{"id":53,"date":"2022-08-16T19:46:25","date_gmt":"2022-08-16T23:46:25","guid":{"rendered":"https:\/\/opentextbc.ca\/alfm2\/?post_type=chapter&#038;p=53"},"modified":"2023-01-05T18:48:39","modified_gmt":"2023-01-05T23:48:39","slug":"addition-with-carrying","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/alfm2\/chapter\/addition-with-carrying\/","title":{"raw":"Topic B: Addition with Carrying","rendered":"Topic B: Addition with Carrying"},"content":{"raw":"When the digits of one column add up to a two digit number (10 or more), you must carry the digit to the next column.<math><mtable columnalign=\"right\"><mtr><mtd><mn><\/mn><\/mtd><\/mtr><\/mtable><\/math>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example A: 27 + 55<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<img class=\"aligncenter wp-image-138 size-full\" src=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture29.png\" alt=\"\" width=\"669\" height=\"175\" \/>\r\n\r\n<strong>Step 1<\/strong>: Add the ones. 7 ones + 5 ones = 12 ones\r\n\r\nRename 12 ones as 1 ten and 2 ones. Write the 2 ones under the ones column and carry the ten to be added with the tens column.\r\n\r\n<strong>Step 2<\/strong>:Add the tens. 1 ten + 2 tens + 5 tens = 8 tens\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: 58 + 76<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<img class=\"aligncenter wp-image-139 size-full\" src=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture30.png\" alt=\"\" width=\"758\" height=\"169\" \/><strong>Step 1<\/strong>: Add the one. 8 ones + 6 ones = 14 ones\r\n\r\nRename the 14 ones as 1 ten and 4 ones.\r\n\r\nWrite the 4 ones under the ones column and carry the ten to be added with the tens column.\r\n\r\n<strong>Step 2<\/strong>: Add the tens. 1 ten + 5 tens + 7 tens = 13 tens\r\n\r\nThe 1 hundred can just be written in the sum because there are no other hundreds to add it to.\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 One<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nFind the sums. Check your work using the answer key at the end of the exercise.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;62\\\\+&amp;18 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;46\\\\+&amp;37 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;49\\\\+&amp;42 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;44\\\\+&amp;26 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;17\\\\+&amp;79 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;23\\\\+&amp;82 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;28\\\\+&amp;91 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;54\\\\+&amp;58 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;68\\\\+&amp;49 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;66\\\\+&amp;35 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;99\\\\+&amp;88 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;89\\\\+&amp;74 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;37\\\\+&amp;15 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;55\\\\+&amp;27 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;29\\\\+&amp;76 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;35\\\\+&amp;69 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;54\\\\+&amp;17 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;72\\\\+&amp;33 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;26\\\\+&amp;56 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;38\\\\+&amp;80 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise One<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>80<\/li>\r\n \t<li>83<\/li>\r\n \t<li>91<\/li>\r\n \t<li>70<\/li>\r\n \t<li>96<\/li>\r\n \t<li>105<\/li>\r\n \t<li>119<\/li>\r\n \t<li>112<\/li>\r\n \t<li>117<\/li>\r\n \t<li>101<\/li>\r\n \t<li>187<\/li>\r\n \t<li>163<\/li>\r\n \t<li>52<\/li>\r\n \t<li>82<\/li>\r\n \t<li>105<\/li>\r\n \t<li>104<\/li>\r\n \t<li>71<\/li>\r\n \t<li>105<\/li>\r\n \t<li>82<\/li>\r\n \t<li>118<\/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\">Need some extra practice? Who's the Pig? A Game of Chance.<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ul>\r\n \t<li>This game is played by two people with one set of dice. Ask your instructor for one set of dice.<\/li>\r\n \t<li>The first player to reach 100 or more points is the winner. Players take turns rolling the dice.<\/li>\r\n \t<li>You add the amounts on the dice to find your score.<\/li>\r\n \t<li>When it is your turn, you may roll as many times in a row as you like. Therefore, it is possible to score 100 or more points in one turn.<\/li>\r\n \t<li>However, during your turn if you roll a 1 on either die, you lose all your points for that turn, and your turn is over.<\/li>\r\n \t<li>If you roll a 1 on both dice, you lose all the points you have, and you have to<\/li>\r\n \t<li>start all over again at zero, and your turn is over.<\/li>\r\n<\/ul>\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: 45 + 37 + 69<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<img class=\"aligncenter wp-image-140 size-full\" src=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture31.png\" alt=\"\" width=\"744\" height=\"190\" \/>\r\n\r\n<strong>Step 1<\/strong>: Add the ones. 5 ones + 7 ones + 9 ones = 21 ones\r\n\r\nRename 21 ones as 2 tens and 1 one.\r\n\r\nWrite the one in the sum under the ones column and carry the 2 tens to the tens column.\r\n\r\n<strong>Step 2<\/strong>: Add the tens. 2 tens + 4 tens + 3 tens + 6 tens = 15 tens\r\n\r\n15 tens is 1 hundred and 5 tens.\r\n\r\nThe one hundred can just be written in the sum because there are no other hundreds to add it to.\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 Two<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nFind the sums. Check your work using the answer key at the end of the exercise.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 67\\\\&amp;78\\\\+&amp;55\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 42\\\\&amp;13\\\\+&amp;25\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 31\\\\&amp;12\\\\+&amp;49\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 23\\\\&amp;27\\\\+&amp;84\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 41\\\\&amp;52\\\\+&amp;65\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 63\\\\&amp;74\\\\+&amp;21\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 47\\\\&amp;18\\\\+&amp;55\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 12\\\\&amp;24\\\\+&amp;89\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 73\\\\&amp;21\\\\+&amp;37\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 25\\\\&amp;60\\\\+&amp;47\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 53\\\\&amp;60\\\\+&amp;71\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 14\\\\&amp;24\\\\+&amp;51\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 56\\\\&amp;23\\\\+&amp;67\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 78\\\\&amp;45\\\\+&amp;89\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 22\\\\&amp;52\\\\+&amp;64\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 35\\\\&amp;11\\\\+&amp;75\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 34\\\\&amp;32\\\\+&amp;85\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 27\\\\&amp;51\\\\+&amp;96\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 25\\\\&amp;46\\\\+&amp;43\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 36\\\\&amp;47\\\\+&amp;52\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 53\\\\&amp;67\\\\+&amp;81\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 41\\\\&amp;59\\\\+&amp;99\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 31\\\\&amp;83\\\\+&amp;27\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 76\\\\&amp;62\\\\+&amp;25\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise Two<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>200<\/li>\r\n \t<li>80<\/li>\r\n \t<li>92<\/li>\r\n \t<li>134<\/li>\r\n \t<li>158<\/li>\r\n \t<li>158<\/li>\r\n \t<li>120<\/li>\r\n \t<li>125<\/li>\r\n \t<li>131<\/li>\r\n \t<li>132<\/li>\r\n \t<li>184<\/li>\r\n \t<li>89<\/li>\r\n \t<li>146<\/li>\r\n \t<li>212<\/li>\r\n \t<li>138<\/li>\r\n \t<li>121<\/li>\r\n \t<li>151<\/li>\r\n \t<li>174<\/li>\r\n \t<li>114<\/li>\r\n \t<li>135<\/li>\r\n \t<li>201<\/li>\r\n \t<li>199<\/li>\r\n \t<li>141<\/li>\r\n \t<li>163<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nUse the same method for carrying when you add the columns of tens, hundreds, thousands, ten thousands, and so on. Look at these examples:\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example D: 347 + 438<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<img class=\"aligncenter wp-image-141 size-full\" src=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture32.png\" alt=\"\" width=\"375\" height=\"178\" \/>\r\n\r\n<strong>Step 1:<\/strong> Add the ones.\r\n\r\n4 ones + 8 ones = 12 ones = 1 ten and 2 ones\r\n\r\nWrite the 2 ones in the sum. Carry the 1 ten to the tens column.\r\n\r\n<strong>Step 2:<\/strong> Add the tens.\r\n\r\n7 + 3 + 1 ten you carried = 11 tens = 1 hundred and 1 ten Write the 1 ten. Carry the 1 hundred to the hundreds column.\r\n\r\n<strong>Step 3:<\/strong> Add the hundreds.\r\n\r\n3 + 4 + 1 hundred you carried = 8 hundreds. Write 8.\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 E: 4 974 + 2 385 + 6 890<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<img class=\"aligncenter wp-image-142 size-full\" src=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture33.png\" alt=\"\" width=\"399\" height=\"196\" \/>\r\n\r\n<strong>Step 1:<\/strong> Add the ones. 9 ones (write 9 ones in the sum)\r\n\r\n<strong>Step 2:<\/strong> Add the tens. 24 tens = 2 hundreds + 4 tens (write 4 tens) Carry the 2 hundreds to the hundreds column.\r\n\r\n<strong>Step 3:<\/strong> Add the hundreds and the 2 hundreds you carried.\r\n\r\n22 hundreds = 2 thousands + 2 hundreds (write 2 hundreds)\r\n\r\n<strong>Step 4:<\/strong> Add the thousands and the 2 thousands you carried.\r\n\r\n14 thousands = 1 ten thousand + 4 thousands Write 14 thousands in the sum.\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 F: 246 476 + 873 706<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<img class=\"aligncenter wp-image-143 size-full\" src=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture34.png\" alt=\"\" width=\"427\" height=\"168\" \/>\r\n\r\n<strong>Step 1:<\/strong> Add the ones. 12 ones = 1 ten + 2 ones Write 2 ones in the sum, carry the 1 ten over.\r\n\r\n<strong>Step 2:<\/strong> Add the tens. 8 tens\r\n\r\nWrite 8 tens in the sum, nothing to carry.\r\n\r\n<strong>Step 3:<\/strong> Add the hundreds. 11 hundreds = 1 thousand + 1 hundred Write 1 hundred in the sum, carry the 1 thousand.\r\n\r\n<strong>Step 4:<\/strong> Add the thousands. 10 thousands = 1 ten thousand + 0 thousands Be sure to write the 0 to hold the thousands place in the sum.\r\n\r\nCarry the 1 ten thousand.\r\n\r\n<strong>Step 5:<\/strong> Add the ten thousands.\r\n\r\n12 ten thousands = 1 hundred thousand + 2 ten thousands\r\n\r\nWrite the 2 ten thousands in the sum, carry the 1 hundred thousand.\r\n\r\n<strong>Step 6:<\/strong> Add the hundred thousands.\r\n\r\n11 hundred thousands = 1 million + 1 hundred thousand Write 1 million and the 1 hundred thousand in the sum.\r\n\r\nAnd to read the answer, say, one million, one hundred twenty thousand, one hundred eight-two.\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 Three<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nFind the sums. Check your work using the answer key at the end of the exercise.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;231\\\\+&amp;452 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;520\\\\+&amp;239 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;481\\\\+&amp;306 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;306\\\\+&amp;83 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;5\\,237\\\\ + 2\\,549 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;2\\,846 \\\\+&amp; 1\\,437 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;5\\,128\\\\+&amp; 4\\,907 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;6\\,005\\\\+&amp; 239 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;8\\,106\\\\+&amp; 3\\,923 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;5\\,028\\\\+&amp; 4\\,907 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;6\\,005\\\\+&amp; 273 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;2\\,648\\\\+&amp; 1\\,838 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;5\\,837\\\\+&amp; 2\\,569 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;2\\,846\\\\+&amp; 1\\,457 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;3\\,517\\\\+&amp; 4\\,296 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;9\\,020\\\\+&amp; 684 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;2\\,648 \\\\+&amp; 1\\,238 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp;5\\,237\\\\+&amp; 6\\,968 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise Three<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>683<\/li>\r\n \t<li>759<\/li>\r\n \t<li>787<\/li>\r\n \t<li>389<\/li>\r\n \t<li>7<span style=\"margin-left: 0.25em;\">786<\/span><\/li>\r\n \t<li>4<span style=\"margin-left: 0.25em;\">283<\/span><\/li>\r\n \t<li>10<span style=\"margin-left: 0.25em;\">035<\/span><\/li>\r\n \t<li>6<span style=\"margin-left: 0.25em;\">244<\/span><\/li>\r\n \t<li>12<span style=\"margin-left: 0.25em;\">029<\/span><\/li>\r\n \t<li>9<span style=\"margin-left: 0.25em;\">935<\/span><\/li>\r\n \t<li>6<span style=\"margin-left: 0.25em;\">278<\/span><\/li>\r\n \t<li>4<span style=\"margin-left: 0.25em;\">486<\/span><\/li>\r\n \t<li>8<span style=\"margin-left: 0.25em;\">406<\/span><\/li>\r\n \t<li>4<span style=\"margin-left: 0.25em;\">303<\/span><\/li>\r\n \t<li>7<span style=\"margin-left: 0.25em;\">813<\/span><\/li>\r\n \t<li>9<span style=\"margin-left: 0.25em;\">704<\/span><\/li>\r\n \t<li>3<span style=\"margin-left: 0.25em;\">886<\/span><\/li>\r\n \t<li>12<span style=\"margin-left: 0.25em;\">205<\/span><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nIf you are having any problems with this work, ask your instructor to check your method of addition with carrying before you go any further.\r\n\r\nIf you feel that you need more practice, your instructor will give you more addition questions to do.\r\n<h1>Adding Across<\/h1>\r\nIf an addition question is written with the numbers side by side, rewrite the question in columns. Put the ones under the ones, the tens under the tens, the hundreds under the hundreds, and so on.\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example G: 263 + 25<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[latex]\\begin{array}[t]{rr}&amp; 263\\\\+&amp;25\\\\ \\hline &amp;288 \\end{array}[\/latex]\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 H: 316 + 9 560<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[latex]\\begin{array}[t]{rr}&amp; 316 \\\\+ &amp;9 560\\\\ \\hline &amp;9876 \\end{array}[\/latex]\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 Four<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nRewrite each question in columns. Be careful to write ones under ones, tens under tens, hundreds under hundreds, and so on. Check your work using the answer key at the end of the exercise.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>476 + 392 + 483 =<\/li>\r\n \t<li>986 + 483 + 524 =<\/li>\r\n \t<li>3<span style=\"margin-left: 0.25em;\">714<\/span> + 3<span style=\"margin-left: 0.25em;\">189<\/span> + 4<span style=\"margin-left: 0.25em;\">582<\/span> =<\/li>\r\n \t<li>466 + 5<span style=\"margin-left: 0.25em;\">973<\/span> + 821 + 83 =<\/li>\r\n \t<li>697 + 7<span style=\"margin-left: 0.25em;\">639<\/span> + 27 + 5<span style=\"margin-left: 0.25em;\">396<\/span> =<\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em;\">436<\/span> + 844 + 16<span style=\"margin-left: 0.25em;\">009<\/span> =<\/li>\r\n \t<li>242<span style=\"margin-left: 0.25em;\">100<\/span> + 62<span style=\"margin-left: 0.25em;\">418<\/span> + 32 + 528<span style=\"margin-left: 0.25em;\">002<\/span> =<\/li>\r\n \t<li>279<span style=\"margin-left: 0.25em;\">661<\/span> + 475 + 49<span style=\"margin-left: 0.25em;\">264<\/span> =<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise Four<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>1<span style=\"margin-left: 0.25em;\">351<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em;\">993<\/span><\/li>\r\n \t<li>11<span style=\"margin-left: 0.25em;\">485<\/span><\/li>\r\n \t<li>7<span style=\"margin-left: 0.25em;\">343<\/span><\/li>\r\n \t<li>13<span style=\"margin-left: 0.25em;\">759<\/span><\/li>\r\n \t<li>18<span style=\"margin-left: 0.25em;\">289<\/span><\/li>\r\n \t<li>832<span style=\"margin-left: 0.25em;\">552<\/span><\/li>\r\n \t<li>329<span style=\"margin-left: 0.25em;\">400<\/span><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Topic B: Self-Test<\/h1>\r\n<strong>Mark\u00a0\u00a0 \/15\u00a0\u00a0\u00a0 Aim 12\/15<\/strong>\r\n<ol type=\"A\">\r\n \t<li>Find the sums. Be sure to check your answers. (12 marks)\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 85\\\\+&amp;57 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 94\\\\+&amp;48 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 982\\\\+&amp;743 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 829\\\\+&amp;303 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 7\\,834\\\\+&amp; 2\\,169\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 5\\,976 \\\\+&amp; 2\\,081\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 46\\,940\\\\+&amp; 86\\,502\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 41\\,801\\\\+&amp; 39\\,199\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 3\\,742 \\\\&amp; 4\\,108 \\\\+&amp; 7\\,336\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 12\\,350 \\\\&amp;17\\,629\\\\+&amp; 23\\,244\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 352\\,641 \\\\&amp;432\\,345 \\\\+&amp; 720\\,250\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}[t]{rr}&amp; 18\\,060 \\\\&amp;62\\,549 \\\\&amp;1\\,375 \\\\+&amp; 399\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Add these numbers. (3 marks)\r\n<ol type=\"a\">\r\n \t<li>74 + 32 + 67 + 85 =<\/li>\r\n \t<li>721 + 8<span style=\"margin-left: 0.25em;\">462<\/span> + 968 + 99 =<\/li>\r\n \t<li>389 + 2<span style=\"margin-left: 0.25em;\">517<\/span> + 2 =<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h2>Answers to Topic B Self-Test<\/h2>\r\n<ol type=\"A\">\r\n \t<li>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>142<\/li>\r\n \t<li>142<\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em;\">725<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em;\">132<\/span><\/li>\r\n \t<li>10<span style=\"margin-left: 0.25em;\">003<\/span><\/li>\r\n \t<li>8<span style=\"margin-left: 0.25em;\">057<\/span><\/li>\r\n \t<li>133<span style=\"margin-left: 0.25em;\">442<\/span><\/li>\r\n \t<li>81<span style=\"margin-left: 0.25em;\">000<\/span><\/li>\r\n \t<li>15<span style=\"margin-left: 0.25em;\">186<\/span><\/li>\r\n \t<li>53<span style=\"margin-left: 0.25em;\">223<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em;\">505<\/span><span style=\"margin-left: 0.25em;\">236<\/span><\/li>\r\n \t<li>82<span style=\"margin-left: 0.25em;\">383<\/span><\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>258<\/li>\r\n \t<li>10<span style=\"margin-left: 0.25em;\">250<\/span><\/li>\r\n \t<li>2<span style=\"margin-left: 0.25em;\">908<\/span><\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>","rendered":"<p>When the digits of one column add up to a two digit number (10 or more), you must carry the digit to the next column.<math><mtable columnalign=\"right\"><mtr><mtd><mn><\/mn><\/mtd><\/mtr><\/mtable><\/math><\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example A: 27 + 55<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-138 size-full\" src=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture29.png\" alt=\"\" width=\"669\" height=\"175\" srcset=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture29.png 669w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture29-300x78.png 300w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture29-65x17.png 65w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture29-225x59.png 225w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture29-350x92.png 350w\" sizes=\"auto, (max-width: 669px) 100vw, 669px\" \/><\/p>\n<p><strong>Step 1<\/strong>: Add the ones. 7 ones + 5 ones = 12 ones<\/p>\n<p>Rename 12 ones as 1 ten and 2 ones. Write the 2 ones under the ones column and carry the ten to be added with the tens column.<\/p>\n<p><strong>Step 2<\/strong>:Add the tens. 1 ten + 2 tens + 5 tens = 8 tens<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example B: 58 + 76<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-139 size-full\" src=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture30.png\" alt=\"\" width=\"758\" height=\"169\" srcset=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture30.png 758w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture30-300x67.png 300w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture30-65x14.png 65w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture30-225x50.png 225w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture30-350x78.png 350w\" sizes=\"auto, (max-width: 758px) 100vw, 758px\" \/><strong>Step 1<\/strong>: Add the one. 8 ones + 6 ones = 14 ones<\/p>\n<p>Rename the 14 ones as 1 ten and 4 ones.<\/p>\n<p>Write the 4 ones under the ones column and carry the ten to be added with the tens column.<\/p>\n<p><strong>Step 2<\/strong>: Add the tens. 1 ten + 5 tens + 7 tens = 13 tens<\/p>\n<p>The 1 hundred can just be written in the sum because there are no other hundreds to add it to.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise One<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Find the sums. Check your work using the answer key at the end of the exercise.<\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>[latex]\\begin{array}[t]{rr}&62\\\\+&18 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&46\\\\+&37 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&49\\\\+&42 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&44\\\\+&26 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&17\\\\+&79 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&23\\\\+&82 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&28\\\\+&91 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&54\\\\+&58 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&68\\\\+&49 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&66\\\\+&35 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&99\\\\+&88 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&89\\\\+&74 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&37\\\\+&15 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&55\\\\+&27 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&29\\\\+&76 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&35\\\\+&69 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&54\\\\+&17 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&72\\\\+&33 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&26\\\\+&56 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&38\\\\+&80 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise One<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>80<\/li>\n<li>83<\/li>\n<li>91<\/li>\n<li>70<\/li>\n<li>96<\/li>\n<li>105<\/li>\n<li>119<\/li>\n<li>112<\/li>\n<li>117<\/li>\n<li>101<\/li>\n<li>187<\/li>\n<li>163<\/li>\n<li>52<\/li>\n<li>82<\/li>\n<li>105<\/li>\n<li>104<\/li>\n<li>71<\/li>\n<li>105<\/li>\n<li>82<\/li>\n<li>118<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Need some extra practice? Who&#8217;s the Pig? A Game of Chance.<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ul>\n<li>This game is played by two people with one set of dice. Ask your instructor for one set of dice.<\/li>\n<li>The first player to reach 100 or more points is the winner. Players take turns rolling the dice.<\/li>\n<li>You add the amounts on the dice to find your score.<\/li>\n<li>When it is your turn, you may roll as many times in a row as you like. Therefore, it is possible to score 100 or more points in one turn.<\/li>\n<li>However, during your turn if you roll a 1 on either die, you lose all your points for that turn, and your turn is over.<\/li>\n<li>If you roll a 1 on both dice, you lose all the points you have, and you have to<\/li>\n<li>start all over again at zero, and your turn is over.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example C: 45 + 37 + 69<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-140 size-full\" src=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture31.png\" alt=\"\" width=\"744\" height=\"190\" srcset=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture31.png 744w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture31-300x77.png 300w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture31-65x17.png 65w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture31-225x57.png 225w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture31-350x89.png 350w\" sizes=\"auto, (max-width: 744px) 100vw, 744px\" \/><\/p>\n<p><strong>Step 1<\/strong>: Add the ones. 5 ones + 7 ones + 9 ones = 21 ones<\/p>\n<p>Rename 21 ones as 2 tens and 1 one.<\/p>\n<p>Write the one in the sum under the ones column and carry the 2 tens to the tens column.<\/p>\n<p><strong>Step 2<\/strong>: Add the tens. 2 tens + 4 tens + 3 tens + 6 tens = 15 tens<\/p>\n<p>15 tens is 1 hundred and 5 tens.<\/p>\n<p>The one hundred can just be written in the sum because there are no other hundreds to add it to.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise Two<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Find the sums. Check your work using the answer key at the end of the exercise.<\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>[latex]\\begin{array}[t]{rr}& 67\\\\&78\\\\+&55\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 42\\\\&13\\\\+&25\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 31\\\\&12\\\\+&49\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 23\\\\&27\\\\+&84\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 41\\\\&52\\\\+&65\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 63\\\\&74\\\\+&21\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 47\\\\&18\\\\+&55\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 12\\\\&24\\\\+&89\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 73\\\\&21\\\\+&37\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 25\\\\&60\\\\+&47\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 53\\\\&60\\\\+&71\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 14\\\\&24\\\\+&51\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 56\\\\&23\\\\+&67\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 78\\\\&45\\\\+&89\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 22\\\\&52\\\\+&64\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 35\\\\&11\\\\+&75\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 34\\\\&32\\\\+&85\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 27\\\\&51\\\\+&96\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 25\\\\&46\\\\+&43\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 36\\\\&47\\\\+&52\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 53\\\\&67\\\\+&81\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 41\\\\&59\\\\+&99\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 31\\\\&83\\\\+&27\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 76\\\\&62\\\\+&25\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise Two<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>200<\/li>\n<li>80<\/li>\n<li>92<\/li>\n<li>134<\/li>\n<li>158<\/li>\n<li>158<\/li>\n<li>120<\/li>\n<li>125<\/li>\n<li>131<\/li>\n<li>132<\/li>\n<li>184<\/li>\n<li>89<\/li>\n<li>146<\/li>\n<li>212<\/li>\n<li>138<\/li>\n<li>121<\/li>\n<li>151<\/li>\n<li>174<\/li>\n<li>114<\/li>\n<li>135<\/li>\n<li>201<\/li>\n<li>199<\/li>\n<li>141<\/li>\n<li>163<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>Use the same method for carrying when you add the columns of tens, hundreds, thousands, ten thousands, and so on. Look at these examples:<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example D: 347 + 438<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-141 size-full\" src=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture32.png\" alt=\"\" width=\"375\" height=\"178\" srcset=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture32.png 375w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture32-300x142.png 300w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture32-65x31.png 65w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture32-225x107.png 225w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture32-350x166.png 350w\" sizes=\"auto, (max-width: 375px) 100vw, 375px\" \/><\/p>\n<p><strong>Step 1:<\/strong> Add the ones.<\/p>\n<p>4 ones + 8 ones = 12 ones = 1 ten and 2 ones<\/p>\n<p>Write the 2 ones in the sum. Carry the 1 ten to the tens column.<\/p>\n<p><strong>Step 2:<\/strong> Add the tens.<\/p>\n<p>7 + 3 + 1 ten you carried = 11 tens = 1 hundred and 1 ten Write the 1 ten. Carry the 1 hundred to the hundreds column.<\/p>\n<p><strong>Step 3:<\/strong> Add the hundreds.<\/p>\n<p>3 + 4 + 1 hundred you carried = 8 hundreds. Write 8.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example E: 4 974 + 2 385 + 6 890<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-142 size-full\" src=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture33.png\" alt=\"\" width=\"399\" height=\"196\" srcset=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture33.png 399w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture33-300x147.png 300w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture33-65x32.png 65w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture33-225x111.png 225w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture33-350x172.png 350w\" sizes=\"auto, (max-width: 399px) 100vw, 399px\" \/><\/p>\n<p><strong>Step 1:<\/strong> Add the ones. 9 ones (write 9 ones in the sum)<\/p>\n<p><strong>Step 2:<\/strong> Add the tens. 24 tens = 2 hundreds + 4 tens (write 4 tens) Carry the 2 hundreds to the hundreds column.<\/p>\n<p><strong>Step 3:<\/strong> Add the hundreds and the 2 hundreds you carried.<\/p>\n<p>22 hundreds = 2 thousands + 2 hundreds (write 2 hundreds)<\/p>\n<p><strong>Step 4:<\/strong> Add the thousands and the 2 thousands you carried.<\/p>\n<p>14 thousands = 1 ten thousand + 4 thousands Write 14 thousands in the sum.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example F: 246 476 + 873 706<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-143 size-full\" src=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture34.png\" alt=\"\" width=\"427\" height=\"168\" srcset=\"https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture34.png 427w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture34-300x118.png 300w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture34-65x26.png 65w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture34-225x89.png 225w, https:\/\/opentextbc.ca\/alfm2\/wp-content\/uploads\/sites\/407\/2022\/08\/Picture34-350x138.png 350w\" sizes=\"auto, (max-width: 427px) 100vw, 427px\" \/><\/p>\n<p><strong>Step 1:<\/strong> Add the ones. 12 ones = 1 ten + 2 ones Write 2 ones in the sum, carry the 1 ten over.<\/p>\n<p><strong>Step 2:<\/strong> Add the tens. 8 tens<\/p>\n<p>Write 8 tens in the sum, nothing to carry.<\/p>\n<p><strong>Step 3:<\/strong> Add the hundreds. 11 hundreds = 1 thousand + 1 hundred Write 1 hundred in the sum, carry the 1 thousand.<\/p>\n<p><strong>Step 4:<\/strong> Add the thousands. 10 thousands = 1 ten thousand + 0 thousands Be sure to write the 0 to hold the thousands place in the sum.<\/p>\n<p>Carry the 1 ten thousand.<\/p>\n<p><strong>Step 5:<\/strong> Add the ten thousands.<\/p>\n<p>12 ten thousands = 1 hundred thousand + 2 ten thousands<\/p>\n<p>Write the 2 ten thousands in the sum, carry the 1 hundred thousand.<\/p>\n<p><strong>Step 6:<\/strong> Add the hundred thousands.<\/p>\n<p>11 hundred thousands = 1 million + 1 hundred thousand Write 1 million and the 1 hundred thousand in the sum.<\/p>\n<p>And to read the answer, say, one million, one hundred twenty thousand, one hundred eight-two.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise Three<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Find the sums. Check your work using the answer key at the end of the exercise.<\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>[latex]\\begin{array}[t]{rr}&231\\\\+&452 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&520\\\\+&239 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&481\\\\+&306 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&306\\\\+&83 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&5\\,237\\\\ + 2\\,549 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&2\\,846 \\\\+& 1\\,437 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&5\\,128\\\\+& 4\\,907 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&6\\,005\\\\+& 239 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&8\\,106\\\\+& 3\\,923 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&5\\,028\\\\+& 4\\,907 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&6\\,005\\\\+& 273 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&2\\,648\\\\+& 1\\,838 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&5\\,837\\\\+& 2\\,569 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&2\\,846\\\\+& 1\\,457 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&3\\,517\\\\+& 4\\,296 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&9\\,020\\\\+& 684 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&2\\,648 \\\\+& 1\\,238 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}&5\\,237\\\\+& 6\\,968 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise Three<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>683<\/li>\n<li>759<\/li>\n<li>787<\/li>\n<li>389<\/li>\n<li>7<span style=\"margin-left: 0.25em;\">786<\/span><\/li>\n<li>4<span style=\"margin-left: 0.25em;\">283<\/span><\/li>\n<li>10<span style=\"margin-left: 0.25em;\">035<\/span><\/li>\n<li>6<span style=\"margin-left: 0.25em;\">244<\/span><\/li>\n<li>12<span style=\"margin-left: 0.25em;\">029<\/span><\/li>\n<li>9<span style=\"margin-left: 0.25em;\">935<\/span><\/li>\n<li>6<span style=\"margin-left: 0.25em;\">278<\/span><\/li>\n<li>4<span style=\"margin-left: 0.25em;\">486<\/span><\/li>\n<li>8<span style=\"margin-left: 0.25em;\">406<\/span><\/li>\n<li>4<span style=\"margin-left: 0.25em;\">303<\/span><\/li>\n<li>7<span style=\"margin-left: 0.25em;\">813<\/span><\/li>\n<li>9<span style=\"margin-left: 0.25em;\">704<\/span><\/li>\n<li>3<span style=\"margin-left: 0.25em;\">886<\/span><\/li>\n<li>12<span style=\"margin-left: 0.25em;\">205<\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>If you are having any problems with this work, ask your instructor to check your method of addition with carrying before you go any further.<\/p>\n<p>If you feel that you need more practice, your instructor will give you more addition questions to do.<\/p>\n<h1>Adding Across<\/h1>\n<p>If an addition question is written with the numbers side by side, rewrite the question in columns. Put the ones under the ones, the tens under the tens, the hundreds under the hundreds, and so on.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example G: 263 + 25<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>[latex]\\begin{array}[t]{rr}& 263\\\\+&25\\\\ \\hline &288 \\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example H: 316 + 9 560<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>[latex]\\begin{array}[t]{rr}& 316 \\\\+ &9 560\\\\ \\hline &9876 \\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise Four<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Rewrite each question in columns. Be careful to write ones under ones, tens under tens, hundreds under hundreds, and so on. Check your work using the answer key at the end of the exercise.<\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>476 + 392 + 483 =<\/li>\n<li>986 + 483 + 524 =<\/li>\n<li>3<span style=\"margin-left: 0.25em;\">714<\/span> + 3<span style=\"margin-left: 0.25em;\">189<\/span> + 4<span style=\"margin-left: 0.25em;\">582<\/span> =<\/li>\n<li>466 + 5<span style=\"margin-left: 0.25em;\">973<\/span> + 821 + 83 =<\/li>\n<li>697 + 7<span style=\"margin-left: 0.25em;\">639<\/span> + 27 + 5<span style=\"margin-left: 0.25em;\">396<\/span> =<\/li>\n<li>1<span style=\"margin-left: 0.25em;\">436<\/span> + 844 + 16<span style=\"margin-left: 0.25em;\">009<\/span> =<\/li>\n<li>242<span style=\"margin-left: 0.25em;\">100<\/span> + 62<span style=\"margin-left: 0.25em;\">418<\/span> + 32 + 528<span style=\"margin-left: 0.25em;\">002<\/span> =<\/li>\n<li>279<span style=\"margin-left: 0.25em;\">661<\/span> + 475 + 49<span style=\"margin-left: 0.25em;\">264<\/span> =<\/li>\n<\/ol>\n<p><strong>Answers to Exercise Four<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>1<span style=\"margin-left: 0.25em;\">351<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em;\">993<\/span><\/li>\n<li>11<span style=\"margin-left: 0.25em;\">485<\/span><\/li>\n<li>7<span style=\"margin-left: 0.25em;\">343<\/span><\/li>\n<li>13<span style=\"margin-left: 0.25em;\">759<\/span><\/li>\n<li>18<span style=\"margin-left: 0.25em;\">289<\/span><\/li>\n<li>832<span style=\"margin-left: 0.25em;\">552<\/span><\/li>\n<li>329<span style=\"margin-left: 0.25em;\">400<\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Topic B: Self-Test<\/h1>\n<p><strong>Mark\u00a0\u00a0 \/15\u00a0\u00a0\u00a0 Aim 12\/15<\/strong><\/p>\n<ol type=\"A\">\n<li>Find the sums. Be sure to check your answers. (12 marks)\n<ol class=\"threecolumn\" type=\"a\">\n<li>[latex]\\begin{array}[t]{rr}& 85\\\\+&57 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 94\\\\+&48 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 982\\\\+&743 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 829\\\\+&303 \\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 7\\,834\\\\+& 2\\,169\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 5\\,976 \\\\+& 2\\,081\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 46\\,940\\\\+& 86\\,502\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 41\\,801\\\\+& 39\\,199\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 3\\,742 \\\\& 4\\,108 \\\\+& 7\\,336\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 12\\,350 \\\\&17\\,629\\\\+& 23\\,244\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 352\\,641 \\\\&432\\,345 \\\\+& 720\\,250\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}[t]{rr}& 18\\,060 \\\\&62\\,549 \\\\&1\\,375 \\\\+& 399\\\\ \\hline \\\\ \\end{array}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Add these numbers. (3 marks)\n<ol type=\"a\">\n<li>74 + 32 + 67 + 85 =<\/li>\n<li>721 + 8<span style=\"margin-left: 0.25em;\">462<\/span> + 968 + 99 =<\/li>\n<li>389 + 2<span style=\"margin-left: 0.25em;\">517<\/span> + 2 =<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h2>Answers to Topic B Self-Test<\/h2>\n<ol type=\"A\">\n<li>\n<ol class=\"threecolumn\" type=\"a\">\n<li>142<\/li>\n<li>142<\/li>\n<li>1<span style=\"margin-left: 0.25em;\">725<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em;\">132<\/span><\/li>\n<li>10<span style=\"margin-left: 0.25em;\">003<\/span><\/li>\n<li>8<span style=\"margin-left: 0.25em;\">057<\/span><\/li>\n<li>133<span style=\"margin-left: 0.25em;\">442<\/span><\/li>\n<li>81<span style=\"margin-left: 0.25em;\">000<\/span><\/li>\n<li>15<span style=\"margin-left: 0.25em;\">186<\/span><\/li>\n<li>53<span style=\"margin-left: 0.25em;\">223<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em;\">505<\/span><span style=\"margin-left: 0.25em;\">236<\/span><\/li>\n<li>82<span style=\"margin-left: 0.25em;\">383<\/span><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol class=\"threecolumn\" type=\"a\">\n<li>258<\/li>\n<li>10<span style=\"margin-left: 0.25em;\">250<\/span><\/li>\n<li>2<span style=\"margin-left: 0.25em;\">908<\/span><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n","protected":false},"author":90,"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-53","chapter","type-chapter","status-publish","hentry"],"part":49,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/alfm2\/wp-json\/pressbooks\/v2\/chapters\/53","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/alfm2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/alfm2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/alfm2\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":26,"href":"https:\/\/opentextbc.ca\/alfm2\/wp-json\/pressbooks\/v2\/chapters\/53\/revisions"}],"predecessor-version":[{"id":664,"href":"https:\/\/opentextbc.ca\/alfm2\/wp-json\/pressbooks\/v2\/chapters\/53\/revisions\/664"}],"part":[{"href":"https:\/\/opentextbc.ca\/alfm2\/wp-json\/pressbooks\/v2\/parts\/49"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/alfm2\/wp-json\/pressbooks\/v2\/chapters\/53\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/alfm2\/wp-json\/wp\/v2\/media?parent=53"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/alfm2\/wp-json\/pressbooks\/v2\/chapter-type?post=53"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/alfm2\/wp-json\/wp\/v2\/contributor?post=53"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/alfm2\/wp-json\/wp\/v2\/license?post=53"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}