Definition<\/h3>\r\n
In the quotative model of division<\/strong>, you are given a dividend<\/strong> (here it is 3906), and you are asked to split it into equal-sized groups, where the size of the group is given by the divisor<\/strong> (here it is 3).<\/p>\r\n\r\n<\/div>\r\n In our dots and boxes model, the dividend 3906 looks like this:<\/p>\r\n and three dots looks like this: So we are really asking:<\/p>\r\n \u201cHow many groups of There is one group of 3 at the thousands level, and three at the hundreds level, none at the tens level, and two at the ones level.<\/p>\r\n Notice what we have in the picture:<\/p>\r\n \u2022\u00a0 One group of 3 in the thousands box.<\/p>\r\n \u2022\u00a0 Three groups of 3 in the hundreds box.<\/p>\r\n \u2022\u00a0 Zero groups of 3 in the tens box.<\/p>\r\n \u2022\u00a0 Two groups of 3 in the ones box.<\/p>\r\n This shows that 3 goes into 3906 one thousand, three hundreds and two ones times. That is,<\/p>\r\n\\[\u00a03906 \\div 3 = 1302. \\]\r\n\r\n<\/div>\r\n Let\u2019s try a harder one! Consider 402 \u00f7 3. Here\u2019s the picture:<\/p>\r\n We are still looking for groups of three dots: There is certainly one group at the 100's level.<\/p>\r\n and now it seems we are stuck\u00a0 there are no more groups of three!<\/p>\r\n\r\n What can we do now? Are we really stuck? Can you finish the division problem?<\/p>\r\n\r\n<\/div>\r\n \r\n Here are the details worked out for 402 \u00f7 3. But don\u2019t read this until you\u2019ve thought about it yourself!<\/p>\r\n Since each dot is worth ten dots in the box to the right we can write:<\/p>\r\n Now we can find more groups of three:<\/p>\r\n There is still a troublesome extra dot. Let\u2019s unexplode it too<\/p>\r\n This gives us more groups of three:<\/p>\r\n In the picture we have:<\/p>\r\n \u2022\u00a0 One group of 3 in the hundreds box.<\/p>\r\n \u2022\u00a0 Three groups of 3 in the tens box.<\/p>\r\n \u2022\u00a0 Four groups of 3 in the ones box.<\/p>\r\n Finally we have the answer!<\/p>\r\n \\[ 402 \\div 3 = 134.\\]<\/p>\r\n\r\n<\/div>\r\n \r\n Solve each of these exercises using the dots and boxes method:<\/p>\r\n 62124 \u00f7 3 \u00a0 \u00a0 \u00a0 \u00a0 61230 \u00f7 5<\/p>\r\n\r\n<\/div>\r\n \r\n Let\u2019s turn up the difficulty a notch. Consider 156 \u00f7 12. Here we are looking for groups of 12 in this picture:<\/p>\r\n What does 12 look like? It can be twelve dots in a single box:<\/p>\r\n But most often we would write 12 this way, as a ten and 2 ones:<\/p>\r\n We certainly see some of these in the picture.\u00a0 There is certainly one at the tens level:<\/p>\r\n Note:<\/b> With an unexplosion this would be twelve dots in the tens box, so we mark one group of 12 above the tens box.<\/p>\r\n We also see three groups of twelve ones:<\/p>\r\n So in the picture we have:<\/p>\r\n \u2022\u00a0 One group of 12 dots in the tens box.<\/p>\r\n \u2022\u00a0 Three groups of 12 dots in the ones box.<\/p>\r\n That means<\/p>\r\n 156 \u00f7 12 = 13.<\/p>\r\n\r\n<\/div>\r\n \r\n Use the dots and boxes model to compute each of the following:<\/p>\r\n 13453 \u00f7 11<\/p>\r\n 4853 \u00f7 23<\/p>\r\n 214506 \u00f7 102<\/p>\r\n\r\n<\/div>\r\n \r\n Remember that base five numbers are in a 1 \u2190 5 dots-and-boxes system. What are the place values in the 1\u00a0\u2190 5 system? Fill in the\u00a0blanks:<\/p>\r\n 2130 \u00f7 10<\/p>\r\n 41300 \u00f7 100<\/p>\r\n\r\n We used dots and boxes to show that 402 \u00f7 3 = 134.<\/p>\r\n In elementary school, you might have learned to solve this division problem by using a diagram like the following:<\/p>\r\n At first glance this seems very mysterious, but it is really no different from the dots and boxes method. Here is what the table means.<\/p>\r\n To compute 402 \u00f7 3, we first make a big estimation as to how many groups of 3 there are in 402. Let\u2019s guess that there are 100 groups of three.<\/p>\r\n How much is left over after taking away 100 groups of 3?\u00a0 We subtract to find that there is 102 left.<\/p>\r\n How many groups of 3 are in 102? Let\u2019s try 30:<\/p>\r\n How many are left? There are 12 left and there are four groups of 3 in 12.<\/p>\r\n That accounts for entire number 402. And where do we find the final answer? Just add the total count of groups of three that we tallied:<\/p>\r\n 402 \u00f7 3 = 100 + 30 + 4 = 134.<\/p>\r\n\r\n We saw that 402 is evenly divisible by 3:\u00a0 402 \u00f7 3 = 134.\u00a0 This means that 403, one more, shouldn\u2019t be divisible by three. It should be one dot too big.<\/p>\r\n\r\n Yes we do! We have one dot left at the end that can\u2019t be divided.\u00a0 This is how it looks in the standard algorithm.<\/p>\r\n In school, we say that we have a remainder<\/i> of one and sometimes write:<\/p>\r\n \\[403 \\div 3 = 134\\\u00a0 \\textup{R}1.\\]<\/p>\r\n But what does that really mean?\u00a0 It means that we have 134 groups of three with one dot left over. So<\/p>\r\n \\[ 402 = 134\\cdot 3 + 1.\\]<\/p>\r\n\r\n<\/div>\r\n \r\n Let\u2019s try another one: 263 \u00f7 12. Here\u2019s what we have:<\/p>\r\n And we are looking for groups like this:<\/p>\r\n Here goes!<\/p>\r\n Unexploding won\u2019t help any further and we are indeed left with one remaining dot in the tens position and a dot in the ones position. We have 21 groups of twelve, and a remainder of eleven.<\/p>\r\n \\[263 = 21\\cdot 12 + 11.\\]<\/p>\r\n\r\n<\/div>\r\n \r\n 5210 \u00f7 4<\/p>\r\n 4857 \u00f7 23<\/p>\r\n 31533 \u00f7 101<\/p>\r\n\r\n Suppose you are asked to compute 3906 \u00f7 3. One way to interpret this question (there are others) is:<\/p>\n \u201cHow many groups of 3 fit into 3906?\u201d<\/p>\n In the quotative model of division<\/strong>, you are given a dividend<\/strong> (here it is 3906), and you are asked to split it into equal-sized groups, where the size of the group is given by the divisor<\/strong> (here it is 3).<\/p>\n<\/div>\n In our dots and boxes model, the dividend 3906 looks like this:<\/p>\n and three dots looks like this: So we are really asking:<\/p>\n \u201cHow many groups of There is one group of 3 at the thousands level, and three at the hundreds level, none at the tens level, and two at the ones level.<\/p>\n Notice what we have in the picture:<\/p>\n \u2022\u00a0 One group of 3 in the thousands box.<\/p>\n \u2022\u00a0 Three groups of 3 in the hundreds box.<\/p>\n \u2022\u00a0 Zero groups of 3 in the tens box.<\/p>\n \u2022\u00a0 Two groups of 3 in the ones box.<\/p>\n This shows that 3 goes into 3906 one thousand, three hundreds and two ones times. That is,<\/p>\n <\/span> <\/span> Let\u2019s try a harder one! Consider 402 \u00f7 3. Here\u2019s the picture:<\/p>\n We are still looking for groups of three dots: There is certainly one group at the 100’s level.<\/p>\n and now it seems we are stuck\u00a0 there are no more groups of three!<\/p>\n What can we do now? Are we really stuck? Can you finish the division problem?<\/p>\n<\/div>\n <\/p>\n Here are the details worked out for 402 \u00f7 3. But don\u2019t read this until you\u2019ve thought about it yourself!<\/p>\n Since each dot is worth ten dots in the box to the right we can write:<\/p>\n Now we can find more groups of three:<\/p>\n There is still a troublesome extra dot. Let\u2019s unexplode it too<\/p>\n This gives us more groups of three:<\/p>\n In the picture we have:<\/p>\n \u2022\u00a0 One group of 3 in the hundreds box.<\/p>\n \u2022\u00a0 Three groups of 3 in the tens box.<\/p>\n \u2022\u00a0 Four groups of 3 in the ones box.<\/p>\n Finally we have the answer!<\/p>\n \n <\/span> <\/span> <\/p>\n Solve each of these exercises using the dots and boxes method:<\/p>\n 62124 \u00f7 3 \u00a0 \u00a0 \u00a0 \u00a0 61230 \u00f7 5<\/p>\n<\/div>\n <\/p>\n Let\u2019s turn up the difficulty a notch. Consider 156 \u00f7 12. Here we are looking for groups of 12 in this picture:<\/p>\n What does 12 look like? It can be twelve dots in a single box:<\/p>\n But most often we would write 12 this way, as a ten and 2 ones:<\/p>\n We certainly see some of these in the picture.\u00a0 There is certainly one at the tens level:<\/p>\n Note:<\/b> With an unexplosion this would be twelve dots in the tens box, so we mark one group of 12 above the tens box.<\/p>\n We also see three groups of twelve ones:<\/p>\n So in the picture we have:<\/p>\n \u2022\u00a0 One group of 12 dots in the tens box.<\/p>\n \u2022\u00a0 Three groups of 12 dots in the ones box.<\/p>\n That means<\/p>\n 156 \u00f7 12 = 13.<\/p>\n<\/div>\n <\/p>\n Use the dots and boxes model to compute each of the following:<\/p>\n 13453 \u00f7 11<\/p>\n 4853 \u00f7 23<\/p>\n 214506 \u00f7 102<\/p>\n<\/div>\n <\/p>\n Remember that base five numbers are in a 1 \u2190 5 dots-and-boxes system. What are the place values in the 1\u00a0\u2190 5 system? Fill in the\u00a0blanks:<\/p>\n <\/p>\n 2130 \u00f7 10<\/p>\n 41300 \u00f7 100<\/p>\n We used dots and boxes to show that 402 \u00f7 3 = 134.<\/p>\n In elementary school, you might have learned to solve this division problem by using a diagram like the following:<\/p>\n At first glance this seems very mysterious, but it is really no different from the dots and boxes method. Here is what the table means.<\/p>\n To compute 402 \u00f7 3, we first make a big estimation as to how many groups of 3 there are in 402. Let\u2019s guess that there are 100 groups of three.<\/p>\n How much is left over after taking away 100 groups of 3?\u00a0 We subtract to find that there is 102 left.<\/p>\n How many groups of 3 are in 102? Let\u2019s try 30:<\/p>\n How many are left? There are 12 left and there are four groups of 3 in 12.<\/p>\n That accounts for entire number 402. And where do we find the final answer? Just add the total count of groups of three that we tallied:<\/p>\n 402 \u00f7 3 = 100 + 30 + 4 = 134.<\/p>\n <\/p>\n <\/p>\n We saw that 402 is evenly divisible by 3:\u00a0 402 \u00f7 3 = 134.\u00a0 This means that 403, one more, shouldn\u2019t be divisible by three. It should be one dot too big.<\/p>\n Do we see the extra dot if we compute 402 \u00f7 3 with dots and boxes?<\/p>\n Yes we do! We have one dot left at the end that can\u2019t be divided.\u00a0 This is how it looks in the standard algorithm.<\/p>\n In school, we say that we have a remainder<\/i> of one and sometimes write:<\/p>\n \n <\/span> <\/span> But what does that really mean?\u00a0 It means that we have 134 groups of three with one dot left over. So<\/p>\n \n <\/span> <\/span> <\/p>\n Let\u2019s try another one: 263 \u00f7 12. Here\u2019s what we have:<\/p>\n And we are looking for groups like this:<\/p>\n Here goes!<\/p>\n Unexploding won\u2019t help any further and we are indeed left with one remaining dot in the tens position and a dot in the ones position. We have 21 groups of twelve, and a remainder of eleven.<\/p>\n \n <\/span> <\/span> <\/p>\n 5210 \u00f7 4<\/p>\n 4857 \u00f7 23<\/p>\n 31533 \u00f7 101<\/p>\n <\/span> <\/span>![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide1-300x74.png\")
<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide2.png\")
<\/p>\r\n fit into the picture of 3906?\u201d<\/p>\r\n\r\nExample:\u00a03906 \u00f7 3<\/h3>\r\n
![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide3-300x153.png\")
<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide4-300x67.png\")
<\/p>\r\n<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide5-300x93.png\")
<\/p>\r\nThink \/ Pair \/ Share<\/h3>\r\n
Example:\u00a0402 \u00f7 3<\/h3>\r\n
![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide6-300x85.png\")
<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide7-300x83.png\")
<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide8-300x94.png\")
<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide9-300x84.png\")
<\/p>\r\nThink \/ Pair \/ Share<\/h3>\r\n
Example:\u00a0156 \u00f7 12<\/h3>\r\n
![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide10-300x75.png\")
<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide11.png\")
<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide12.png\")
<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide13-300x100.png\")
<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide14-300x104.png\")
<\/p>\r\nProblem 6<\/h3>\r\n
Problem 7<\/h3>\r\n
![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/base5blanks-300x85.png\"){kind=spacer}
<\/p>\r\n\r\n\r\n \t
Think \/ Pair \/ Share<\/h3>\r\n
\r\n \t
\r\n \t
The Standard Algorithm for Division<\/h1>\r\n
<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide15.png\")
<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide16-300x102.png\")
<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide17-300x135.png\")
<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide18-300x155.png\")
<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide19-300x250.png\")
<\/p>\r\nThink \/ Pair \/ Share<\/h3>\r\n
\r\n \t
<\/p>\r\n \r\n<\/p>\r\n \r\n<\/p>\r\n\r\n\r\n \t
Division with Remainders<\/h1>\r\n
Example:\u00a0403 \u00f7 3<\/h3>\r\nDo we see the extra dot if we compute 402 \u00f7 3 with dots and boxes?\r\n
![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide20-300x280.png\")
<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide23.png\")
<\/p>\r\nExample: 263 \u00f7 12<\/h3>\r\n
![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide21-300x68.png\")
<\/p>\r\n<\/p>\r\n![\"\"](\"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide22-300x125.png\")
<\/p>\r\nThink \/ Pair \/ Share<\/h3>\r\n
\r\n \t
\r\n \t
<\/p>\r\n\\[402 = 134\\cdot 3 + 1.\\]\r\n\r\n \t
Quotative Model of Division<\/h1>\n
Definition<\/h3>\n
![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide1-300x74.png\")
<\/p>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide2.png\")
<\/p>\n fit into the picture of 3906?\u201d<\/p>\nExample:\u00a03906 \u00f7 3<\/h3>\n
![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide3-300x153.png\")
<\/p>\n![\"\[ 3906 \div 3 = 1302. \]\"](\"https:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/ql-cache\/quicklatex.com-901dd8a27f88c525709621bc9eab4ba2_l3.png\" "\\"Rendered")
<\/p>\n<\/div>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide4-300x67.png\")
<\/p>\n<\/p>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide5-300x93.png\")
<\/p>\nThink \/ Pair \/ Share<\/h3>\n
Example:\u00a0402 \u00f7 3<\/h3>\n
![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide6-300x85.png\")
<\/p>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide7-300x83.png\")
<\/p>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide8-300x94.png\")
<\/p>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide9-300x84.png\")
<\/p>\n![\"\[ 402 \div 3 = 134.\]\"](\"https:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/ql-cache\/quicklatex.com-b91673b99d367f5c329158f1e86d979e_l3.png\" "\\"Rendered")
<\/p>\n<\/div>\nThink \/ Pair \/ Share<\/h3>\n
Example:\u00a0156 \u00f7 12<\/h3>\n
![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide10-300x75.png\")
<\/p>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide11.png\")
<\/p>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide12.png\")
<\/p>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide13-300x100.png\")
<\/p>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide14-300x104.png\")
<\/p>\nProblem 6<\/h3>\n
Problem 7<\/h3>\n
![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/base5blanks-300x85.png\"){kind=spacer}
<\/p>\n\n
![\"424_\text{five}\"](\"https:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/ql-cache\/quicklatex.com-8b98474aa3d723047dfbb03ad2f254bd_l3.png\" "\\"Rendered")
.<\/li>\n![\"11_\text{five}\"](\"https:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/ql-cache\/quicklatex.com-0f6a87da692446a53733b7bc67ac7beb_l3.png\" "\\"Rendered")
.<\/li>\n![\"424_\text{five} \div 11_\text{five}\"](\"https:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/ql-cache\/quicklatex.com-9d49f43031cad0e5f5aa2eead5f2d6d3_l3.png\" "\\"Rendered")
.<\/li>\n![\"424_\text{five} \div 11_\text{five} = 34_\text{five}\"](\"https:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/ql-cache\/quicklatex.com-f91f9c60269325271851c88164f8c514_l3.png\" "\\"Rendered")
in base ten, and check that it\u2019s correct.<\/li>\n![\"2021_\text{five} \div 12_\text{five}\"](\"https:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/ql-cache\/quicklatex.com-6dbbb6839ba2d0d30c44b5ceea6cab5a_l3.png\" "\\"Rendered")
.\u00a0Don\u2019t convert to base 10!<\/i><\/li>\n<\/ol>\n<\/div>\nThink \/ Pair \/ Share<\/h3>\n
\n
\n
The Standard Algorithm for Division<\/h1>\n
<\/p>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide15.png\")
<\/p>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide16-300x102.png\")
<\/p>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide17-300x135.png\")
<\/p>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide18-300x155.png\")
<\/p>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide19-300x250.png\")
<\/p>\nThink \/ Pair \/ Share<\/h3>\n
\n
<\/p>\n<\/p>\n<\/p>\n\n
Division with Remainders<\/h1>\n
Example:\u00a0403 \u00f7 3<\/h3>\n
![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide20-300x280.png\")
<\/p>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide23.png\")
<\/p>\n![\"\[403 \div 3 = 134\ \textup{R}1.\]\"](\"https:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/ql-cache\/quicklatex.com-7f407b845a8e3cb86f2a798aa230975d_l3.png\" "\\"Rendered")
<\/p>\n![\"\[ 402 = 134\cdot 3 + 1.\]\"](\"https:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/ql-cache\/quicklatex.com-cf9dee4244b7b66f5dcf9297d5da856b_l3.png\" "\\"Rendered")
<\/p>\n<\/div>\nExample: 263 \u00f7 12<\/h3>\n
![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide21-300x68.png\")
<\/p>\n<\/p>\n![\"\"](\"\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/uploads\/sites\/17\/2017\/10\/divide22-300x125.png\")
<\/p>\n![\"\[263 = 21\cdot 12 + 11.\]\"](\"https:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/ql-cache\/quicklatex.com-c66f86d2222f22dcb1b1df4a4d241327_l3.png\" "\\"Rendered")
<\/p>\n<\/div>\nThink \/ Pair \/ Share<\/h3>\n
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<\/p>\n![\"\[402 = 134\cdot 3 + 1.\]\"](\"https:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/wp-content\/ql-cache\/quicklatex.com-d7d1260310eeb07e35e01c5b6760eb45_l3.png\" "\\"Rendered")
<\/p>\n\n