{"id":46,"date":"2023-01-10T18:10:10","date_gmt":"2023-01-10T23:10:10","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math023\/chapter\/dividing-larger-numbers-by-one-digit-divisors\/"},"modified":"2025-07-03T22:50:17","modified_gmt":"2025-07-04T02:50:17","slug":"dividing-larger-numbers-by-one-digit-divisors","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math023\/chapter\/dividing-larger-numbers-by-one-digit-divisors\/","title":{"raw":"Topic C: Dividing Larger Numbers by One-Digit Divisors","rendered":"Topic C: Dividing Larger Numbers by One-Digit Divisors"},"content":{"raw":"Several methods are used to divide larger numbers. This book will only teach one method. If you have learned a different method for dividing, ask your instructor to review it with you. You can use the practice exercises in this workbook using whichever method you prefer.\r\n<h1>One-Digit Divisors without Remainders<\/h1>\r\nDivision has four steps which are repeated until the dividend is completely divided. Work through the three examples which show these steps.\r\n<ol>\r\n \t<li>Divide.<\/li>\r\n \t<li>Multiply<\/li>\r\n \t<li>Subtract and compare the remainder to the divisor.<\/li>\r\n \t<li>Bring down the next digit in the dividend and repeat.<\/li>\r\n<\/ol>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example A<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n294 \u00f7 7 =\r\n\r\nRewrite as [latex]7\\enclose{longdiv}{294}[\/latex]\r\n\r\n<strong>Step 1: Divide.<\/strong>\r\n<ol type=\"a\">\r\n \t<li>Find a trial quotient using multiplication tables or division facts.<\/li>\r\n \t<li>Look at the dividend one digit at a time.\r\n<ol type=\"i\">\r\n \t<li>The first digit is a 2, which is really 2 hundreds.<\/li>\r\n \t<li>Will 7 go into 2? Can you divide 2 by 7? No.<\/li>\r\n \t<li>Look at the first 2 digits, 29, which is really 29 tens.<\/li>\r\n \t<li>Will 7 go into 29? Yes. 4 \u00d7 7 = 28.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>The first number in the quotient is 4. Place the 4 in the quotient directly above the 9 tens. The 4 is 4 tens in the quotient.<\/li>\r\n<\/ol>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}4\\hspace{0.8em}\\\\7 \\enclose{longdiv}{294}\\end{array}[\/latex]<\/p>\r\n<strong>Step 2: Multiply.<\/strong>\r\n<ol type=\"a\">\r\n \t<li>Multiply 4 \u00d7 7\u00a0 = 28.<\/li>\r\n \t<li>Write the 28 under the 29. Draw a line.<\/li>\r\n<\/ol>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}4\\hspace{0.8em}\\\\7 \\enclose{longdiv}{294}\\\\28\\hspace{0.8em}\\\\\\hline\\end{array}[\/latex]<\/p>\r\n<strong>Step 3: Subtract.<\/strong>\r\n<ol type=\"a\">\r\n \t<li>Subtract 29 \u2212 28 = 1 (ten).<\/li>\r\n \t<li>Check 1 &lt; 7.<\/li>\r\n<\/ol>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}4\\hspace{0.8em}\\\\7 \\enclose{longdiv}{294}\\\\-28\\hspace{0.8em}\\\\\\hline1\\hspace{0.8em}\\end{array}[\/latex]<\/p>\r\n<strong>Step 4: Bring down the next number in the dividend.<\/strong>\r\n<ol type=\"a\">\r\n \t<li>Bring down the next number in the dividend (4), and put it beside the result of the subtraction you just completed (1)<strong>.\r\n<\/strong><\/li>\r\n \t<li>Together, they make 14. This 14 is the number that you must now divide.<\/li>\r\n<\/ol>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}4\\hspace{0.8em}\\\\7 \\enclose{longdiv}{294}\\\\-28\\hspace{0.8em}\\\\\\hline14\\end{array}[\/latex]<\/p>\r\n<strong>Repeat Step 1: Divide.<\/strong>\r\n<ol type=\"a\">\r\n \t<li>Divide 14 \u00f7 7 = 2<\/li>\r\n \t<li>Put the 2 in the quotient right after the 4 in the ones place.<\/li>\r\n<\/ol>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}42\\\\7 \\enclose{longdiv}{294}\\\\-28\\hspace{0.8em}\\\\\\hline14\\end{array}[\/latex]<\/p>\r\n<strong>Repeat Step 2: Multiply.<\/strong>\r\n<ol type=\"a\">\r\n \t<li>Multiply 2 \u00d7 7 = 14.<\/li>\r\n \t<li>Write the 14 under the 14. Draw a line.<\/li>\r\n<\/ol>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}42\\\\7 \\enclose{longdiv}{294}\\\\-28\\hspace{0.8em}\\\\\\hline14\\\\14\\\\\\hline\\end{array}[\/latex]<\/p>\r\n<strong>Repeat Step 3: Subtract.<\/strong>\r\n<ol type=\"a\">\r\n \t<li>Subtract 14 \u2212 14 = 0. There is 0 remainder.<\/li>\r\n \t<li>Check 0 &lt; 7.<\/li>\r\n<\/ol>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}42\\\\7 \\enclose{longdiv}{294}\\\\-28\\hspace{0.8em}\\\\\\hline14\\\\-14\\\\\\hline0\\end{array}[\/latex]<\/p>\r\n<strong>There are no more numbers in the dividend to bring down, so you are done.<\/strong>\r\n<p style=\"text-align: center\">294 \u00f7 7 = 42<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example B<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n128 \u00f7 2 =\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}64\\\\2 \\enclose{longdiv}{128}\\\\-12\\hspace{0.8em}\\\\\\hline08\\\\-8\\\\\\hline0\\end{array}[\/latex]<\/p>\r\n<strong>Step 1: Divide.<\/strong>\r\n<ol type=\"a\">\r\n \t<li>Can 2 go into 1? No.<\/li>\r\n \t<li>Can 2 go into 12? Yes.<\/li>\r\n \t<li>How many times?\r\n<ul>\r\n \t<li>2 \u00d7 6 = 12; 12 \u00f7 2 = 6<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>The first number in the trial quotient is 6. Put the 6 in the quotient directly above the 2 tens dividend.<\/li>\r\n<\/ol>\r\n<strong>Step 2: Multiply.<\/strong>\r\n<ol type=\"a\">\r\n \t<li>6 \u00d7 2 = 12.<\/li>\r\n \t<li>Write the 12 under the 12. Draw a line.<\/li>\r\n<\/ol>\r\n<strong>Step 3: Subtract.<\/strong>\r\n<ol type=\"a\">\r\n \t<li>12 \u2212 12 = 0<\/li>\r\n \t<li>Check 0 &lt; 12<\/li>\r\n<\/ol>\r\n<strong>Step 4: Bring down the next number in the dividend.<\/strong>\r\n<ol type=\"a\">\r\n \t<li>Bring down the next number in the dividend (8), and put it beside the result of the subtraction you just completed (0)<strong>.<\/strong><\/li>\r\n \t<li>8 is now the number to be divided.<\/li>\r\n<\/ol>\r\n<strong>Repeat<\/strong>\r\n<ol>\r\n \t<li>Divide: 8 \u00f7 2 = 4<\/li>\r\n \t<li>Multiple: 4 \u00d7 2 = 8<\/li>\r\n \t<li>Subtract: 8 \u2212 8 = 0\r\n<ol type=\"a\">\r\n \t<li>Check 0 &lt; 2<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Bring down the next digit. There are no more digits in the dividend.<\/li>\r\n<\/ol>\r\n<p style=\"text-align: center\">128 \u00f7 2 = 64<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nFind the quotients (divide, multiply, subtract, compare). Check your work using the answer key at the end of the exercise.\r\n<ol class=\"threecolumn bigspace\" type=\"a\">\r\n \t<li>[latex]4\\enclose{longdiv}{364}[\/latex]<\/li>\r\n \t<li>[latex]2\\enclose{longdiv}{144}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{455}[\/latex]<\/li>\r\n \t<li>[latex]7\\enclose{longdiv}{651}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{144}[\/latex]<\/li>\r\n \t<li>[latex]2\\enclose{longdiv}{166}[\/latex]<\/li>\r\n \t<li>[latex]7\\enclose{longdiv}{588}[\/latex]<\/li>\r\n \t<li>[latex]2\\enclose{longdiv}{196}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{230}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{584}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{366}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{244}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{375}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{200}[\/latex]<\/li>\r\n \t<li>[latex]2\\enclose{longdiv}{628}[\/latex]<\/li>\r\n \t<li>[latex]7\\enclose{longdiv}{357}[\/latex]<\/li>\r\n \t<li>[latex]9\\enclose{longdiv}{837}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{248}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{312}[\/latex]<\/li>\r\n \t<li>[latex]7\\enclose{longdiv}{462}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{295}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{384}[\/latex]<\/li>\r\n \t<li>[latex]2\\enclose{longdiv}{276}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{372}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 1<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>91<\/li>\r\n \t<li>72<\/li>\r\n \t<li>91<\/li>\r\n \t<li>93<\/li>\r\n \t<li>18<\/li>\r\n \t<li>83<\/li>\r\n \t<li>84<\/li>\r\n \t<li>98<\/li>\r\n \t<li>46<\/li>\r\n \t<li>73<\/li>\r\n \t<li>61<\/li>\r\n \t<li>61<\/li>\r\n \t<li>75<\/li>\r\n \t<li>25<\/li>\r\n \t<li>314<\/li>\r\n \t<li>51<\/li>\r\n \t<li>93<\/li>\r\n \t<li>31<\/li>\r\n \t<li>39<\/li>\r\n \t<li>66<\/li>\r\n \t<li>59<\/li>\r\n \t<li>64<\/li>\r\n \t<li>138<\/li>\r\n \t<li>93<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example C<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n856 \u00f7 8 =\r\n\r\n[latex]8\\enclose{longdiv}{856}[\/latex]\r\n\r\n<strong>Divide<\/strong>\r\n\r\nDoes 8 go into 8? Yes. 8 \u00f7 8 = 1.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}1\\hspace{1.2em}\\\\8 \\enclose{longdiv}{856}\\end{array}[\/latex]<\/p>\r\n<strong>Multiply<\/strong>\r\n\r\n1 \u00d7 8 = 8\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}1\\hspace{1.2em}\\\\8 \\enclose{longdiv}{856}\\\\8\\hspace{1.2em}\\end{array}[\/latex]<\/p>\r\n<strong>Subtract<\/strong>\r\n\r\n8 \u2212 8 = 0. Check 0 &lt; 8.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}1\\hspace{1.2em}\\\\8 \\enclose{longdiv}{856}\\\\-8\\hspace{1.2em}\\\\\\hline0\\hspace{1.2em}\\end{array}[\/latex]<\/p>\r\n<strong>Bring down the next digit\u00a0<\/strong>\r\n\r\n5 is now the number to be divided.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}1\\hspace{1.2em}\\\\8 \\enclose{longdiv}{856}\\\\-8\\hspace{1.2em}\\\\\\hline05\\hspace{0.8em}\\end{array}[\/latex]<\/p>\r\nNow repeat.\r\n\r\n<strong>Divide<\/strong>\r\n\r\nDoes 8 go into 5? No.\r\n<div class=\"textbox\">\r\n\r\nYou must put a zero to hold the place in the quotient. If a digit is brought down, a digit must be placed in the quotient.\r\n\r\n<\/div>\r\n<strong>Multiply<\/strong>\r\n\r\n0 \u00d7 8 = 0\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}10\\hspace{0.8em}\\\\8 \\enclose{longdiv}{856}\\\\-8\\hspace{1.2em}\\\\\\hline05\\hspace{0.8em}\\end{array}[\/latex]<\/p>\r\n<strong>Subtract<\/strong>\r\n\r\n5 \u2212 0 = 5. Check 5 &lt; 8.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}10\\hspace{0.8em}\\\\8 \\enclose{longdiv}{856}\\\\-8\\hspace{1.2em}\\\\\\hline05\\hspace{0.8em}\\\\-0\\hspace{0.8em}\\\\\\hline5\\hspace{0.8em}\\end{array}[\/latex]<\/p>\r\n<strong>Bring down the next digit<\/strong>\r\n\r\n56 is now the number to be divided.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}10\\hspace{0.8em}\\\\8 \\enclose{longdiv}{856}\\\\-8\\hspace{1.2em}\\\\\\hline05\\hspace{0.8em}\\\\-0\\hspace{0.8em}\\\\\\hline56\\end{array}[\/latex]<\/p>\r\nNow repeat.\r\n\r\n<strong>Divide<\/strong>\r\n\r\nDoes 8 go into 56? Yes. 56 \u00f7 8 = 7.\r\n\r\nWrite 7 in the quotient in the ones place above the 6 in the dividend.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}107\\\\8 \\enclose{longdiv}{856}\\\\-8\\hspace{1.2em}\\\\\\hline05\\hspace{0.8em}\\\\-0\\hspace{0.8em}\\\\\\hline56\\end{array}[\/latex]<\/p>\r\n<strong>Multiply<\/strong>\r\n\r\n7 \u00d7 8 = 56\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}107\\\\8 \\enclose{longdiv}{856}\\\\-8\\hspace{1.2em}\\\\\\hline05\\hspace{0.8em}\\\\-0\\hspace{0.8em}\\\\\\hline56\\\\56\\end{array}[\/latex]<\/p>\r\n<strong>Subtract<\/strong>\r\n\r\n56 \u2212 56 = 0. Check 0 &lt; 8.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}107\\\\8 \\enclose{longdiv}{856}\\\\-8\\hspace{1.2em}\\\\\\hline05\\hspace{0.8em}\\\\-0\\hspace{0.8em}\\\\\\hline56\\\\-56\\\\\\hline0\\end{array}[\/latex]<\/p>\r\n<strong>Bring down the next digit.<\/strong>\r\n\r\nNo more digits.\r\n<p style=\"text-align: center\">856 \u00f7 8 = 107<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nFind the quotients (divide, multiply, subtract, compare). Check your work using the answer key at the end of the exercise.\r\n<ol class=\"threecolumn bigspace\" type=\"a\">\r\n \t<li>[latex]7\\enclose{longdiv}{721}[\/latex]<\/li>\r\n \t<li>[latex]9\\enclose{longdiv}{954}[\/latex]<\/li>\r\n \t<li>[latex]3\\enclose{longdiv}{927}[\/latex]<\/li>\r\n \t<li>[latex]3\\enclose{longdiv}{621}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{824}[\/latex]<\/li>\r\n \t<li>[latex]9\\enclose{longdiv}{972}[\/latex]<\/li>\r\n \t<li>[latex]7\\enclose{longdiv}{714}[\/latex]<\/li>\r\n \t<li>[latex]2\\enclose{longdiv}{416}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{540}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{654}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{832}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{436}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{515}[\/latex]<\/li>\r\n \t<li>[latex]2\\enclose{longdiv}{814}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{648}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{856}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{525}[\/latex]<\/li>\r\n \t<li>[latex]7\\enclose{longdiv}{763}[\/latex]<\/li>\r\n \t<li>[latex]9\\enclose{longdiv}{945}[\/latex]<\/li>\r\n \t<li>[latex]3\\enclose{longdiv}{315}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{872}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{416}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{618}[\/latex]<\/li>\r\n \t<li>[latex]2\\enclose{longdiv}{612}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 2<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>103<\/li>\r\n \t<li>106<\/li>\r\n \t<li>309<\/li>\r\n \t<li>207<\/li>\r\n \t<li>206<\/li>\r\n \t<li>108<\/li>\r\n \t<li>102<\/li>\r\n \t<li>208<\/li>\r\n \t<li>108<\/li>\r\n \t<li>109<\/li>\r\n \t<li>104<\/li>\r\n \t<li>109<\/li>\r\n \t<li>103<\/li>\r\n \t<li>407<\/li>\r\n \t<li>108<\/li>\r\n \t<li>107<\/li>\r\n \t<li>105<\/li>\r\n \t<li>109<\/li>\r\n \t<li>105<\/li>\r\n \t<li>105<\/li>\r\n \t<li>109<\/li>\r\n \t<li>104<\/li>\r\n \t<li>103<\/li>\r\n \t<li>306<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>One-Digit Divisors with Remainders<\/h1>\r\nDo the division exactly the same way that you have been learning. Often there is a remainder after the last subtraction. Write it with the quotient as you already know how to do.\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example D<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n259 \u00f7 8 =\r\n<p style=\"text-align: center\">[latex]\\begin{array}{l}\\hspace{1.5em}32\\text{ R}3\\\\8 \\enclose{longdiv}{259}\\\\\\hspace{0.3em}-24\\\\\\hline\\hspace{1.7em}19\\\\\\hspace{1em}-16\\\\\\hline\\hspace{2.3em}3\\end{array}[\/latex]<\/p>\r\n259 \u00f7 8 = 32 R3\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nDivide and show any remainders. Check your work using the answer key at the end of the exercise.\r\n<ol class=\"threecolumn bigspace\" type=\"a\">\r\n \t<li>[latex]2\\enclose{longdiv}{93}[\/latex]<\/li>\r\n \t<li>[latex]3\\enclose{longdiv}{52}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{94}[\/latex]<\/li>\r\n \t<li>[latex]7\\enclose{longdiv}{74}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{95}[\/latex]<\/li>\r\n \t<li>[latex]9\\enclose{longdiv}{96}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{97}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{99}[\/latex]<\/li>\r\n \t<li>[latex]9\\enclose{longdiv}{98}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{59}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{76}[\/latex]<\/li>\r\n \t<li>[latex]3\\enclose{longdiv}{79}[\/latex]<\/li>\r\n \t<li>[latex]7\\enclose{longdiv}{96}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{57}[\/latex]<\/li>\r\n \t<li>[latex]2\\enclose{longdiv}{47}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{91}[\/latex]<\/li>\r\n \t<li>[latex]7\\enclose{longdiv}{89}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{82}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{67}[\/latex]<\/li>\r\n \t<li>[latex]2\\enclose{longdiv}{85}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{71}[\/latex]<\/li>\r\n \t<li>[latex]3\\enclose{longdiv}{65}[\/latex]<\/li>\r\n \t<li>[latex]9\\enclose{longdiv}{92}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{94}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 3<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>46 R1<\/li>\r\n \t<li>17 R1<\/li>\r\n \t<li>18 R4<\/li>\r\n \t<li>10 R4<\/li>\r\n \t<li>23 R3<\/li>\r\n \t<li>10 R6<\/li>\r\n \t<li>16 R1<\/li>\r\n \t<li>12 R3<\/li>\r\n \t<li>10 R8<\/li>\r\n \t<li>14 R3<\/li>\r\n \t<li>12 R4<\/li>\r\n \t<li>26 R1<\/li>\r\n \t<li>13 R5<\/li>\r\n \t<li>11 R2<\/li>\r\n \t<li>23 R1<\/li>\r\n \t<li>11 R3<\/li>\r\n \t<li>12 R5<\/li>\r\n \t<li>13 R4<\/li>\r\n \t<li>13 R2<\/li>\r\n \t<li>42 R1<\/li>\r\n \t<li>17 R3<\/li>\r\n \t<li>21 R2<\/li>\r\n \t<li>10 R2<\/li>\r\n \t<li>11 R6<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Check Division by Multiplying<\/h1>\r\nTo check your division, do this:\r\n<ol>\r\n \t<li>Multiply the quotient by the divisor.<\/li>\r\n \t<li>Add on any remainder.<\/li>\r\n<\/ol>\r\nThe product will equal the dividend if your arithmetic is correct.\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example E<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p style=\"text-align: center\">[latex]\\begin{array}{l}\\hspace{1.5em}52\\text{ R}1\\\\9 \\enclose{longdiv}{469}\\\\\\hspace{0.3em}-45\\\\\\hline\\hspace{1.7em}19\\\\\\hspace{1em}-18\\\\\\hline\\hspace{2.3em}1\\end{array}[\/latex] \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]\\begin{array}{rr}&amp;52\\\\\\times&amp;9\\\\\\hline&amp;468\\end{array}[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]468+1=469[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nDivide and check your answer by multiplying. Check your work using the answer key at the end of the exercise.\r\n<ol class=\"threecolumn bigspace\" type=\"a\">\r\n \t<li>[latex]7\\enclose{longdiv}{709}[\/latex]<\/li>\r\n \t<li>[latex]2\\enclose{longdiv}{423}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{538}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{609}[\/latex]<\/li>\r\n \t<li>[latex]9\\enclose{longdiv}{406}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{125}[\/latex]<\/li>\r\n \t<li>[latex]3\\enclose{longdiv}{605}[\/latex]<\/li>\r\n \t<li>[latex]9\\enclose{longdiv}{928}[\/latex]<\/li>\r\n \t<li>[latex]3\\enclose{longdiv}{962}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{805}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{301}[\/latex]<\/li>\r\n \t<li>[latex]2\\enclose{longdiv}{807}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{725}[\/latex]<\/li>\r\n \t<li>[latex]7\\enclose{longdiv}{320}[\/latex]<\/li>\r\n \t<li>[latex]9\\enclose{longdiv}{140}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{483}[\/latex]<\/li>\r\n \t<li>[latex]2\\enclose{longdiv}{197}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{307}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{504}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{709}[\/latex]<\/li>\r\n \t<li>[latex]7\\enclose{longdiv}{876}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{101}[\/latex]<\/li>\r\n \t<li>[latex]3\\enclose{longdiv}{269}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{473}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 4<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>101 R2<\/li>\r\n \t<li>211 R1<\/li>\r\n \t<li>107 R3<\/li>\r\n \t<li>152 R1<\/li>\r\n \t<li>45 R1<\/li>\r\n \t<li>20 R5<\/li>\r\n \t<li>201 R2<\/li>\r\n \t<li>103 R1<\/li>\r\n \t<li>320 R2<\/li>\r\n \t<li>201 R1<\/li>\r\n \t<li>37 R5<\/li>\r\n \t<li>403 R1<\/li>\r\n \t<li>120 R5<\/li>\r\n \t<li>45 R5<\/li>\r\n \t<li>15 R5<\/li>\r\n \t<li>60 R3<\/li>\r\n \t<li>98 R1<\/li>\r\n \t<li>51 R1<\/li>\r\n \t<li>100 R4<\/li>\r\n \t<li>88 R5<\/li>\r\n \t<li>125 R1<\/li>\r\n \t<li>25 R1<\/li>\r\n \t<li>89 R2<\/li>\r\n \t<li>94 R3<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1 class=\"page-break-before\">Topic C: Self-Test<\/h1>\r\n<strong>Mark\u00a0 \/24 \u00a0 Aim\u00a0 19\/24<\/strong>\r\n<ol type=\"A\">\r\n \t<li>Find the quotient. (6 marks)\r\n<ol class=\"threecolumn bigspace\" type=\"a\">\r\n \t<li>[latex]6\\enclose{longdiv}{96}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{92}[\/latex]<\/li>\r\n \t<li>[latex]7\\enclose{longdiv}{91}[\/latex]<\/li>\r\n \t<li>[latex]2\\enclose{longdiv}{93}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{94}[\/latex]<\/li>\r\n \t<li>[latex]3\\enclose{longdiv}{52}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Divide. (6 marks)\r\n<ol class=\"threecolumn bigspace\" type=\"a\">\r\n \t<li>[latex]7\\enclose{longdiv}{182}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{736}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{162}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{295}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{184}[\/latex]<\/li>\r\n \t<li>[latex]9\\enclose{longdiv}{576}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Divide and show your check for each answer (12 marks - 1 mark for question, 1 mark for check).\r\n<ol class=\"threecolumn bigspace\" type=\"a\">\r\n \t<li>[latex]9\\enclose{longdiv}{705}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{257}[\/latex]<\/li>\r\n \t<li>[latex]7\\enclose{longdiv}{899}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{538}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{876}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{628}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h2>Answers to Topic C Self-Test<\/h2>\r\n<ol type=\"A\">\r\n \t<li>Find the quotient.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>16<\/li>\r\n \t<li>23<\/li>\r\n \t<li>13<\/li>\r\n \t<li>46 R1<\/li>\r\n \t<li>18 R4<\/li>\r\n \t<li>17 R1<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Divide.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>26<\/li>\r\n \t<li>92<\/li>\r\n \t<li>27<\/li>\r\n \t<li>59<\/li>\r\n \t<li>46<\/li>\r\n \t<li>64<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Divide and show your check for each answer.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>78 R3<\/li>\r\n \t<li>64 R1<\/li>\r\n \t<li>128 R3<\/li>\r\n \t<li>107 R3<\/li>\r\n \t<li>109 R4<\/li>\r\n \t<li>104 R4<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>","rendered":"<p>Several methods are used to divide larger numbers. This book will only teach one method. If you have learned a different method for dividing, ask your instructor to review it with you. You can use the practice exercises in this workbook using whichever method you prefer.<\/p>\n<h1>One-Digit Divisors without Remainders<\/h1>\n<p>Division has four steps which are repeated until the dividend is completely divided. Work through the three examples which show these steps.<\/p>\n<ol>\n<li>Divide.<\/li>\n<li>Multiply<\/li>\n<li>Subtract and compare the remainder to the divisor.<\/li>\n<li>Bring down the next digit in the dividend and repeat.<\/li>\n<\/ol>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example A<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>294 \u00f7 7 =<\/p>\n<p>Rewrite as [latex]7\\enclose{longdiv}{294}[\/latex]<\/p>\n<p><strong>Step 1: Divide.<\/strong><\/p>\n<ol type=\"a\">\n<li>Find a trial quotient using multiplication tables or division facts.<\/li>\n<li>Look at the dividend one digit at a time.\n<ol type=\"i\">\n<li>The first digit is a 2, which is really 2 hundreds.<\/li>\n<li>Will 7 go into 2? Can you divide 2 by 7? No.<\/li>\n<li>Look at the first 2 digits, 29, which is really 29 tens.<\/li>\n<li>Will 7 go into 29? Yes. 4 \u00d7 7 = 28.<\/li>\n<\/ol>\n<\/li>\n<li>The first number in the quotient is 4. Place the 4 in the quotient directly above the 9 tens. The 4 is 4 tens in the quotient.<\/li>\n<\/ol>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}4\\hspace{0.8em}\\\\7 \\enclose{longdiv}{294}\\end{array}[\/latex]<\/p>\n<p><strong>Step 2: Multiply.<\/strong><\/p>\n<ol type=\"a\">\n<li>Multiply 4 \u00d7 7\u00a0 = 28.<\/li>\n<li>Write the 28 under the 29. Draw a line.<\/li>\n<\/ol>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}4\\hspace{0.8em}\\\\7 \\enclose{longdiv}{294}\\\\28\\hspace{0.8em}\\\\\\hline\\end{array}[\/latex]<\/p>\n<p><strong>Step 3: Subtract.<\/strong><\/p>\n<ol type=\"a\">\n<li>Subtract 29 \u2212 28 = 1 (ten).<\/li>\n<li>Check 1 &lt; 7.<\/li>\n<\/ol>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}4\\hspace{0.8em}\\\\7 \\enclose{longdiv}{294}\\\\-28\\hspace{0.8em}\\\\\\hline1\\hspace{0.8em}\\end{array}[\/latex]<\/p>\n<p><strong>Step 4: Bring down the next number in the dividend.<\/strong><\/p>\n<ol type=\"a\">\n<li>Bring down the next number in the dividend (4), and put it beside the result of the subtraction you just completed (1)<strong>.<br \/>\n<\/strong><\/li>\n<li>Together, they make 14. This 14 is the number that you must now divide.<\/li>\n<\/ol>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}4\\hspace{0.8em}\\\\7 \\enclose{longdiv}{294}\\\\-28\\hspace{0.8em}\\\\\\hline14\\end{array}[\/latex]<\/p>\n<p><strong>Repeat Step 1: Divide.<\/strong><\/p>\n<ol type=\"a\">\n<li>Divide 14 \u00f7 7 = 2<\/li>\n<li>Put the 2 in the quotient right after the 4 in the ones place.<\/li>\n<\/ol>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}42\\\\7 \\enclose{longdiv}{294}\\\\-28\\hspace{0.8em}\\\\\\hline14\\end{array}[\/latex]<\/p>\n<p><strong>Repeat Step 2: Multiply.<\/strong><\/p>\n<ol type=\"a\">\n<li>Multiply 2 \u00d7 7 = 14.<\/li>\n<li>Write the 14 under the 14. Draw a line.<\/li>\n<\/ol>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}42\\\\7 \\enclose{longdiv}{294}\\\\-28\\hspace{0.8em}\\\\\\hline14\\\\14\\\\\\hline\\end{array}[\/latex]<\/p>\n<p><strong>Repeat Step 3: Subtract.<\/strong><\/p>\n<ol type=\"a\">\n<li>Subtract 14 \u2212 14 = 0. There is 0 remainder.<\/li>\n<li>Check 0 &lt; 7.<\/li>\n<\/ol>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}42\\\\7 \\enclose{longdiv}{294}\\\\-28\\hspace{0.8em}\\\\\\hline14\\\\-14\\\\\\hline0\\end{array}[\/latex]<\/p>\n<p><strong>There are no more numbers in the dividend to bring down, so you are done.<\/strong><\/p>\n<p style=\"text-align: center\">294 \u00f7 7 = 42<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example B<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>128 \u00f7 2 =<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}64\\\\2 \\enclose{longdiv}{128}\\\\-12\\hspace{0.8em}\\\\\\hline08\\\\-8\\\\\\hline0\\end{array}[\/latex]<\/p>\n<p><strong>Step 1: Divide.<\/strong><\/p>\n<ol type=\"a\">\n<li>Can 2 go into 1? No.<\/li>\n<li>Can 2 go into 12? Yes.<\/li>\n<li>How many times?\n<ul>\n<li>2 \u00d7 6 = 12; 12 \u00f7 2 = 6<\/li>\n<\/ul>\n<\/li>\n<li>The first number in the trial quotient is 6. Put the 6 in the quotient directly above the 2 tens dividend.<\/li>\n<\/ol>\n<p><strong>Step 2: Multiply.<\/strong><\/p>\n<ol type=\"a\">\n<li>6 \u00d7 2 = 12.<\/li>\n<li>Write the 12 under the 12. Draw a line.<\/li>\n<\/ol>\n<p><strong>Step 3: Subtract.<\/strong><\/p>\n<ol type=\"a\">\n<li>12 \u2212 12 = 0<\/li>\n<li>Check 0 &lt; 12<\/li>\n<\/ol>\n<p><strong>Step 4: Bring down the next number in the dividend.<\/strong><\/p>\n<ol type=\"a\">\n<li>Bring down the next number in the dividend (8), and put it beside the result of the subtraction you just completed (0)<strong>.<\/strong><\/li>\n<li>8 is now the number to be divided.<\/li>\n<\/ol>\n<p><strong>Repeat<\/strong><\/p>\n<ol>\n<li>Divide: 8 \u00f7 2 = 4<\/li>\n<li>Multiple: 4 \u00d7 2 = 8<\/li>\n<li>Subtract: 8 \u2212 8 = 0\n<ol type=\"a\">\n<li>Check 0 &lt; 2<\/li>\n<\/ol>\n<\/li>\n<li>Bring down the next digit. There are no more digits in the dividend.<\/li>\n<\/ol>\n<p style=\"text-align: center\">128 \u00f7 2 = 64<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Find the quotients (divide, multiply, subtract, compare). Check your work using the answer key at the end of the exercise.<\/p>\n<ol class=\"threecolumn bigspace\" type=\"a\">\n<li>[latex]4\\enclose{longdiv}{364}[\/latex]<\/li>\n<li>[latex]2\\enclose{longdiv}{144}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{455}[\/latex]<\/li>\n<li>[latex]7\\enclose{longdiv}{651}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{144}[\/latex]<\/li>\n<li>[latex]2\\enclose{longdiv}{166}[\/latex]<\/li>\n<li>[latex]7\\enclose{longdiv}{588}[\/latex]<\/li>\n<li>[latex]2\\enclose{longdiv}{196}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{230}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{584}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{366}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{244}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{375}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{200}[\/latex]<\/li>\n<li>[latex]2\\enclose{longdiv}{628}[\/latex]<\/li>\n<li>[latex]7\\enclose{longdiv}{357}[\/latex]<\/li>\n<li>[latex]9\\enclose{longdiv}{837}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{248}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{312}[\/latex]<\/li>\n<li>[latex]7\\enclose{longdiv}{462}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{295}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{384}[\/latex]<\/li>\n<li>[latex]2\\enclose{longdiv}{276}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{372}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 1<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>91<\/li>\n<li>72<\/li>\n<li>91<\/li>\n<li>93<\/li>\n<li>18<\/li>\n<li>83<\/li>\n<li>84<\/li>\n<li>98<\/li>\n<li>46<\/li>\n<li>73<\/li>\n<li>61<\/li>\n<li>61<\/li>\n<li>75<\/li>\n<li>25<\/li>\n<li>314<\/li>\n<li>51<\/li>\n<li>93<\/li>\n<li>31<\/li>\n<li>39<\/li>\n<li>66<\/li>\n<li>59<\/li>\n<li>64<\/li>\n<li>138<\/li>\n<li>93<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example C<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>856 \u00f7 8 =<\/p>\n<p>[latex]8\\enclose{longdiv}{856}[\/latex]<\/p>\n<p><strong>Divide<\/strong><\/p>\n<p>Does 8 go into 8? Yes. 8 \u00f7 8 = 1.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}1\\hspace{1.2em}\\\\8 \\enclose{longdiv}{856}\\end{array}[\/latex]<\/p>\n<p><strong>Multiply<\/strong><\/p>\n<p>1 \u00d7 8 = 8<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}1\\hspace{1.2em}\\\\8 \\enclose{longdiv}{856}\\\\8\\hspace{1.2em}\\end{array}[\/latex]<\/p>\n<p><strong>Subtract<\/strong><\/p>\n<p>8 \u2212 8 = 0. Check 0 &lt; 8.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}1\\hspace{1.2em}\\\\8 \\enclose{longdiv}{856}\\\\-8\\hspace{1.2em}\\\\\\hline0\\hspace{1.2em}\\end{array}[\/latex]<\/p>\n<p><strong>Bring down the next digit\u00a0<\/strong><\/p>\n<p>5 is now the number to be divided.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}1\\hspace{1.2em}\\\\8 \\enclose{longdiv}{856}\\\\-8\\hspace{1.2em}\\\\\\hline05\\hspace{0.8em}\\end{array}[\/latex]<\/p>\n<p>Now repeat.<\/p>\n<p><strong>Divide<\/strong><\/p>\n<p>Does 8 go into 5? No.<\/p>\n<div class=\"textbox\">\n<p>You must put a zero to hold the place in the quotient. If a digit is brought down, a digit must be placed in the quotient.<\/p>\n<\/div>\n<p><strong>Multiply<\/strong><\/p>\n<p>0 \u00d7 8 = 0<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}10\\hspace{0.8em}\\\\8 \\enclose{longdiv}{856}\\\\-8\\hspace{1.2em}\\\\\\hline05\\hspace{0.8em}\\end{array}[\/latex]<\/p>\n<p><strong>Subtract<\/strong><\/p>\n<p>5 \u2212 0 = 5. Check 5 &lt; 8.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}10\\hspace{0.8em}\\\\8 \\enclose{longdiv}{856}\\\\-8\\hspace{1.2em}\\\\\\hline05\\hspace{0.8em}\\\\-0\\hspace{0.8em}\\\\\\hline5\\hspace{0.8em}\\end{array}[\/latex]<\/p>\n<p><strong>Bring down the next digit<\/strong><\/p>\n<p>56 is now the number to be divided.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}10\\hspace{0.8em}\\\\8 \\enclose{longdiv}{856}\\\\-8\\hspace{1.2em}\\\\\\hline05\\hspace{0.8em}\\\\-0\\hspace{0.8em}\\\\\\hline56\\end{array}[\/latex]<\/p>\n<p>Now repeat.<\/p>\n<p><strong>Divide<\/strong><\/p>\n<p>Does 8 go into 56? Yes. 56 \u00f7 8 = 7.<\/p>\n<p>Write 7 in the quotient in the ones place above the 6 in the dividend.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}107\\\\8 \\enclose{longdiv}{856}\\\\-8\\hspace{1.2em}\\\\\\hline05\\hspace{0.8em}\\\\-0\\hspace{0.8em}\\\\\\hline56\\end{array}[\/latex]<\/p>\n<p><strong>Multiply<\/strong><\/p>\n<p>7 \u00d7 8 = 56<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}107\\\\8 \\enclose{longdiv}{856}\\\\-8\\hspace{1.2em}\\\\\\hline05\\hspace{0.8em}\\\\-0\\hspace{0.8em}\\\\\\hline56\\\\56\\end{array}[\/latex]<\/p>\n<p><strong>Subtract<\/strong><\/p>\n<p>56 \u2212 56 = 0. Check 0 &lt; 8.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}107\\\\8 \\enclose{longdiv}{856}\\\\-8\\hspace{1.2em}\\\\\\hline05\\hspace{0.8em}\\\\-0\\hspace{0.8em}\\\\\\hline56\\\\-56\\\\\\hline0\\end{array}[\/latex]<\/p>\n<p><strong>Bring down the next digit.<\/strong><\/p>\n<p>No more digits.<\/p>\n<p style=\"text-align: center\">856 \u00f7 8 = 107<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Find the quotients (divide, multiply, subtract, compare). Check your work using the answer key at the end of the exercise.<\/p>\n<ol class=\"threecolumn bigspace\" type=\"a\">\n<li>[latex]7\\enclose{longdiv}{721}[\/latex]<\/li>\n<li>[latex]9\\enclose{longdiv}{954}[\/latex]<\/li>\n<li>[latex]3\\enclose{longdiv}{927}[\/latex]<\/li>\n<li>[latex]3\\enclose{longdiv}{621}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{824}[\/latex]<\/li>\n<li>[latex]9\\enclose{longdiv}{972}[\/latex]<\/li>\n<li>[latex]7\\enclose{longdiv}{714}[\/latex]<\/li>\n<li>[latex]2\\enclose{longdiv}{416}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{540}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{654}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{832}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{436}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{515}[\/latex]<\/li>\n<li>[latex]2\\enclose{longdiv}{814}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{648}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{856}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{525}[\/latex]<\/li>\n<li>[latex]7\\enclose{longdiv}{763}[\/latex]<\/li>\n<li>[latex]9\\enclose{longdiv}{945}[\/latex]<\/li>\n<li>[latex]3\\enclose{longdiv}{315}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{872}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{416}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{618}[\/latex]<\/li>\n<li>[latex]2\\enclose{longdiv}{612}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 2<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>103<\/li>\n<li>106<\/li>\n<li>309<\/li>\n<li>207<\/li>\n<li>206<\/li>\n<li>108<\/li>\n<li>102<\/li>\n<li>208<\/li>\n<li>108<\/li>\n<li>109<\/li>\n<li>104<\/li>\n<li>109<\/li>\n<li>103<\/li>\n<li>407<\/li>\n<li>108<\/li>\n<li>107<\/li>\n<li>105<\/li>\n<li>109<\/li>\n<li>105<\/li>\n<li>105<\/li>\n<li>109<\/li>\n<li>104<\/li>\n<li>103<\/li>\n<li>306<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>One-Digit Divisors with Remainders<\/h1>\n<p>Do the division exactly the same way that you have been learning. Often there is a remainder after the last subtraction. Write it with the quotient as you already know how to do.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example D<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>259 \u00f7 8 =<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{l}\\hspace{1.5em}32\\text{ R}3\\\\8 \\enclose{longdiv}{259}\\\\\\hspace{0.3em}-24\\\\\\hline\\hspace{1.7em}19\\\\\\hspace{1em}-16\\\\\\hline\\hspace{2.3em}3\\end{array}[\/latex]<\/p>\n<p>259 \u00f7 8 = 32 R3<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Divide and show any remainders. Check your work using the answer key at the end of the exercise.<\/p>\n<ol class=\"threecolumn bigspace\" type=\"a\">\n<li>[latex]2\\enclose{longdiv}{93}[\/latex]<\/li>\n<li>[latex]3\\enclose{longdiv}{52}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{94}[\/latex]<\/li>\n<li>[latex]7\\enclose{longdiv}{74}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{95}[\/latex]<\/li>\n<li>[latex]9\\enclose{longdiv}{96}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{97}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{99}[\/latex]<\/li>\n<li>[latex]9\\enclose{longdiv}{98}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{59}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{76}[\/latex]<\/li>\n<li>[latex]3\\enclose{longdiv}{79}[\/latex]<\/li>\n<li>[latex]7\\enclose{longdiv}{96}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{57}[\/latex]<\/li>\n<li>[latex]2\\enclose{longdiv}{47}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{91}[\/latex]<\/li>\n<li>[latex]7\\enclose{longdiv}{89}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{82}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{67}[\/latex]<\/li>\n<li>[latex]2\\enclose{longdiv}{85}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{71}[\/latex]<\/li>\n<li>[latex]3\\enclose{longdiv}{65}[\/latex]<\/li>\n<li>[latex]9\\enclose{longdiv}{92}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{94}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 3<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>46 R1<\/li>\n<li>17 R1<\/li>\n<li>18 R4<\/li>\n<li>10 R4<\/li>\n<li>23 R3<\/li>\n<li>10 R6<\/li>\n<li>16 R1<\/li>\n<li>12 R3<\/li>\n<li>10 R8<\/li>\n<li>14 R3<\/li>\n<li>12 R4<\/li>\n<li>26 R1<\/li>\n<li>13 R5<\/li>\n<li>11 R2<\/li>\n<li>23 R1<\/li>\n<li>11 R3<\/li>\n<li>12 R5<\/li>\n<li>13 R4<\/li>\n<li>13 R2<\/li>\n<li>42 R1<\/li>\n<li>17 R3<\/li>\n<li>21 R2<\/li>\n<li>10 R2<\/li>\n<li>11 R6<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Check Division by Multiplying<\/h1>\n<p>To check your division, do this:<\/p>\n<ol>\n<li>Multiply the quotient by the divisor.<\/li>\n<li>Add on any remainder.<\/li>\n<\/ol>\n<p>The product will equal the dividend if your arithmetic is correct.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example E<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p style=\"text-align: center\">[latex]\\begin{array}{l}\\hspace{1.5em}52\\text{ R}1\\\\9 \\enclose{longdiv}{469}\\\\\\hspace{0.3em}-45\\\\\\hline\\hspace{1.7em}19\\\\\\hspace{1em}-18\\\\\\hline\\hspace{2.3em}1\\end{array}[\/latex] \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]\\begin{array}{rr}&52\\\\\\times&9\\\\\\hline&468\\end{array}[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]468+1=469[\/latex]<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Divide and check your answer by multiplying. Check your work using the answer key at the end of the exercise.<\/p>\n<ol class=\"threecolumn bigspace\" type=\"a\">\n<li>[latex]7\\enclose{longdiv}{709}[\/latex]<\/li>\n<li>[latex]2\\enclose{longdiv}{423}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{538}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{609}[\/latex]<\/li>\n<li>[latex]9\\enclose{longdiv}{406}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{125}[\/latex]<\/li>\n<li>[latex]3\\enclose{longdiv}{605}[\/latex]<\/li>\n<li>[latex]9\\enclose{longdiv}{928}[\/latex]<\/li>\n<li>[latex]3\\enclose{longdiv}{962}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{805}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{301}[\/latex]<\/li>\n<li>[latex]2\\enclose{longdiv}{807}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{725}[\/latex]<\/li>\n<li>[latex]7\\enclose{longdiv}{320}[\/latex]<\/li>\n<li>[latex]9\\enclose{longdiv}{140}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{483}[\/latex]<\/li>\n<li>[latex]2\\enclose{longdiv}{197}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{307}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{504}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{709}[\/latex]<\/li>\n<li>[latex]7\\enclose{longdiv}{876}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{101}[\/latex]<\/li>\n<li>[latex]3\\enclose{longdiv}{269}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{473}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 4<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>101 R2<\/li>\n<li>211 R1<\/li>\n<li>107 R3<\/li>\n<li>152 R1<\/li>\n<li>45 R1<\/li>\n<li>20 R5<\/li>\n<li>201 R2<\/li>\n<li>103 R1<\/li>\n<li>320 R2<\/li>\n<li>201 R1<\/li>\n<li>37 R5<\/li>\n<li>403 R1<\/li>\n<li>120 R5<\/li>\n<li>45 R5<\/li>\n<li>15 R5<\/li>\n<li>60 R3<\/li>\n<li>98 R1<\/li>\n<li>51 R1<\/li>\n<li>100 R4<\/li>\n<li>88 R5<\/li>\n<li>125 R1<\/li>\n<li>25 R1<\/li>\n<li>89 R2<\/li>\n<li>94 R3<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1 class=\"page-break-before\">Topic C: Self-Test<\/h1>\n<p><strong>Mark\u00a0 \/24 \u00a0 Aim\u00a0 19\/24<\/strong><\/p>\n<ol type=\"A\">\n<li>Find the quotient. (6 marks)\n<ol class=\"threecolumn bigspace\" type=\"a\">\n<li>[latex]6\\enclose{longdiv}{96}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{92}[\/latex]<\/li>\n<li>[latex]7\\enclose{longdiv}{91}[\/latex]<\/li>\n<li>[latex]2\\enclose{longdiv}{93}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{94}[\/latex]<\/li>\n<li>[latex]3\\enclose{longdiv}{52}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Divide. (6 marks)\n<ol class=\"threecolumn bigspace\" type=\"a\">\n<li>[latex]7\\enclose{longdiv}{182}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{736}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{162}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{295}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{184}[\/latex]<\/li>\n<li>[latex]9\\enclose{longdiv}{576}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Divide and show your check for each answer (12 marks &#8211; 1 mark for question, 1 mark for check).\n<ol class=\"threecolumn bigspace\" type=\"a\">\n<li>[latex]9\\enclose{longdiv}{705}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{257}[\/latex]<\/li>\n<li>[latex]7\\enclose{longdiv}{899}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{538}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{876}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{628}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h2>Answers to Topic C Self-Test<\/h2>\n<ol type=\"A\">\n<li>Find the quotient.\n<ol class=\"threecolumn\" type=\"a\">\n<li>16<\/li>\n<li>23<\/li>\n<li>13<\/li>\n<li>46 R1<\/li>\n<li>18 R4<\/li>\n<li>17 R1<\/li>\n<\/ol>\n<\/li>\n<li>Divide.\n<ol class=\"threecolumn\" type=\"a\">\n<li>26<\/li>\n<li>92<\/li>\n<li>27<\/li>\n<li>59<\/li>\n<li>46<\/li>\n<li>64<\/li>\n<\/ol>\n<\/li>\n<li>Divide and show your check for each answer.\n<ol class=\"threecolumn\" type=\"a\">\n<li>78 R3<\/li>\n<li>64 R1<\/li>\n<li>128 R3<\/li>\n<li>107 R3<\/li>\n<li>109 R4<\/li>\n<li>104 R4<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n","protected":false},"author":999,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-46","chapter","type-chapter","status-publish","hentry"],"part":35,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/46","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":2,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/46\/revisions"}],"predecessor-version":[{"id":207,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/46\/revisions\/207"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/parts\/35"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/46\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/media?parent=46"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapter-type?post=46"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/contributor?post=46"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/license?post=46"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}