainder to 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]