{"id":42,"date":"2023-01-06T18:48:51","date_gmt":"2023-01-06T23:48:51","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math023\/chapter\/introduction-and-division-facts\/"},"modified":"2025-07-03T22:48:28","modified_gmt":"2025-07-04T02:48:28","slug":"introduction-and-division-facts","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math023\/chapter\/introduction-and-division-facts\/","title":{"raw":"Topic A: Introduction and Division Facts","rendered":"Topic A: Introduction and Division Facts"},"content":{"raw":"Division is an interesting operation. Both these signs tell you to divide:\r\n<p style=\"text-align: center\">[latex]8\\div4[\/latex] \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 \u00a0\u00a0 \u00a0 [latex]\\require{enclose}4\\enclose{longdiv}{8}[\/latex]<\/p>\r\nDivision is the opposite of multiplication.\r\n\r\nMultiplication takes equal-sized groups and puts the groups together to find the total.\r\n<p style=\"text-align: center\">3 \u00d7 4 = 12<\/p>\r\n<img class=\"aligncenter wp-image-36 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2381\/2023\/01\/3x4.jpg\" alt=\"3 groups of four dots that add up to 12.\" width=\"363\" height=\"34\" \/>\r\n\r\nDivision takes the total and separates that amount into equal groups. You can find the number of equal groups or the size of each group.\r\n<p style=\"text-align: center\">12 \u00f7 4 = 3<\/p>\r\n<img class=\"aligncenter wp-image-37 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2381\/2025\/01\/12div4.jpg\" alt=\"12 dots that are broken up into three groups of four dots.\" width=\"553\" height=\"31\" \/>\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 33.3333%;text-align: center\">[latex]4 \u00d7 3 = 12[\/latex]<\/td>\r\n<td style=\"width: 33.3333%;text-align: center\">[latex]12 \u00f7 3 = 4[\/latex]<\/td>\r\n<td style=\"width: 33.3333%;text-align: center\">[latex]\\begin{array}{r}4\\\\3 \\enclose{longdiv}{12} \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;text-align: center\">[latex]3 \u00d7 4 = 12[\/latex]<\/td>\r\n<td style=\"width: 33.3333%;text-align: center\">[latex]12 \u00f7 4 = 3[\/latex]<\/td>\r\n<td style=\"width: 33.3333%;text-align: center\">[latex]\\begin{array}{r}3\\\\4 \\enclose{longdiv}{12} \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<strong>Learn this vocabulary for division:<\/strong>\r\n<ul>\r\n \t<li>Dividend \u2013 The number or quantity to be divided; the amount altogether.<\/li>\r\n \t<li>Divisor \u2013 The number we divide by. The divisor tells us the number of groups or the quantity in each group that the dividend is to be separated into.<\/li>\r\n \t<li>Quotient \u2013 (\u201ckw \u014d shent\u201d) The answer to a division question.<\/li>\r\n<\/ul>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\text{quotient}\\\\\\text{divisor} \\enclose{longdiv}{\\text{dividend}}\\end{array}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [latex]\\text{dividend}\\div\\text{divisor}=\\text{quotient}[\/latex]<\/p>\r\n\r\n<div class=\"textbox\">If you have learned your times tables well, the division facts will be easier. The times table chart can be used to find division facts.<\/div>\r\nTo use the times table chart for division facts:\r\n<ul>\r\n \t<li>Find the divisor in the column on the left of the times table chart.<\/li>\r\n \t<li>Run your finger in a straight line across the divisor row until you come to the dividend.<\/li>\r\n \t<li>Go straight up that column and the quotient should be the top number.<\/li>\r\n<\/ul>\r\nTry a few while you are doing Exercise 1.\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\nComplete this chart to help yourself understand the connection between multiplication and division. The first one is done for you. Check your work using the answer key at the end of the exercise.\r\n<table style=\"border-collapse: collapse;width: 100%;height: 176px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 16px\">\r\n<th style=\"width: 8%;height: 16px\" scope=\"col\">#<\/th>\r\n<th style=\"width: 23%;height: 16px\" scope=\"col\">Multiplication<\/th>\r\n<th style=\"width: 23%;height: 16px\" scope=\"col\">Division<\/th>\r\n<th style=\"width: 23%;height: 16px\" scope=\"col\">Division<\/th>\r\n<th style=\"width: 23%;height: 16px\" scope=\"col\">\"Say\"<\/th>\r\n<\/tr>\r\n<tr style=\"height: 96px\">\r\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">a<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">\r\n<ul class=\"left\">\r\n \t<li>5 \u00d7 3 = 15<\/li>\r\n \t<li>3 \u00d7 5 = 15<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">\r\n<ul class=\"left\">\r\n \t<li>15 \u00f7 3 = 5<\/li>\r\n \t<li>15 \u00f7 5 = 3<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">\r\n<ul class=\"left\">\r\n \t<li>[latex]\\begin{array}{r}5\\\\3 \\enclose{longdiv}{15} \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{r}3\\\\5 \\enclose{longdiv}{15} \\end{array}[\/latex]<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">\r\n<ul class=\"left\">\r\n \t<li>15 divided by 3 is 5<\/li>\r\n \t<li>15 divided by 5 is 3<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">b<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">\r\n<ul class=\"left\">\r\n \t<li>8 \u00d7 6 = 48<\/li>\r\n \t<li>6 \u00d7 8 = 48<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">\r\n<ul class=\"left\">\r\n \t<li>48 \u00f7 6 = 8<\/li>\r\n \t<li>48 \u00f7 8 = 6<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">\r\n<ul class=\"left\">\r\n \t<li>[latex]\\begin{array}{r}8\\\\6 \\enclose{longdiv}{48} \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{r}6\\\\8 \\enclose{longdiv}{48} \\end{array}[\/latex]<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">\r\n<ul class=\"left\">\r\n \t<li>48 divided by 6 is 8.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">c<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">3 \u00d7 7 = 21<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">d<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">5 \u00d7 9 = 45<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">e<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">4 \u00d7 6 = 24<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">f<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">2 \u00d7 8 = 16<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">g<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">7 \u00d7 10 = 70<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">h<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">6 \u00d7 9 = 54<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">i<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">9 \u00d7 4 = 36<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">j<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">6 \u00d7 7 = 42<\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<strong>Answers to Exercise 1<\/strong>\r\n<table style=\"width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 8%\" scope=\"col\">#<\/th>\r\n<th style=\"width: 23%\" scope=\"col\">Multiplication<\/th>\r\n<th style=\"width: 23%\" scope=\"col\">Division<\/th>\r\n<th style=\"width: 23%\" scope=\"col\">Division<\/th>\r\n<th style=\"width: 23%\" scope=\"col\">\"Say\"<\/th>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 8%\">a<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>5 \u00d7 3 = 15<\/li>\r\n \t<li>3 \u00d7 5 = 15<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>15 \u00f7 3 = 5<\/li>\r\n \t<li>15 \u00f7 5 = 3<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>[latex]\\begin{array}{r}5\\\\3 \\enclose{longdiv}{15} \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{r}3\\\\5 \\enclose{longdiv}{15} \\end{array}[\/latex]<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>15 divided by 3 is 5<\/li>\r\n \t<li>15 divided by 5 is 3<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 8%\">b<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>8 \u00d7 6 = 48<\/li>\r\n \t<li>6 \u00d7 8 = 48<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>48 \u00f7 6 = 8<\/li>\r\n \t<li>48 \u00f7 8 = 6<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>[latex]\\begin{array}{r}8\\\\6 \\enclose{longdiv}{48} \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{r}6\\\\8 \\enclose{longdiv}{48} \\end{array}[\/latex]<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>48 divided by 6 is 8.<\/li>\r\n \t<li>48 divided by 8 is 6.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 8%\">c<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>3 \u00d7 7 = 21<\/li>\r\n \t<li>7 \u00d7 3 = 21<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>21 \u00f7 7 = 3<\/li>\r\n \t<li>21 \u00f7 3 = 7<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>[latex]\\begin{array}{r}3\\\\7 \\enclose{longdiv}{21} \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{r}7\\\\3 \\enclose{longdiv}{21} \\end{array}[\/latex]<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>21 divided by 7 is 3.<\/li>\r\n \t<li>21 divided by 3 is 7.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 8%\">d<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>5 \u00d7 9 = 45<\/li>\r\n \t<li>9 \u00d7 5 = 45<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>45 \u00f7 9 = 5<\/li>\r\n \t<li>45 \u00f7 5 = 9<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>[latex]\\begin{array}{r}5\\\\9 \\enclose{longdiv}{45} \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{r}9\\\\5 \\enclose{longdiv}{45} \\end{array}[\/latex]<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>45 divided by 9 is 5.<\/li>\r\n \t<li>45 divided by 5 is 9.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 8%\">e<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>4 \u00d7 6 = 24<\/li>\r\n \t<li>6 \u00d7 4= 24<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>24 \u00f7 6 = 4<\/li>\r\n \t<li>24 \u00f7 4 = 6<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>[latex]\\begin{array}{r}4\\\\6 \\enclose{longdiv}{24} \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{r}6\\\\4 \\enclose{longdiv}{24} \\end{array}[\/latex]<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>24 divided by 6 is 4.<\/li>\r\n \t<li>24 divided by 4 is 6.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 8%\">f<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>2 \u00d7 8 = 16<\/li>\r\n \t<li>8 \u00d7 2 = 16<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>16 \u00f7 8 = 2<\/li>\r\n \t<li>16 \u00f7 2 = 8<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>[latex]\\begin{array}{r}2\\\\8 \\enclose{longdiv}{16} \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{r}8\\\\2 \\enclose{longdiv}{16} \\end{array}[\/latex]<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>16 divided by 8 is 2.<\/li>\r\n \t<li>16 divided by 2 is 8.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 8%\">g<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>7 \u00d7 10 = 70<\/li>\r\n \t<li>10 \u00d7 7 = 70<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>70 \u00f7 10 = 7<\/li>\r\n \t<li>70 \u00f7 7 = 10<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>[latex]\\begin{array}{r}7\\\\10 \\enclose{longdiv}{70} \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{r}10\\\\7 \\enclose{longdiv}{70} \\end{array}[\/latex]<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>70 divided by 10 is 7.<\/li>\r\n \t<li>70 divided by 7 is 10.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 8%\">h<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>6 \u00d7 9 = 54<\/li>\r\n \t<li>9 \u00d7 6 = 54<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>54 \u00f7 9 = 6<\/li>\r\n \t<li>54 \u00f7 6 = 9<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>[latex]\\begin{array}{r}6\\\\9 \\enclose{longdiv}{54} \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{r}9\\\\6 \\enclose{longdiv}{54} \\end{array}[\/latex]<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>54 divided by 9 is 6.<\/li>\r\n \t<li>54 divided by 6 is 9.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 8%\">i<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>9 \u00d7 4 = 36<\/li>\r\n \t<li>4 \u00d7 9 = 36<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>36 \u00f7 4 = 9<\/li>\r\n \t<li>36 \u00f7 9 = 4<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>[latex]\\begin{array}{r}9\\\\4 \\enclose{longdiv}{36} \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{r}4\\\\9 \\enclose{longdiv}{36} \\end{array}[\/latex]<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>36 divided by 4 is 9.<\/li>\r\n \t<li>36 divided by 9 is 4.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 8%\">j<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>6 \u00d7 7 = 42<\/li>\r\n \t<li>7 \u00d7 6 = 42<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>42 \u00f7 7 = 6<\/li>\r\n \t<li>42 \u00f7 6 = 7<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>[latex]\\begin{array}{r}6\\\\7 \\enclose{longdiv}{42} \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{r}7\\\\6 \\enclose{longdiv}{42} \\end{array}[\/latex]<\/li>\r\n<\/ul>\r\n<\/td>\r\n<td>\r\n<ul class=\"left\">\r\n \t<li>42 divided by 7 is 6.<\/li>\r\n \t<li>42 divided by 6 is 7.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\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\nCheck your division facts by <strong>quickly <\/strong>doing this exercise. Check your work using the answer key at the end of the exercise.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>72 \u00f7 6 =<\/li>\r\n \t<li>12 \u00f7 2 =<\/li>\r\n \t<li>3 \u00f7 1 =<\/li>\r\n \t<li>80 \u00f7 10 =<\/li>\r\n \t<li>18 \u00f7 6 =<\/li>\r\n \t<li>40 \u00f7\u00a0 4 =<\/li>\r\n \t<li>21 \u00f7 7 =<\/li>\r\n \t<li>50 \u00f7 5 =<\/li>\r\n \t<li>54 \u00f7 9 =<\/li>\r\n \t<li>8 \u00f7\u00a0 2 =<\/li>\r\n \t<li>22 \u00f7 11 =<\/li>\r\n \t<li>45 \u00f7 9 =<\/li>\r\n \t<li>4 \u00f7 4 =<\/li>\r\n \t<li>24 \u00f7\u00a0 6<\/li>\r\n \t<li>81 \u00f7 9 =<\/li>\r\n \t<li>88 \u00f7 8 =<\/li>\r\n \t<li>30 \u00f7 3 =<\/li>\r\n \t<li>12 \u00f7 4 =<\/li>\r\n \t<li>33 \u00f7 3 =<\/li>\r\n \t<li>66 \u00f7 11 =<\/li>\r\n \t<li>20 \u00f7 5 =<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 2<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>12<\/li>\r\n \t<li>6<\/li>\r\n \t<li>3<\/li>\r\n \t<li>8<\/li>\r\n \t<li>3<\/li>\r\n \t<li>10<\/li>\r\n \t<li>3<\/li>\r\n \t<li>10<\/li>\r\n \t<li>6<\/li>\r\n \t<li>4<\/li>\r\n \t<li>2<\/li>\r\n \t<li>5<\/li>\r\n \t<li>1<\/li>\r\n \t<li>4<\/li>\r\n \t<li>9<\/li>\r\n \t<li>11<\/li>\r\n \t<li>10<\/li>\r\n \t<li>3<\/li>\r\n \t<li>11<\/li>\r\n \t<li>6<\/li>\r\n \t<li>4<\/li>\r\n<\/ol>\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\nCheck your division facts by quickly doing this exercise. Check your work using the answer key at the end of the exercise.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>90 \u00f7 10 =<\/li>\r\n \t<li>70 \u00f7 7 =<\/li>\r\n \t<li>28 \u00f7 7 =<\/li>\r\n \t<li>32 \u00f7 8 =<\/li>\r\n \t<li>24 \u00f7 3 =<\/li>\r\n \t<li>36 \u00f7 12 =<\/li>\r\n \t<li>84 \u00f7 7 =<\/li>\r\n \t<li>10 \u00f7 2 =<\/li>\r\n \t<li>64 \u00f7 8 =<\/li>\r\n \t<li>6 \u00f7 6 =<\/li>\r\n \t<li>60 \u00f7 12 =<\/li>\r\n \t<li>48 \u00f7 4 =<\/li>\r\n \t<li>72 \u00f7 9 =<\/li>\r\n \t<li>20 \u00f7 10 =<\/li>\r\n \t<li>49 \u00f7 7 =<\/li>\r\n \t<li>48 \u00f7 6 =<\/li>\r\n \t<li>36 \u00f7 9 =<\/li>\r\n \t<li>21 \u00f7 3 =<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 3<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>9<\/li>\r\n \t<li>10<\/li>\r\n \t<li>4<\/li>\r\n \t<li>4<\/li>\r\n \t<li>8<\/li>\r\n \t<li>3<\/li>\r\n \t<li>12<\/li>\r\n \t<li>5<\/li>\r\n \t<li>8<\/li>\r\n \t<li>1<\/li>\r\n \t<li>5<\/li>\r\n \t<li>12<\/li>\r\n \t<li>8<\/li>\r\n \t<li>2<\/li>\r\n \t<li>7<\/li>\r\n \t<li>8<\/li>\r\n \t<li>4<\/li>\r\n \t<li>7<\/li>\r\n<\/ol>\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\nCheck your division facts by quickly doing this exercise. Check your work using the answer key at the end of the exercise.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>12 \u00f7 6 =<\/li>\r\n \t<li>27 \u00f7 9 =<\/li>\r\n \t<li>56 \u00f7 7 =<\/li>\r\n \t<li>3 \u00f7 1 =<\/li>\r\n \t<li>20 \u00f7 2 =<\/li>\r\n \t<li>9 \u00f7 3 =<\/li>\r\n \t<li>55 \u00f7 5 =<\/li>\r\n \t<li>14 \u00f7 7 =<\/li>\r\n \t<li>42 \u00f7 6 =<\/li>\r\n \t<li>18 \u00f7 3 =<\/li>\r\n \t<li>88 \u00f7 11 =<\/li>\r\n \t<li>63 \u00f7 9 =<\/li>\r\n \t<li>28 \u00f7 4 =<\/li>\r\n \t<li>6 \u00f7 1 =<\/li>\r\n \t<li>30 \u00f7 5 =<\/li>\r\n \t<li>4 \u00f7 2 =<\/li>\r\n \t<li>7 \u00f7 7 =<\/li>\r\n \t<li>48 \u00f7 12 =<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 4<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>2<\/li>\r\n \t<li>3<\/li>\r\n \t<li>8<\/li>\r\n \t<li>3<\/li>\r\n \t<li>10<\/li>\r\n \t<li>3<\/li>\r\n \t<li>11<\/li>\r\n \t<li>2<\/li>\r\n \t<li>7<\/li>\r\n \t<li>6<\/li>\r\n \t<li>8<\/li>\r\n \t<li>7<\/li>\r\n \t<li>7<\/li>\r\n \t<li>6<\/li>\r\n \t<li>6<\/li>\r\n \t<li>2<\/li>\r\n \t<li>1<\/li>\r\n \t<li>4<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div><\/div>\r\n<\/div>\r\n<div class=\"textbox\">Tip: Make a list of any errors that you made and the facts that you had to really think about. If you have any more than five facts on your list, ask your instructor for suggestions on learning and drilling the division facts.<\/div>\r\n<h1>Remainders<\/h1>\r\nYou have been practicing the division facts that always work out evenly \u2013 nothing is left over.\r\n\r\nWell, in the real world things are not usually so perfect!\r\n\r\nYou have 7 candies to share among your 3 children.\r\n\r\n<img class=\"aligncenter wp-image-38 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2381\/2025\/01\/image347.jpeg\" alt=\"Seven candies. There are three groups of two candies with one left over.\" width=\"340\" height=\"277\" \/>\r\n\r\nWe call the left-over the remainder. For now, put R and the left over number after your quotient.\r\n<p style=\"text-align: center\">[latex]7\\div3=2\\text{ R}1[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]\\begin{array}{r}2\\text{ R}1\\\\3 \\enclose{longdiv}{7}\\hspace{1.3em}\\end{array}[\/latex]<\/p>\r\n\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\nHere are 22 cookies. Circle groups of 5. How many groups of 5 in 22?\r\n\r\n<img class=\"aligncenter size-full wp-image-39\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2381\/2025\/01\/22-cookies.jpg\" alt=\"Twenty-two ginger-person cookies.\" width=\"1176\" height=\"349\" \/>\r\n\r\nYou should have 4 groups with 2 left over.\r\n<p style=\"text-align: center\">[latex]22\\div5=4\\text{ R}2[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]\\begin{array}{r}4\\text{ R}2\\\\5 \\enclose{longdiv}{22}\\hspace{1.3em}\\end{array}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\nThe remainder must not be the same size or bigger than the divisor. If it is bigger, it means another group could be made.\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\nHere are 66 suns. Make groups of 9. How many groups of 9 in 66?\r\n\r\n<img class=\"aligncenter size-full wp-image-40\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2381\/2025\/01\/66-suns.jpg\" alt=\"Sixty-six suns.\" width=\"1350\" height=\"196\" \/>\r\n\r\nHow many groups? 7\r\n\r\nHow many left over? 3\r\n<p style=\"text-align: center\">[latex]66\\div9=7\\text{ R}3[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]\\begin{array}{r}7\\text{ R}3\\\\9 \\enclose{longdiv}{66}\\hspace{1.3em}\\end{array}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox\">Tip: The remainder must <strong>not<\/strong> be the same size or bigger than the divisor. Why not? It would make another group.<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nDraw pictures to find the quotient and the remainder. Write each question using the other division sign as well. Have your instructor check your work.\r\n<ol type=\"a\">\r\n \t<li>[latex]23\\div10=2\\text{ R}3[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]\\begin{array}{r}2\\text{ R}3\\\\10 \\enclose{longdiv}{23}\\hspace{1.3em}\\end{array}[\/latex]<img class=\"aligncenter wp-image-41\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2381\/2025\/01\/23div10.jpg\" alt=\"23 circles. Two groups of ten circles are circled. There are three circles left over.\" width=\"300\" height=\"156\" \/><\/li>\r\n<\/ol>\r\n<ol class=\"space\" start=\"2\" type=\"a\">\r\n \t<li>24 \u00f7 7 =<\/li>\r\n \t<li>19 \u00f7 3 =<\/li>\r\n \t<li>39 \u00f7 12 =<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 5<\/strong>\r\n<ol class=\"threecolumn\" start=\"2\" type=\"a\">\r\n \t<li>3R3<\/li>\r\n \t<li>6R1<\/li>\r\n \t<li>3R3<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nYou cannot always draw pictures, so how should you find the quotients?\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\n29 \u00f7 3 =\r\n\r\nUse multiplication tables or the division facts to find a trial quotient. What can you multiply by 3 to find a number close to 29?\r\n<ul type=\"none\">\r\n \t<li>3 \u00d7 9 = 27<\/li>\r\n \t<li>3 \u00d7 10 = 30<\/li>\r\n<\/ul>\r\nUse 9 as the trial quotient. Do not use 10 because 3 \u00d7 10 = 30, which is more than the dividend 29.\r\n<ol>\r\n \t<li>Divide.\r\n[latex]\\begin{array}{r}9\\\\3 \\enclose{longdiv}{29}\\end{array}[\/latex]<\/li>\r\n \t<li>Multiply. 9 \u00d7 3 = 27. Write the product under the 29.\r\n[latex]\\begin{array}{r}9\\\\3 \\enclose{longdiv}{29}\\\\27\\end{array}[\/latex]<\/li>\r\n \t<li>Subtract 27 from 29 to find the remainder.\r\n[latex]\\begin{array}{r}9\\\\3 \\enclose{longdiv}{29}\\\\-27\\\\\\hline2\\end{array}[\/latex]<\/li>\r\n \t<li>Check (compare) to be sure the remainder is less then (&lt;) the divisor.\r\n2 &lt; 3<\/li>\r\n<\/ol>\r\n<p style=\"text-align: left\"><strong>29 \u00f7 3 = 9 R2<\/strong><\/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 D<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n60 \u00f7 7 =\r\n\r\nThink what can be multiplied by 7 to find a number close to 60.\r\n<ul type=\"none\">\r\n \t<li>7 \u00d7 8 = 56 (good)<\/li>\r\n \t<li>7 \u00d7 9 = 63 (too big)<\/li>\r\n<\/ul>\r\nUse 8 as the trial quotient.\r\n<ol>\r\n \t<li>Divide.\r\n[latex]\\begin{array}{r}8\\\\7 \\enclose{longdiv}{60}\\end{array}[\/latex]<\/li>\r\n \t<li>Multiply.\r\n[latex]\\begin{array}{r}8\\\\7 \\enclose{longdiv}{60}\\\\56\\end{array}[\/latex]<\/li>\r\n \t<li>Subtract.\r\n[latex]\\begin{array}{r}8\\\\7 \\enclose{longdiv}{60}\\\\-56\\\\\\hline4\\end{array}[\/latex]<\/li>\r\n \t<li>Compare to be sure the remainder is less than the divisor.\r\n4 &lt; 7<\/li>\r\n<\/ol>\r\n<p style=\"text-align: center\"><strong>60 \u00f7 7 = 8 R4<\/strong><\/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 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nFind the quotients and remainders (divide, multiply, subtract, compare). Check your work using the answer key at the end of the exercise.\r\n<ol class=\"threecolumn space\" type=\"a\">\r\n \t<li>[latex]5\\enclose{longdiv}{28}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{15}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{47}[\/latex]<\/li>\r\n \t<li>[latex]9\\enclose{longdiv}{37}[\/latex]<\/li>\r\n \t<li>[latex]2\\enclose{longdiv}{13}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{25}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{75}[\/latex]<\/li>\r\n \t<li>[latex]3\\enclose{longdiv}{19}[\/latex]<\/li>\r\n \t<li>[latex]7\\enclose{longdiv}{32}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{9}[\/latex]<\/li>\r\n \t<li>[latex]9\\enclose{longdiv}{55}[\/latex]<\/li>\r\n \t<li>[latex]10\\enclose{longdiv}{98}[\/latex]<\/li>\r\n \t<li>[latex]3\\enclose{longdiv}{26}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{47}[\/latex]<\/li>\r\n \t<li>[latex]9\\enclose{longdiv}{46}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{43}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{49}[\/latex]<\/li>\r\n \t<li>[latex]4\\enclose{longdiv}{38}[\/latex]<\/li>\r\n \t<li>[latex]2\\enclose{longdiv}{19}[\/latex]<\/li>\r\n \t<li>[latex]7\\enclose{longdiv}{61}[\/latex]<\/li>\r\n \t<li>[latex]3\\enclose{longdiv}{23}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{78}[\/latex]<\/li>\r\n \t<li>[latex]9\\enclose{longdiv}{67}[\/latex]<\/li>\r\n \t<li>[latex]6\\enclose{longdiv}{45}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 6<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>5 R3<\/li>\r\n \t<li>3 R3<\/li>\r\n \t<li>7 R5<\/li>\r\n \t<li>4 R1<\/li>\r\n \t<li>6 R1<\/li>\r\n \t<li>4 R1<\/li>\r\n \t<li>9 R3<\/li>\r\n \t<li>6 R1<\/li>\r\n \t<li>4 R4<\/li>\r\n \t<li>2 R1<\/li>\r\n \t<li>6 R1<\/li>\r\n \t<li>9 R8<\/li>\r\n \t<li>8 R2<\/li>\r\n \t<li>5 R7<\/li>\r\n \t<li>5 R1<\/li>\r\n \t<li>7 R1<\/li>\r\n \t<li>9 R4<\/li>\r\n \t<li>9 R2<\/li>\r\n \t<li>9 R1<\/li>\r\n \t<li>8 R5<\/li>\r\n \t<li>7 R2<\/li>\r\n \t<li>9 R6<\/li>\r\n \t<li>7 R4<\/li>\r\n \t<li>7 R3<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nFind the quotients and remainders (divide, multiply, subtract, compare.) Check your work using the answer key at the end of the exercise.\r\n\r\n<strong>Example<\/strong>\r\n\r\n59 \u00f7 7 =\r\n\r\nRewrite: [latex]7\\enclose{longdiv}{59}[\/latex]\r\n\r\nThen solve: [latex]\\begin{array}{r}8\\\\7 \\enclose{longdiv}{59}\\\\-56\\\\\\hline3\\end{array}[\/latex]\r\n\r\nAnswer: 8 R3\r\n<ol class=\"threecolumn space\" type=\"a\">\r\n \t<li>27 \u00f7 5 =<\/li>\r\n \t<li>13 \u00f7 2 =<\/li>\r\n \t<li>46 \u00f7 9 =<\/li>\r\n \t<li>38 \u00f7 6 =<\/li>\r\n \t<li>61 \u00f7 7 =<\/li>\r\n \t<li>14 \u00f7 5 =<\/li>\r\n \t<li>49 \u00f7 8 =<\/li>\r\n \t<li>28 \u00f7 3 =<\/li>\r\n \t<li>78 \u00f7 8 =<\/li>\r\n \t<li>37 \u00f7 4 =<\/li>\r\n \t<li>67 \u00f7 9 =<\/li>\r\n \t<li>52 \u00f7 6 =<\/li>\r\n \t<li>45 \u00f7 8 =<\/li>\r\n \t<li>25 \u00f7 7 =<\/li>\r\n \t<li>11 \u00f7 3 =<\/li>\r\n \t<li>53 \u00f7 9 =<\/li>\r\n \t<li>19 \u00f7 4 =<\/li>\r\n \t<li>77 \u00f7 8 =<\/li>\r\n \t<li>20 \u00f7 3 =<\/li>\r\n \t<li>11 \u00f7 2 =<\/li>\r\n \t<li>23 \u00f7 5 =<\/li>\r\n \t<li>54 \u00f7 7 =<\/li>\r\n \t<li>87 \u00f7 9 =<\/li>\r\n \t<li>9 \u00f7 4 =<\/li>\r\n<\/ol>\r\n<strong>Answers for Exercise 7<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>5 R2<\/li>\r\n \t<li>6 R1<\/li>\r\n \t<li>5 R1<\/li>\r\n \t<li>6 R2<\/li>\r\n \t<li>8 R5<\/li>\r\n \t<li>2 R4<\/li>\r\n \t<li>6 R1<\/li>\r\n \t<li>9 R1<\/li>\r\n \t<li>9 R6<\/li>\r\n \t<li>9 R1<\/li>\r\n \t<li>7 R4<\/li>\r\n \t<li>8 R4<\/li>\r\n \t<li>5 R5<\/li>\r\n \t<li>3 R4<\/li>\r\n \t<li>3 R2<\/li>\r\n \t<li>5 R8<\/li>\r\n \t<li>4 R3<\/li>\r\n \t<li>9 R5<\/li>\r\n \t<li>6 R2<\/li>\r\n \t<li>5 R1<\/li>\r\n \t<li>4 R3<\/li>\r\n \t<li>7 R5<\/li>\r\n \t<li>9 R6<\/li>\r\n \t<li>2 R1<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1 class=\"page-break-before\">Topic A: Self-Test<\/h1>\r\n<strong>Mark \/12\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Aim 9\/12<\/strong>\r\n<ol type=\"A\">\r\n \t<li>Give the answer. (6 marks)\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>63 \u00f7 9 =<\/li>\r\n \t<li>21 \u00f7 7 =<\/li>\r\n \t<li>72 \u00f7 8 =<\/li>\r\n \t<li>36 \u00f7 4 =<\/li>\r\n \t<li>32 \u00f7 4 =<\/li>\r\n \t<li>48 \u00f7 6 =<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Find the quotient. (6 marks)\r\n<ol class=\"threecolumn space\" type=\"a\">\r\n \t<li>[latex]6\\enclose{longdiv}{59}[\/latex]<\/li>\r\n \t<li>[latex]9\\enclose{longdiv}{87}[\/latex]<\/li>\r\n \t<li>[latex]7\\enclose{longdiv}{51}[\/latex]<\/li>\r\n \t<li>[latex]8\\enclose{longdiv}{76}[\/latex]<\/li>\r\n \t<li>[latex]5\\enclose{longdiv}{49}[\/latex]<\/li>\r\n \t<li>[latex]3\\enclose{longdiv}{26}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h2>Answers to Topic A Self-Test<\/h2>\r\n<ol type=\"A\">\r\n \t<li>Give the answer.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>7<\/li>\r\n \t<li>3<\/li>\r\n \t<li>9<\/li>\r\n \t<li>9<\/li>\r\n \t<li>8<\/li>\r\n \t<li>8<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Find the quotient.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>9 R5<\/li>\r\n \t<li>9 R6<\/li>\r\n \t<li>7 R2<\/li>\r\n \t<li>9 R4<\/li>\r\n \t<li>9 R4<\/li>\r\n \t<li>8 R2<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>","rendered":"<p>Division is an interesting operation. Both these signs tell you to divide:<\/p>\n<p style=\"text-align: center\">[latex]8\\div4[\/latex] \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 \u00a0\u00a0 \u00a0 [latex]\\require{enclose}4\\enclose{longdiv}{8}[\/latex]<\/p>\n<p>Division is the opposite of multiplication.<\/p>\n<p>Multiplication takes equal-sized groups and puts the groups together to find the total.<\/p>\n<p style=\"text-align: center\">3 \u00d7 4 = 12<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-36 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2381\/2023\/01\/3x4.jpg\" alt=\"3 groups of four dots that add up to 12.\" width=\"363\" height=\"34\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2023\/01\/3x4.jpg 363w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2023\/01\/3x4-300x28.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2023\/01\/3x4-65x6.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2023\/01\/3x4-225x21.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2023\/01\/3x4-350x33.jpg 350w\" sizes=\"auto, (max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Division takes the total and separates that amount into equal groups. You can find the number of equal groups or the size of each group.<\/p>\n<p style=\"text-align: center\">12 \u00f7 4 = 3<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-37 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2381\/2025\/01\/12div4.jpg\" alt=\"12 dots that are broken up into three groups of four dots.\" width=\"553\" height=\"31\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/12div4.jpg 553w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/12div4-300x17.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/12div4-65x4.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/12div4-225x13.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/12div4-350x20.jpg 350w\" sizes=\"auto, (max-width: 553px) 100vw, 553px\" \/><\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%;text-align: center\">[latex]4 \u00d7 3 = 12[\/latex]<\/td>\n<td style=\"width: 33.3333%;text-align: center\">[latex]12 \u00f7 3 = 4[\/latex]<\/td>\n<td style=\"width: 33.3333%;text-align: center\">[latex]\\begin{array}{r}4\\\\3 \\enclose{longdiv}{12} \\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;text-align: center\">[latex]3 \u00d7 4 = 12[\/latex]<\/td>\n<td style=\"width: 33.3333%;text-align: center\">[latex]12 \u00f7 4 = 3[\/latex]<\/td>\n<td style=\"width: 33.3333%;text-align: center\">[latex]\\begin{array}{r}3\\\\4 \\enclose{longdiv}{12} \\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Learn this vocabulary for division:<\/strong><\/p>\n<ul>\n<li>Dividend \u2013 The number or quantity to be divided; the amount altogether.<\/li>\n<li>Divisor \u2013 The number we divide by. The divisor tells us the number of groups or the quantity in each group that the dividend is to be separated into.<\/li>\n<li>Quotient \u2013 (\u201ckw \u014d shent\u201d) The answer to a division question.<\/li>\n<\/ul>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\text{quotient}\\\\\\text{divisor} \\enclose{longdiv}{\\text{dividend}}\\end{array}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [latex]\\text{dividend}\\div\\text{divisor}=\\text{quotient}[\/latex]<\/p>\n<div class=\"textbox\">If you have learned your times tables well, the division facts will be easier. The times table chart can be used to find division facts.<\/div>\n<p>To use the times table chart for division facts:<\/p>\n<ul>\n<li>Find the divisor in the column on the left of the times table chart.<\/li>\n<li>Run your finger in a straight line across the divisor row until you come to the dividend.<\/li>\n<li>Go straight up that column and the quotient should be the top number.<\/li>\n<\/ul>\n<p>Try a few while you are doing Exercise 1.<\/p>\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>Complete this chart to help yourself understand the connection between multiplication and division. The first one is done for you. Check your work using the answer key at the end of the exercise.<\/p>\n<table style=\"border-collapse: collapse;width: 100%;height: 176px\">\n<tbody>\n<tr style=\"height: 16px\">\n<th style=\"width: 8%;height: 16px\" scope=\"col\">#<\/th>\n<th style=\"width: 23%;height: 16px\" scope=\"col\">Multiplication<\/th>\n<th style=\"width: 23%;height: 16px\" scope=\"col\">Division<\/th>\n<th style=\"width: 23%;height: 16px\" scope=\"col\">Division<\/th>\n<th style=\"width: 23%;height: 16px\" scope=\"col\">&#8220;Say&#8221;<\/th>\n<\/tr>\n<tr style=\"height: 96px\">\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">a<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">\n<ul class=\"left\">\n<li>5 \u00d7 3 = 15<\/li>\n<li>3 \u00d7 5 = 15<\/li>\n<\/ul>\n<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">\n<ul class=\"left\">\n<li>15 \u00f7 3 = 5<\/li>\n<li>15 \u00f7 5 = 3<\/li>\n<\/ul>\n<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">\n<ul class=\"left\">\n<li>[latex]\\begin{array}{r}5\\\\3 \\enclose{longdiv}{15} \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{r}3\\\\5 \\enclose{longdiv}{15} \\end{array}[\/latex]<\/li>\n<\/ul>\n<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">\n<ul class=\"left\">\n<li>15 divided by 3 is 5<\/li>\n<li>15 divided by 5 is 3<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">b<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">\n<ul class=\"left\">\n<li>8 \u00d7 6 = 48<\/li>\n<li>6 \u00d7 8 = 48<\/li>\n<\/ul>\n<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">\n<ul class=\"left\">\n<li>48 \u00f7 6 = 8<\/li>\n<li>48 \u00f7 8 = 6<\/li>\n<\/ul>\n<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">\n<ul class=\"left\">\n<li>[latex]\\begin{array}{r}8\\\\6 \\enclose{longdiv}{48} \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{r}6\\\\8 \\enclose{longdiv}{48} \\end{array}[\/latex]<\/li>\n<\/ul>\n<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">\n<ul class=\"left\">\n<li>48 divided by 6 is 8.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">c<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">3 \u00d7 7 = 21<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">d<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">5 \u00d7 9 = 45<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">e<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">4 \u00d7 6 = 24<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">f<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">2 \u00d7 8 = 16<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">g<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">7 \u00d7 10 = 70<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">h<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">6 \u00d7 9 = 54<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">i<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">9 \u00d7 4 = 36<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8%;height: 100px;text-align: left;vertical-align: top\">j<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\">6 \u00d7 7 = 42<\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<td style=\"width: 23%;height: 100px;text-align: left;vertical-align: top\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Answers to Exercise 1<\/strong><\/p>\n<table style=\"width: 100%\">\n<tbody>\n<tr>\n<th style=\"width: 8%\" scope=\"col\">#<\/th>\n<th style=\"width: 23%\" scope=\"col\">Multiplication<\/th>\n<th style=\"width: 23%\" scope=\"col\">Division<\/th>\n<th style=\"width: 23%\" scope=\"col\">Division<\/th>\n<th style=\"width: 23%\" scope=\"col\">&#8220;Say&#8221;<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 8%\">a<\/td>\n<td>\n<ul class=\"left\">\n<li>5 \u00d7 3 = 15<\/li>\n<li>3 \u00d7 5 = 15<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>15 \u00f7 3 = 5<\/li>\n<li>15 \u00f7 5 = 3<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>[latex]\\begin{array}{r}5\\\\3 \\enclose{longdiv}{15} \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{r}3\\\\5 \\enclose{longdiv}{15} \\end{array}[\/latex]<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>15 divided by 3 is 5<\/li>\n<li>15 divided by 5 is 3<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8%\">b<\/td>\n<td>\n<ul class=\"left\">\n<li>8 \u00d7 6 = 48<\/li>\n<li>6 \u00d7 8 = 48<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>48 \u00f7 6 = 8<\/li>\n<li>48 \u00f7 8 = 6<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>[latex]\\begin{array}{r}8\\\\6 \\enclose{longdiv}{48} \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{r}6\\\\8 \\enclose{longdiv}{48} \\end{array}[\/latex]<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>48 divided by 6 is 8.<\/li>\n<li>48 divided by 8 is 6.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8%\">c<\/td>\n<td>\n<ul class=\"left\">\n<li>3 \u00d7 7 = 21<\/li>\n<li>7 \u00d7 3 = 21<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>21 \u00f7 7 = 3<\/li>\n<li>21 \u00f7 3 = 7<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>[latex]\\begin{array}{r}3\\\\7 \\enclose{longdiv}{21} \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{r}7\\\\3 \\enclose{longdiv}{21} \\end{array}[\/latex]<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>21 divided by 7 is 3.<\/li>\n<li>21 divided by 3 is 7.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8%\">d<\/td>\n<td>\n<ul class=\"left\">\n<li>5 \u00d7 9 = 45<\/li>\n<li>9 \u00d7 5 = 45<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>45 \u00f7 9 = 5<\/li>\n<li>45 \u00f7 5 = 9<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>[latex]\\begin{array}{r}5\\\\9 \\enclose{longdiv}{45} \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{r}9\\\\5 \\enclose{longdiv}{45} \\end{array}[\/latex]<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>45 divided by 9 is 5.<\/li>\n<li>45 divided by 5 is 9.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8%\">e<\/td>\n<td>\n<ul class=\"left\">\n<li>4 \u00d7 6 = 24<\/li>\n<li>6 \u00d7 4= 24<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>24 \u00f7 6 = 4<\/li>\n<li>24 \u00f7 4 = 6<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>[latex]\\begin{array}{r}4\\\\6 \\enclose{longdiv}{24} \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{r}6\\\\4 \\enclose{longdiv}{24} \\end{array}[\/latex]<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>24 divided by 6 is 4.<\/li>\n<li>24 divided by 4 is 6.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8%\">f<\/td>\n<td>\n<ul class=\"left\">\n<li>2 \u00d7 8 = 16<\/li>\n<li>8 \u00d7 2 = 16<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>16 \u00f7 8 = 2<\/li>\n<li>16 \u00f7 2 = 8<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>[latex]\\begin{array}{r}2\\\\8 \\enclose{longdiv}{16} \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{r}8\\\\2 \\enclose{longdiv}{16} \\end{array}[\/latex]<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>16 divided by 8 is 2.<\/li>\n<li>16 divided by 2 is 8.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8%\">g<\/td>\n<td>\n<ul class=\"left\">\n<li>7 \u00d7 10 = 70<\/li>\n<li>10 \u00d7 7 = 70<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>70 \u00f7 10 = 7<\/li>\n<li>70 \u00f7 7 = 10<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>[latex]\\begin{array}{r}7\\\\10 \\enclose{longdiv}{70} \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{r}10\\\\7 \\enclose{longdiv}{70} \\end{array}[\/latex]<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>70 divided by 10 is 7.<\/li>\n<li>70 divided by 7 is 10.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8%\">h<\/td>\n<td>\n<ul class=\"left\">\n<li>6 \u00d7 9 = 54<\/li>\n<li>9 \u00d7 6 = 54<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>54 \u00f7 9 = 6<\/li>\n<li>54 \u00f7 6 = 9<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>[latex]\\begin{array}{r}6\\\\9 \\enclose{longdiv}{54} \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{r}9\\\\6 \\enclose{longdiv}{54} \\end{array}[\/latex]<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>54 divided by 9 is 6.<\/li>\n<li>54 divided by 6 is 9.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8%\">i<\/td>\n<td>\n<ul class=\"left\">\n<li>9 \u00d7 4 = 36<\/li>\n<li>4 \u00d7 9 = 36<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>36 \u00f7 4 = 9<\/li>\n<li>36 \u00f7 9 = 4<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>[latex]\\begin{array}{r}9\\\\4 \\enclose{longdiv}{36} \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{r}4\\\\9 \\enclose{longdiv}{36} \\end{array}[\/latex]<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>36 divided by 4 is 9.<\/li>\n<li>36 divided by 9 is 4.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8%\">j<\/td>\n<td>\n<ul class=\"left\">\n<li>6 \u00d7 7 = 42<\/li>\n<li>7 \u00d7 6 = 42<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>42 \u00f7 7 = 6<\/li>\n<li>42 \u00f7 6 = 7<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>[latex]\\begin{array}{r}6\\\\7 \\enclose{longdiv}{42} \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{r}7\\\\6 \\enclose{longdiv}{42} \\end{array}[\/latex]<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul class=\"left\">\n<li>42 divided by 7 is 6.<\/li>\n<li>42 divided by 6 is 7.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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>Check your division facts by <strong>quickly <\/strong>doing this exercise. Check your work using the answer key at the end of the exercise.<\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>72 \u00f7 6 =<\/li>\n<li>12 \u00f7 2 =<\/li>\n<li>3 \u00f7 1 =<\/li>\n<li>80 \u00f7 10 =<\/li>\n<li>18 \u00f7 6 =<\/li>\n<li>40 \u00f7\u00a0 4 =<\/li>\n<li>21 \u00f7 7 =<\/li>\n<li>50 \u00f7 5 =<\/li>\n<li>54 \u00f7 9 =<\/li>\n<li>8 \u00f7\u00a0 2 =<\/li>\n<li>22 \u00f7 11 =<\/li>\n<li>45 \u00f7 9 =<\/li>\n<li>4 \u00f7 4 =<\/li>\n<li>24 \u00f7\u00a0 6<\/li>\n<li>81 \u00f7 9 =<\/li>\n<li>88 \u00f7 8 =<\/li>\n<li>30 \u00f7 3 =<\/li>\n<li>12 \u00f7 4 =<\/li>\n<li>33 \u00f7 3 =<\/li>\n<li>66 \u00f7 11 =<\/li>\n<li>20 \u00f7 5 =<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 2<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>12<\/li>\n<li>6<\/li>\n<li>3<\/li>\n<li>8<\/li>\n<li>3<\/li>\n<li>10<\/li>\n<li>3<\/li>\n<li>10<\/li>\n<li>6<\/li>\n<li>4<\/li>\n<li>2<\/li>\n<li>5<\/li>\n<li>1<\/li>\n<li>4<\/li>\n<li>9<\/li>\n<li>11<\/li>\n<li>10<\/li>\n<li>3<\/li>\n<li>11<\/li>\n<li>6<\/li>\n<li>4<\/li>\n<\/ol>\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>Check your division facts by quickly doing this exercise. Check your work using the answer key at the end of the exercise.<\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>90 \u00f7 10 =<\/li>\n<li>70 \u00f7 7 =<\/li>\n<li>28 \u00f7 7 =<\/li>\n<li>32 \u00f7 8 =<\/li>\n<li>24 \u00f7 3 =<\/li>\n<li>36 \u00f7 12 =<\/li>\n<li>84 \u00f7 7 =<\/li>\n<li>10 \u00f7 2 =<\/li>\n<li>64 \u00f7 8 =<\/li>\n<li>6 \u00f7 6 =<\/li>\n<li>60 \u00f7 12 =<\/li>\n<li>48 \u00f7 4 =<\/li>\n<li>72 \u00f7 9 =<\/li>\n<li>20 \u00f7 10 =<\/li>\n<li>49 \u00f7 7 =<\/li>\n<li>48 \u00f7 6 =<\/li>\n<li>36 \u00f7 9 =<\/li>\n<li>21 \u00f7 3 =<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 3<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>9<\/li>\n<li>10<\/li>\n<li>4<\/li>\n<li>4<\/li>\n<li>8<\/li>\n<li>3<\/li>\n<li>12<\/li>\n<li>5<\/li>\n<li>8<\/li>\n<li>1<\/li>\n<li>5<\/li>\n<li>12<\/li>\n<li>8<\/li>\n<li>2<\/li>\n<li>7<\/li>\n<li>8<\/li>\n<li>4<\/li>\n<li>7<\/li>\n<\/ol>\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>Check your division facts by quickly doing this exercise. Check your work using the answer key at the end of the exercise.<\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>12 \u00f7 6 =<\/li>\n<li>27 \u00f7 9 =<\/li>\n<li>56 \u00f7 7 =<\/li>\n<li>3 \u00f7 1 =<\/li>\n<li>20 \u00f7 2 =<\/li>\n<li>9 \u00f7 3 =<\/li>\n<li>55 \u00f7 5 =<\/li>\n<li>14 \u00f7 7 =<\/li>\n<li>42 \u00f7 6 =<\/li>\n<li>18 \u00f7 3 =<\/li>\n<li>88 \u00f7 11 =<\/li>\n<li>63 \u00f7 9 =<\/li>\n<li>28 \u00f7 4 =<\/li>\n<li>6 \u00f7 1 =<\/li>\n<li>30 \u00f7 5 =<\/li>\n<li>4 \u00f7 2 =<\/li>\n<li>7 \u00f7 7 =<\/li>\n<li>48 \u00f7 12 =<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 4<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>2<\/li>\n<li>3<\/li>\n<li>8<\/li>\n<li>3<\/li>\n<li>10<\/li>\n<li>3<\/li>\n<li>11<\/li>\n<li>2<\/li>\n<li>7<\/li>\n<li>6<\/li>\n<li>8<\/li>\n<li>7<\/li>\n<li>7<\/li>\n<li>6<\/li>\n<li>6<\/li>\n<li>2<\/li>\n<li>1<\/li>\n<li>4<\/li>\n<\/ol>\n<\/div>\n<div><\/div>\n<\/div>\n<div class=\"textbox\">Tip: Make a list of any errors that you made and the facts that you had to really think about. If you have any more than five facts on your list, ask your instructor for suggestions on learning and drilling the division facts.<\/div>\n<h1>Remainders<\/h1>\n<p>You have been practicing the division facts that always work out evenly \u2013 nothing is left over.<\/p>\n<p>Well, in the real world things are not usually so perfect!<\/p>\n<p>You have 7 candies to share among your 3 children.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-38 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2381\/2025\/01\/image347.jpeg\" alt=\"Seven candies. There are three groups of two candies with one left over.\" width=\"340\" height=\"277\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/image347.jpeg 340w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/image347-300x244.jpeg 300w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/image347-65x53.jpeg 65w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/image347-225x183.jpeg 225w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/p>\n<p>We call the left-over the remainder. For now, put R and the left over number after your quotient.<\/p>\n<p style=\"text-align: center\">[latex]7\\div3=2\\text{ R}1[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]\\begin{array}{r}2\\text{ R}1\\\\3 \\enclose{longdiv}{7}\\hspace{1.3em}\\end{array}[\/latex]<\/p>\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>Here are 22 cookies. Circle groups of 5. How many groups of 5 in 22?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-39\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2381\/2025\/01\/22-cookies.jpg\" alt=\"Twenty-two ginger-person cookies.\" width=\"1176\" height=\"349\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/22-cookies.jpg 1176w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/22-cookies-300x89.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/22-cookies-1024x304.jpg 1024w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/22-cookies-768x228.jpg 768w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/22-cookies-65x19.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/22-cookies-225x67.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/22-cookies-350x104.jpg 350w\" sizes=\"auto, (max-width: 1176px) 100vw, 1176px\" \/><\/p>\n<p>You should have 4 groups with 2 left over.<\/p>\n<p style=\"text-align: center\">[latex]22\\div5=4\\text{ R}2[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]\\begin{array}{r}4\\text{ R}2\\\\5 \\enclose{longdiv}{22}\\hspace{1.3em}\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>The remainder must not be the same size or bigger than the divisor. If it is bigger, it means another group could be made.<\/p>\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>Here are 66 suns. Make groups of 9. How many groups of 9 in 66?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-40\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2381\/2025\/01\/66-suns.jpg\" alt=\"Sixty-six suns.\" width=\"1350\" height=\"196\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/66-suns.jpg 1350w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/66-suns-300x44.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/66-suns-1024x149.jpg 1024w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/66-suns-768x112.jpg 768w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/66-suns-65x9.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/66-suns-225x33.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/66-suns-350x51.jpg 350w\" sizes=\"auto, (max-width: 1350px) 100vw, 1350px\" \/><\/p>\n<p>How many groups? 7<\/p>\n<p>How many left over? 3<\/p>\n<p style=\"text-align: center\">[latex]66\\div9=7\\text{ R}3[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]\\begin{array}{r}7\\text{ R}3\\\\9 \\enclose{longdiv}{66}\\hspace{1.3em}\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox\">Tip: The remainder must <strong>not<\/strong> be the same size or bigger than the divisor. Why not? It would make another group.<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Draw pictures to find the quotient and the remainder. Write each question using the other division sign as well. Have your instructor check your work.<\/p>\n<ol type=\"a\">\n<li>[latex]23\\div10=2\\text{ R}3[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]\\begin{array}{r}2\\text{ R}3\\\\10 \\enclose{longdiv}{23}\\hspace{1.3em}\\end{array}[\/latex]<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-41\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2381\/2025\/01\/23div10.jpg\" alt=\"23 circles. Two groups of ten circles are circled. There are three circles left over.\" width=\"300\" height=\"156\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/23div10.jpg 589w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/23div10-300x156.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/23div10-65x34.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/23div10-225x117.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math023\/wp-content\/uploads\/sites\/2381\/2025\/01\/23div10-350x182.jpg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<\/ol>\n<ol class=\"space\" start=\"2\" type=\"a\">\n<li>24 \u00f7 7 =<\/li>\n<li>19 \u00f7 3 =<\/li>\n<li>39 \u00f7 12 =<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 5<\/strong><\/p>\n<ol class=\"threecolumn\" start=\"2\" type=\"a\">\n<li>3R3<\/li>\n<li>6R1<\/li>\n<li>3R3<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>You cannot always draw pictures, so how should you find the quotients?<\/p>\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>29 \u00f7 3 =<\/p>\n<p>Use multiplication tables or the division facts to find a trial quotient. What can you multiply by 3 to find a number close to 29?<\/p>\n<ul type=\"none\">\n<li>3 \u00d7 9 = 27<\/li>\n<li>3 \u00d7 10 = 30<\/li>\n<\/ul>\n<p>Use 9 as the trial quotient. Do not use 10 because 3 \u00d7 10 = 30, which is more than the dividend 29.<\/p>\n<ol>\n<li>Divide.<br \/>\n[latex]\\begin{array}{r}9\\\\3 \\enclose{longdiv}{29}\\end{array}[\/latex]<\/li>\n<li>Multiply. 9 \u00d7 3 = 27. Write the product under the 29.<br \/>\n[latex]\\begin{array}{r}9\\\\3 \\enclose{longdiv}{29}\\\\27\\end{array}[\/latex]<\/li>\n<li>Subtract 27 from 29 to find the remainder.<br \/>\n[latex]\\begin{array}{r}9\\\\3 \\enclose{longdiv}{29}\\\\-27\\\\\\hline2\\end{array}[\/latex]<\/li>\n<li>Check (compare) to be sure the remainder is less then (&lt;) the divisor.<br \/>\n2 &lt; 3<\/li>\n<\/ol>\n<p style=\"text-align: left\"><strong>29 \u00f7 3 = 9 R2<\/strong><\/p>\n<\/div>\n<\/div>\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>60 \u00f7 7 =<\/p>\n<p>Think what can be multiplied by 7 to find a number close to 60.<\/p>\n<ul type=\"none\">\n<li>7 \u00d7 8 = 56 (good)<\/li>\n<li>7 \u00d7 9 = 63 (too big)<\/li>\n<\/ul>\n<p>Use 8 as the trial quotient.<\/p>\n<ol>\n<li>Divide.<br \/>\n[latex]\\begin{array}{r}8\\\\7 \\enclose{longdiv}{60}\\end{array}[\/latex]<\/li>\n<li>Multiply.<br \/>\n[latex]\\begin{array}{r}8\\\\7 \\enclose{longdiv}{60}\\\\56\\end{array}[\/latex]<\/li>\n<li>Subtract.<br \/>\n[latex]\\begin{array}{r}8\\\\7 \\enclose{longdiv}{60}\\\\-56\\\\\\hline4\\end{array}[\/latex]<\/li>\n<li>Compare to be sure the remainder is less than the divisor.<br \/>\n4 &lt; 7<\/li>\n<\/ol>\n<p style=\"text-align: center\"><strong>60 \u00f7 7 = 8 R4<\/strong><\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Find the quotients and remainders (divide, multiply, subtract, compare). Check your work using the answer key at the end of the exercise.<\/p>\n<ol class=\"threecolumn space\" type=\"a\">\n<li>[latex]5\\enclose{longdiv}{28}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{15}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{47}[\/latex]<\/li>\n<li>[latex]9\\enclose{longdiv}{37}[\/latex]<\/li>\n<li>[latex]2\\enclose{longdiv}{13}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{25}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{75}[\/latex]<\/li>\n<li>[latex]3\\enclose{longdiv}{19}[\/latex]<\/li>\n<li>[latex]7\\enclose{longdiv}{32}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{9}[\/latex]<\/li>\n<li>[latex]9\\enclose{longdiv}{55}[\/latex]<\/li>\n<li>[latex]10\\enclose{longdiv}{98}[\/latex]<\/li>\n<li>[latex]3\\enclose{longdiv}{26}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{47}[\/latex]<\/li>\n<li>[latex]9\\enclose{longdiv}{46}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{43}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{49}[\/latex]<\/li>\n<li>[latex]4\\enclose{longdiv}{38}[\/latex]<\/li>\n<li>[latex]2\\enclose{longdiv}{19}[\/latex]<\/li>\n<li>[latex]7\\enclose{longdiv}{61}[\/latex]<\/li>\n<li>[latex]3\\enclose{longdiv}{23}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{78}[\/latex]<\/li>\n<li>[latex]9\\enclose{longdiv}{67}[\/latex]<\/li>\n<li>[latex]6\\enclose{longdiv}{45}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 6<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>5 R3<\/li>\n<li>3 R3<\/li>\n<li>7 R5<\/li>\n<li>4 R1<\/li>\n<li>6 R1<\/li>\n<li>4 R1<\/li>\n<li>9 R3<\/li>\n<li>6 R1<\/li>\n<li>4 R4<\/li>\n<li>2 R1<\/li>\n<li>6 R1<\/li>\n<li>9 R8<\/li>\n<li>8 R2<\/li>\n<li>5 R7<\/li>\n<li>5 R1<\/li>\n<li>7 R1<\/li>\n<li>9 R4<\/li>\n<li>9 R2<\/li>\n<li>9 R1<\/li>\n<li>8 R5<\/li>\n<li>7 R2<\/li>\n<li>9 R6<\/li>\n<li>7 R4<\/li>\n<li>7 R3<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Find the quotients and remainders (divide, multiply, subtract, compare.) Check your work using the answer key at the end of the exercise.<\/p>\n<p><strong>Example<\/strong><\/p>\n<p>59 \u00f7 7 =<\/p>\n<p>Rewrite: [latex]7\\enclose{longdiv}{59}[\/latex]<\/p>\n<p>Then solve: [latex]\\begin{array}{r}8\\\\7 \\enclose{longdiv}{59}\\\\-56\\\\\\hline3\\end{array}[\/latex]<\/p>\n<p>Answer: 8 R3<\/p>\n<ol class=\"threecolumn space\" type=\"a\">\n<li>27 \u00f7 5 =<\/li>\n<li>13 \u00f7 2 =<\/li>\n<li>46 \u00f7 9 =<\/li>\n<li>38 \u00f7 6 =<\/li>\n<li>61 \u00f7 7 =<\/li>\n<li>14 \u00f7 5 =<\/li>\n<li>49 \u00f7 8 =<\/li>\n<li>28 \u00f7 3 =<\/li>\n<li>78 \u00f7 8 =<\/li>\n<li>37 \u00f7 4 =<\/li>\n<li>67 \u00f7 9 =<\/li>\n<li>52 \u00f7 6 =<\/li>\n<li>45 \u00f7 8 =<\/li>\n<li>25 \u00f7 7 =<\/li>\n<li>11 \u00f7 3 =<\/li>\n<li>53 \u00f7 9 =<\/li>\n<li>19 \u00f7 4 =<\/li>\n<li>77 \u00f7 8 =<\/li>\n<li>20 \u00f7 3 =<\/li>\n<li>11 \u00f7 2 =<\/li>\n<li>23 \u00f7 5 =<\/li>\n<li>54 \u00f7 7 =<\/li>\n<li>87 \u00f7 9 =<\/li>\n<li>9 \u00f7 4 =<\/li>\n<\/ol>\n<p><strong>Answers for Exercise 7<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>5 R2<\/li>\n<li>6 R1<\/li>\n<li>5 R1<\/li>\n<li>6 R2<\/li>\n<li>8 R5<\/li>\n<li>2 R4<\/li>\n<li>6 R1<\/li>\n<li>9 R1<\/li>\n<li>9 R6<\/li>\n<li>9 R1<\/li>\n<li>7 R4<\/li>\n<li>8 R4<\/li>\n<li>5 R5<\/li>\n<li>3 R4<\/li>\n<li>3 R2<\/li>\n<li>5 R8<\/li>\n<li>4 R3<\/li>\n<li>9 R5<\/li>\n<li>6 R2<\/li>\n<li>5 R1<\/li>\n<li>4 R3<\/li>\n<li>7 R5<\/li>\n<li>9 R6<\/li>\n<li>2 R1<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1 class=\"page-break-before\">Topic A: Self-Test<\/h1>\n<p><strong>Mark \/12\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Aim 9\/12<\/strong><\/p>\n<ol type=\"A\">\n<li>Give the answer. (6 marks)\n<ol class=\"threecolumn\" type=\"a\">\n<li>63 \u00f7 9 =<\/li>\n<li>21 \u00f7 7 =<\/li>\n<li>72 \u00f7 8 =<\/li>\n<li>36 \u00f7 4 =<\/li>\n<li>32 \u00f7 4 =<\/li>\n<li>48 \u00f7 6 =<\/li>\n<\/ol>\n<\/li>\n<li>Find the quotient. (6 marks)\n<ol class=\"threecolumn space\" type=\"a\">\n<li>[latex]6\\enclose{longdiv}{59}[\/latex]<\/li>\n<li>[latex]9\\enclose{longdiv}{87}[\/latex]<\/li>\n<li>[latex]7\\enclose{longdiv}{51}[\/latex]<\/li>\n<li>[latex]8\\enclose{longdiv}{76}[\/latex]<\/li>\n<li>[latex]5\\enclose{longdiv}{49}[\/latex]<\/li>\n<li>[latex]3\\enclose{longdiv}{26}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h2>Answers to Topic A Self-Test<\/h2>\n<ol type=\"A\">\n<li>Give the answer.\n<ol class=\"threecolumn\" type=\"a\">\n<li>7<\/li>\n<li>3<\/li>\n<li>9<\/li>\n<li>9<\/li>\n<li>8<\/li>\n<li>8<\/li>\n<\/ol>\n<\/li>\n<li>Find the quotient.\n<ol class=\"threecolumn\" type=\"a\">\n<li>9 R5<\/li>\n<li>9 R6<\/li>\n<li>7 R2<\/li>\n<li>9 R4<\/li>\n<li>9 R4<\/li>\n<li>8 R2<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n","protected":false},"author":999,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-42","chapter","type-chapter","status-publish","hentry"],"part":35,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/42","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":5,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/42\/revisions"}],"predecessor-version":[{"id":206,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapters\/42\/revisions\/206"}],"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\/42\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/media?parent=42"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/pressbooks\/v2\/chapter-type?post=42"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/contributor?post=42"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math023\/wp-json\/wp\/v2\/license?post=42"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}