{"id":4595,"date":"2020-04-21T00:19:05","date_gmt":"2020-04-21T00:19:05","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/adding-whole-numbers-properties-of-addition\/"},"modified":"2022-04-05T00:04:28","modified_gmt":"2022-04-05T00:04:28","slug":"adding-whole-numbers-properties-of-addition","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/adding-whole-numbers-properties-of-addition\/","title":{"raw":"Adding Whole Numbers: Properties of Addition","rendered":"Adding Whole Numbers: Properties of Addition"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Identify and use the identity property of addition<\/li>\r\n \t<li>Identify and use the commutative property of addition<\/li>\r\n \t<li>Add multiple-digit numbers using columns for place value<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<h2>Add Whole Numbers Without Models<\/h2>\r\nNow that we have used models to add numbers, we can move on to adding without models. Before we do that, make sure you know all the one digit addition facts. You will need to use these number facts when you add larger numbers.\r\n\r\nImagine filling in the table below\u00a0by adding each row number along the left side to each column number across the top.\u00a0You can use this table for reference, but it will make your work faster and easier if you have the sums memorized.\r\n<table id=\"fs-id2300206\" class=\"column-header\" style=\"width: 40%;\" summary=\"No Summary\">\r\n<thead>\r\n<tr style=\"height: 15px;\" valign=\"middle\">\r\n<th style=\"width: 20px; height: 15px;\">+<\/th>\r\n<th style=\"width: 20px; height: 15px;\">[latex]0[\/latex]<\/th>\r\n<th style=\"width: 26.6667px; height: 15px;\">[latex]1[\/latex]<\/th>\r\n<th style=\"width: 26.6667px; height: 15px;\">[latex]2[\/latex]<\/th>\r\n<th style=\"width: 26.6667px; height: 15px;\">[latex]3[\/latex]<\/th>\r\n<th style=\"width: 26.6667px; height: 15px;\">[latex]4[\/latex]<\/th>\r\n<th style=\"width: 26.6667px; height: 15px;\">[latex]5[\/latex]<\/th>\r\n<th style=\"width: 26.6667px; height: 15px;\">[latex]6[\/latex]<\/th>\r\n<th style=\"width: 26.6667px; height: 15px;\">[latex]7[\/latex]<\/th>\r\n<th style=\"width: 26.6667px; height: 15px;\">[latex]8[\/latex]<\/th>\r\n<th style=\"width: 27.7778px; height: 15px;\">[latex]9[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 15px;\" valign=\"middle\">\r\n<td style=\"width: 20px; height: 15px;\">[latex]0[\/latex]<\/td>\r\n<td style=\"width: 20px; height: 15px;\">[latex]0[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]1[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]2[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]3[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]4[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]5[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]6[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]7[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]8[\/latex]<\/td>\r\n<td style=\"width: 27.7778px; height: 15px;\">[latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\" valign=\"middle\">\r\n<td style=\"width: 20px; height: 15px;\">[latex]1[\/latex]<\/td>\r\n<td style=\"width: 20px; height: 15px;\">[latex]1[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]2[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]3[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]4[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]5[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]6[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]7[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]8[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]9[\/latex]<\/td>\r\n<td style=\"width: 27.7778px; height: 15px;\">[latex]10[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15.9688px;\" valign=\"middle\">\r\n<td style=\"width: 20px; height: 15.9688px;\">[latex]2[\/latex]<\/td>\r\n<td style=\"width: 20px; height: 15.9688px;\">[latex]2[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15.9688px;\">[latex]3[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15.9688px;\">[latex]4[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15.9688px;\">[latex]5[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15.9688px;\">[latex]6[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15.9688px;\">[latex]7[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15.9688px;\">[latex]8[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15.9688px;\">[latex]9[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15.9688px;\">[latex]10[\/latex]<\/td>\r\n<td style=\"width: 27.7778px; height: 15.9688px;\">[latex]11[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\" valign=\"middle\">\r\n<td style=\"width: 20px; height: 15px;\">[latex]3[\/latex]<\/td>\r\n<td style=\"width: 20px; height: 15px;\">[latex]3[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]4[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]5[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]6[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]7[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]8[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]9[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]10[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]11[\/latex]<\/td>\r\n<td style=\"width: 27.7778px; height: 15px;\">[latex]12[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\" valign=\"middle\">\r\n<td style=\"width: 20px; height: 15px;\">[latex]4[\/latex]<\/td>\r\n<td style=\"width: 20px; height: 15px;\">[latex]4[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]5[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]6[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]7[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]8[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]9[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]10[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]11[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]12[\/latex]<\/td>\r\n<td style=\"width: 27.7778px; height: 15px;\">[latex]13[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\" valign=\"middle\">\r\n<td style=\"width: 20px; height: 15px;\">[latex]5[\/latex]<\/td>\r\n<td style=\"width: 20px; height: 15px;\">[latex]5[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]6[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]7[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]8[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]9[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]10[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]11[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]12[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]13[\/latex]<\/td>\r\n<td style=\"width: 27.7778px; height: 15px;\">[latex]14[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\" valign=\"middle\">\r\n<td style=\"width: 20px; height: 15px;\">[latex]6[\/latex]<\/td>\r\n<td style=\"width: 20px; height: 15px;\">[latex]6[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]7[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]8[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]9[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]10[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]11[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]12[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]13[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]14[\/latex]<\/td>\r\n<td style=\"width: 27.7778px; height: 15px;\">[latex]15[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\" valign=\"middle\">\r\n<td style=\"width: 20px; height: 15px;\">[latex]7[\/latex]<\/td>\r\n<td style=\"width: 20px; height: 15px;\">[latex]7[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]8[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]9[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]10[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]11[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]12[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]13[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]14[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]15[\/latex]<\/td>\r\n<td style=\"width: 27.7778px; height: 15px;\">[latex]16[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\" valign=\"middle\">\r\n<td style=\"width: 20px; height: 15px;\">[latex]8[\/latex]<\/td>\r\n<td style=\"width: 20px; height: 15px;\">[latex]8[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]9[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]10[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]11[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]12[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]13[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]14[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]15[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]16[\/latex]<\/td>\r\n<td style=\"width: 27.7778px; height: 15px;\">[latex]17[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\" valign=\"middle\">\r\n<td style=\"width: 20px; height: 15px;\">[latex]9[\/latex]<\/td>\r\n<td style=\"width: 20px; height: 15px;\">[latex]9[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]10[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]11[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]12[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]13[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]14[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]15[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]16[\/latex]<\/td>\r\n<td style=\"width: 26.6667px; height: 15px;\">[latex]17[\/latex]<\/td>\r\n<td style=\"width: 27.7778px; height: 15px;\">[latex]18[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nDid you notice what happens when you add zero to a number? The sum of any number and zero is the number itself. We call this the Identity Property of Addition. Zero is called the additive identity.\r\n<div class=\"textbox shaded\">\r\n<h3>Identity Property of Addition<\/h3>\r\nThe sum of any number [latex]a[\/latex] and [latex]0[\/latex] is the number.\r\n\r\n[latex]\\begin{array}{}\\\\ a+0=a\\\\ 0+a=a\\end{array}[\/latex]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nFind each sum:\r\n<ol>\r\n \t<li>[latex]0+11[\/latex]<\/li>\r\n \t<li>[latex]42+0[\/latex]<\/li>\r\n<\/ol>\r\nSolution\r\n<table id=\"eip-629\" class=\"unnumbered unstyled\" summary=\"Solution for A: The first addend is zero. The sum of any number and zero is the number. 0+11=11 Solution for B: The second addend is zero. The sum of any number and zero is the number. 42 + 0 = 42\">\r\n<tbody>\r\n<tr>\r\n<td>1. \u00a0The first addend is zero. The sum of any number and zero is the number.<\/td>\r\n<td>[latex]0+11=11[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2. The second addend is zero. The sum of any number and zero is the number.<\/td>\r\n<td>[latex]42+0=42[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]143190[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nLook at the pairs of sums:\r\n<table id=\"eip-id1168287208889\" class=\"unnumbered unstyled\" summary=\" \">\r\n<tbody>\r\n<tr>\r\n<td>[latex]2+3=5[\/latex]<\/td>\r\n<td>[latex]3+2=5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]4+7=11[\/latex]<\/td>\r\n<td>[latex]7+4=11[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]8+9=17[\/latex]<\/td>\r\n<td>[latex]9+8=17[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNotice that when the order of the addends is reversed, the sum does not change. This property is called the Commutative Property of Addition, which states that changing the order of the addends does not change their sum.\r\n<div class=\"textbox shaded\">\r\n<h3>Commutative Property of Addition<\/h3>\r\nChanging the order of the addends [latex]a[\/latex] and [latex]b[\/latex] does not change their sum.\r\n\r\n[latex]a+b=b+a[\/latex]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAdd:\r\n<ol id=\"eip-id1168288474909\" class=\"circled\">\r\n \t<li>[latex]8+7[\/latex]<\/li>\r\n \t<li>[latex]7+8[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"203214\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"203214\"]\r\n\r\nSolution\r\n\r\n&nbsp;\r\n<table id=\"eip-id1168288224694\" class=\"unnumbered unstyled aligncenter\" style=\"width: 60%;\" summary=\" \">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td style=\"text-align: left;\">[latex]8+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]15[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id11688224694\" class=\"unnumbered unstyled aligncenter\" style=\"width: 60%;\" summary=\" \">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]7+8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]15[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p style=\"text-align: left;\">[\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\nDid you notice that changing the order of the addends did not change their sum? We could have immediately known the sum from part 2 just by recognizing that the addends were the same as in part 1, but in the reverse order. As a result, both sums are the same.\r\n\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]143191[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAdd: [latex]28+61[\/latex]\r\n[reveal-answer q=\"775723\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"775723\"]\r\n\r\nSolution\r\nTo add numbers with more than one digit, it is often easier to write the numbers vertically in columns.\r\n<table id=\"eip-id1168288293873\" class=\"unnumbered unstyled\" style=\"width: 70%;\" summary=\"a\">\r\n<tbody>\r\n<tr>\r\n<td>Write the numbers so the ones and tens digits line up vertically.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill 28\\\\ \\\\ \\hfill \\underset{\\text{____}}{+61}\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Then add the digits in each place value.\r\n\r\nAdd the ones: [latex]8+1=9[\/latex]\r\n\r\nAdd the tens: [latex]2+6=8[\/latex]<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill 28\\\\ \\\\ \\hfill \\underset{\\text{____}}{+61}\\\\ \\hfill 89\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]143196[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nIn the previous example, the sum of the ones and the sum of the tens were both less than [latex]10[\/latex]. But what happens if the sum is [latex]10[\/latex] or more? Let\u2019s use our [latex]\\text{base - 10}[\/latex] model to find out.\r\n\r\nThe graphic below\u00a0shows the addition of [latex]17[\/latex] and [latex]26[\/latex] again.\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215337\/CNX_BMath_Figure_01_02_001.png\" alt=\"An image containing two groups of items. The left group includes 1 horizontal rod with 10 blocks and 7 individual blocks 2 horizontal rods with 10 blocks each and 6 individual blocks. The label to the left of this group of items is \" \/>\r\n\r\n&nbsp;\r\n\r\nWhen we add the ones, [latex]7+6[\/latex], we get [latex]13[\/latex] ones. Because we have more than [latex]10[\/latex] ones, we can exchange [latex]10[\/latex] of the ones for [latex]1[\/latex] ten. Now we have [latex]4[\/latex] tens and [latex]3[\/latex] ones. Without using the model, we show this as a small red [latex]1[\/latex] above the digits in the tens place.\r\n\r\nWhen the sum in a place value column is greater than [latex]9[\/latex], we carry over to the next column to the left. Carrying is the same as regrouping by exchanging. For example, [latex]10[\/latex] ones for [latex]1[\/latex] ten or [latex]10[\/latex] tens for [latex]1[\/latex] hundred.\r\n<div class=\"textbox shaded\">\r\n<h3>Add whole numbers<\/h3>\r\n<ol id=\"eip-id1168288474750\" class=\"stepwise\">\r\n \t<li>Write the numbers so each place value lines up vertically.<\/li>\r\n \t<li>Add the digits in each place value. Work from right to left starting with the ones place. If a sum in a place value is more than [latex]9[\/latex], carry to the next place value.<\/li>\r\n \t<li>Continue adding each place value from right to left, adding each place value and carrying if needed.<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAdd: [latex]43+69[\/latex].\r\n[reveal-answer q=\"61333\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"61333\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168287505854\" class=\"unnumbered unstyled\" style=\"width: 70%;\" summary=\"a\">\r\n<tbody>\r\n<tr>\r\n<td>Write the numbers so the digits line up vertically.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill 43\\\\ \\\\ \\hfill \\underset{\\text{____}}{+69}\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the digits in each place.\r\n\r\nAdd the ones: [latex]3+9=12[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the [latex]2[\/latex] in the ones place in the sum.\r\n\r\nAdd the [latex]1[\/latex] ten to the tens place.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill \\stackrel{1}{4}3\\\\ \\hfill \\underset{\\text{____}}{+69}\\\\ \\hfill 2\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Now add the tens: [latex]1+4+6=11[\/latex]\r\n\r\nWrite the\r\n\r\n[latex]11\r\n\r\n[\/latex] in the sum.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill \\stackrel{1}{4}3\\\\ \\hfill \\underset{\\text{____}}{+69}\\\\ \\hfill 112\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]147154[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAdd: [latex]324+586[\/latex].\r\n[reveal-answer q=\"390190\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"390190\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168287251210\" class=\"unnumbered unstyled\" style=\"width: 80%;\" summary=\"a\">\r\n<tbody>\r\n<tr>\r\n<td>Write the numbers so the digits line up vertically.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215338\/CNX_BMath_Figure_01_02_020-01.png\" alt=\"...\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the digits in each place value.\r\n\r\nAdd the ones: [latex]4+6=10[\/latex]\r\n\r\nWrite the [latex]0[\/latex] in the ones place in the sum and carry the [latex]1[\/latex] ten to the tens place.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215339\/CNX_BMath_Figure_01_02_020-02.png\" alt=\"...\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the tens: [latex]1+2+8=11[\/latex]\r\n\r\nWrite the [latex]1[\/latex] in the tens place in the sum and carry the [latex]1[\/latex] hundred to the hundreds<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215340\/CNX_BMath_Figure_01_02_020-03.png\" alt=\"...\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the hundreds: [latex]1+3+5=9[\/latex]\r\n\r\nWrite the [latex]9[\/latex] in the hundreds place.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215341\/CNX_BMath_Figure_01_02_020-04.png\" alt=\"...\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]147156[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAdd: [latex]1,683+479[\/latex].\r\n[reveal-answer q=\"603010\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"603010\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168288687380\" class=\"unnumbered unstyled\" style=\"width: 80%;\" summary=\"a\">\r\n<tbody>\r\n<tr>\r\n<td>Write the numbers so the digits line up vertically.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill 1,683\\\\ \\\\ \\hfill \\underset{\\text{______}}{+479}\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the digits in each place value.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the ones: [latex]3+9=12[\/latex].\r\n\r\nWrite the [latex]2[\/latex] in the ones place of the sum and carry the [latex]1[\/latex] ten to the tens place.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill 1,6\\stackrel{1}{8}3\\\\ \\\\ \\hfill \\underset{\\text{______}}{+479}\\\\ \\hfill 2\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the tens: [latex]1+7+8=16[\/latex]\r\n\r\nWrite the [latex]6[\/latex] in the tens place and carry the [latex]1[\/latex] hundred to the hundreds place.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill 1,\\stackrel{1}{6}\\stackrel{1}{8}3\\\\ \\\\ \\hfill \\underset{\\text{______}}{+479}\\\\ \\hfill 62\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the hundreds: [latex]1+6+4=11[\/latex]\r\n\r\nWrite the [latex]1[\/latex] in the hundreds place and carry the [latex]1[\/latex] thousand to the thousands place.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill \\stackrel{1}{1},\\stackrel{1}{6}\\stackrel{1}{8}3\\\\ \\\\ \\hfill \\underset{\\text{______}}{+479}\\\\ \\hfill 162\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the thousands [latex]1+1=2[\/latex] .\r\n\r\nWrite the [latex]2[\/latex] in the thousands place of the sum.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill \\stackrel{1}{1},\\stackrel{1}{6}\\stackrel{1}{8}3\\\\ \\\\ \\hfill \\underset{\\text{______}}{+479}\\\\ \\hfill 2,162\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nWhen the addends have different numbers of digits, be careful to line up the corresponding place values starting with the ones and moving toward the left.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]143197[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAdd: [latex]21,357+861+8,596[\/latex].\r\n[reveal-answer q=\"725487\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"725487\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168288531101\" class=\"unnumbered unstyled\" style=\"width: 80%;\" summary=\"a\">\r\n<tbody>\r\n<tr>\r\n<td>Write the numbers so the place values line up vertically.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill 21,357\\\\ \\hfill 861\\\\ \\\\ \\hfill \\underset{\\text{_______}}{+8,596}\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the digits in each place value.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the ones: [latex]7+1+6=14[\/latex]\r\n\r\nWrite the [latex]4[\/latex] in the ones place of the sum and carry the [latex]1[\/latex] to the tens place.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill 21,3\\stackrel{1}{5}7\\\\ \\hfill 861\\\\ \\\\ \\hfill \\underset{\\text{_______}}{+8,596}\\\\ \\hfill 4\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the tens: [latex]1+5+6+9=21[\/latex]\r\n\r\nWrite the [latex]1[\/latex] in the tens place and carry the [latex]2[\/latex] to the hundreds place.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill 21,\\stackrel{2}{3}\\stackrel{1}{5}7\\\\ \\hfill 861\\\\ \\\\ \\hfill \\underset{\\text{_______}}{+8,596}\\\\ \\hfill 14\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the hundreds: [latex]2+3+8+5=18[\/latex]\r\n\r\nWrite the [latex]8[\/latex] in the hundreds place and carry the [latex]1[\/latex] to the thousands place.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill 2\\stackrel{1}{1,}\\stackrel{2}{3}\\stackrel{1}{5}7\\\\ \\hfill 861\\\\ \\\\ \\hfill \\underset{\\text{_______}}{+8,596}\\\\ \\hfill 814\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the thousands [latex]1+1+8=10[\/latex] .\r\n\r\nWrite the [latex]0[\/latex] in the thousands place and carry the [latex]1[\/latex] to the ten thousands place.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill \\stackrel{1}{2}\\stackrel{1}{1,}\\stackrel{2}{3}\\stackrel{1}{5}7\\\\ \\hfill 861\\\\ \\\\ \\hfill \\underset{\\text{_______}}{+8,596}\\\\ \\hfill 0814\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the ten-thousands [latex]1+2=3[\/latex] .\r\n\r\nWrite the [latex]3[\/latex] in the ten thousands place in the sum.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill \\stackrel{1}{2}\\stackrel{1}{1,}\\stackrel{2}{3}\\stackrel{1}{5}7\\\\ \\hfill 861\\\\ \\\\ \\hfill \\underset{\\text{_______}}{+8,596}\\\\ \\hfill 30,814\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nThis example had three addends. We can add any number of addends using the same process as long as we are careful to line up the place values correctly.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]143204[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nWatch the video below for another example of how to add three whole numbers by lining up place values.\r\nhttps:\/\/youtu.be\/N3I6OiO5mKI","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Identify and use the identity property of addition<\/li>\n<li>Identify and use the commutative property of addition<\/li>\n<li>Add multiple-digit numbers using columns for place value<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Add Whole Numbers Without Models<\/h2>\n<p>Now that we have used models to add numbers, we can move on to adding without models. Before we do that, make sure you know all the one digit addition facts. You will need to use these number facts when you add larger numbers.<\/p>\n<p>Imagine filling in the table below\u00a0by adding each row number along the left side to each column number across the top.\u00a0You can use this table for reference, but it will make your work faster and easier if you have the sums memorized.<\/p>\n<table id=\"fs-id2300206\" class=\"column-header\" style=\"width: 40%;\" summary=\"No Summary\">\n<thead>\n<tr style=\"height: 15px;\" valign=\"middle\">\n<th style=\"width: 20px; height: 15px;\">+<\/th>\n<th style=\"width: 20px; height: 15px;\">[latex]0[\/latex]<\/th>\n<th style=\"width: 26.6667px; height: 15px;\">[latex]1[\/latex]<\/th>\n<th style=\"width: 26.6667px; height: 15px;\">[latex]2[\/latex]<\/th>\n<th style=\"width: 26.6667px; height: 15px;\">[latex]3[\/latex]<\/th>\n<th style=\"width: 26.6667px; height: 15px;\">[latex]4[\/latex]<\/th>\n<th style=\"width: 26.6667px; height: 15px;\">[latex]5[\/latex]<\/th>\n<th style=\"width: 26.6667px; height: 15px;\">[latex]6[\/latex]<\/th>\n<th style=\"width: 26.6667px; height: 15px;\">[latex]7[\/latex]<\/th>\n<th style=\"width: 26.6667px; height: 15px;\">[latex]8[\/latex]<\/th>\n<th style=\"width: 27.7778px; height: 15px;\">[latex]9[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 15px;\" valign=\"middle\">\n<td style=\"width: 20px; height: 15px;\">[latex]0[\/latex]<\/td>\n<td style=\"width: 20px; height: 15px;\">[latex]0[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]1[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]2[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]3[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]4[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]5[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]6[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]7[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]8[\/latex]<\/td>\n<td style=\"width: 27.7778px; height: 15px;\">[latex]9[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"middle\">\n<td style=\"width: 20px; height: 15px;\">[latex]1[\/latex]<\/td>\n<td style=\"width: 20px; height: 15px;\">[latex]1[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]2[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]3[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]4[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]5[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]6[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]7[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]8[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]9[\/latex]<\/td>\n<td style=\"width: 27.7778px; height: 15px;\">[latex]10[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15.9688px;\" valign=\"middle\">\n<td style=\"width: 20px; height: 15.9688px;\">[latex]2[\/latex]<\/td>\n<td style=\"width: 20px; height: 15.9688px;\">[latex]2[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15.9688px;\">[latex]3[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15.9688px;\">[latex]4[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15.9688px;\">[latex]5[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15.9688px;\">[latex]6[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15.9688px;\">[latex]7[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15.9688px;\">[latex]8[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15.9688px;\">[latex]9[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15.9688px;\">[latex]10[\/latex]<\/td>\n<td style=\"width: 27.7778px; height: 15.9688px;\">[latex]11[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"middle\">\n<td style=\"width: 20px; height: 15px;\">[latex]3[\/latex]<\/td>\n<td style=\"width: 20px; height: 15px;\">[latex]3[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]4[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]5[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]6[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]7[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]8[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]9[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]10[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]11[\/latex]<\/td>\n<td style=\"width: 27.7778px; height: 15px;\">[latex]12[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"middle\">\n<td style=\"width: 20px; height: 15px;\">[latex]4[\/latex]<\/td>\n<td style=\"width: 20px; height: 15px;\">[latex]4[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]5[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]6[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]7[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]8[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]9[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]10[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]11[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]12[\/latex]<\/td>\n<td style=\"width: 27.7778px; height: 15px;\">[latex]13[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"middle\">\n<td style=\"width: 20px; height: 15px;\">[latex]5[\/latex]<\/td>\n<td style=\"width: 20px; height: 15px;\">[latex]5[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]6[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]7[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]8[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]9[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]10[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]11[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]12[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]13[\/latex]<\/td>\n<td style=\"width: 27.7778px; height: 15px;\">[latex]14[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"middle\">\n<td style=\"width: 20px; height: 15px;\">[latex]6[\/latex]<\/td>\n<td style=\"width: 20px; height: 15px;\">[latex]6[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]7[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]8[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]9[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]10[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]11[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]12[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]13[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]14[\/latex]<\/td>\n<td style=\"width: 27.7778px; height: 15px;\">[latex]15[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"middle\">\n<td style=\"width: 20px; height: 15px;\">[latex]7[\/latex]<\/td>\n<td style=\"width: 20px; height: 15px;\">[latex]7[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]8[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]9[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]10[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]11[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]12[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]13[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]14[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]15[\/latex]<\/td>\n<td style=\"width: 27.7778px; height: 15px;\">[latex]16[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"middle\">\n<td style=\"width: 20px; height: 15px;\">[latex]8[\/latex]<\/td>\n<td style=\"width: 20px; height: 15px;\">[latex]8[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]9[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]10[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]11[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]12[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]13[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]14[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]15[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]16[\/latex]<\/td>\n<td style=\"width: 27.7778px; height: 15px;\">[latex]17[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"middle\">\n<td style=\"width: 20px; height: 15px;\">[latex]9[\/latex]<\/td>\n<td style=\"width: 20px; height: 15px;\">[latex]9[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]10[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]11[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]12[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]13[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]14[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]15[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]16[\/latex]<\/td>\n<td style=\"width: 26.6667px; height: 15px;\">[latex]17[\/latex]<\/td>\n<td style=\"width: 27.7778px; height: 15px;\">[latex]18[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Did you notice what happens when you add zero to a number? The sum of any number and zero is the number itself. We call this the Identity Property of Addition. Zero is called the additive identity.<\/p>\n<div class=\"textbox shaded\">\n<h3>Identity Property of Addition<\/h3>\n<p>The sum of any number [latex]a[\/latex] and [latex]0[\/latex] is the number.<\/p>\n<p>[latex]\\begin{array}{}\\\\ a+0=a\\\\ 0+a=a\\end{array}[\/latex]<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Find each sum:<\/p>\n<ol>\n<li>[latex]0+11[\/latex]<\/li>\n<li>[latex]42+0[\/latex]<\/li>\n<\/ol>\n<p>Solution<\/p>\n<table id=\"eip-629\" class=\"unnumbered unstyled\" summary=\"Solution for A: The first addend is zero. The sum of any number and zero is the number. 0+11=11 Solution for B: The second addend is zero. The sum of any number and zero is the number. 42 + 0 = 42\">\n<tbody>\n<tr>\n<td>1. \u00a0The first addend is zero. The sum of any number and zero is the number.<\/td>\n<td>[latex]0+11=11[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>2. The second addend is zero. The sum of any number and zero is the number.<\/td>\n<td>[latex]42+0=42[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm143190\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143190&theme=oea&iframe_resize_id=ohm143190&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Look at the pairs of sums:<\/p>\n<table id=\"eip-id1168287208889\" class=\"unnumbered unstyled\" summary=\"\">\n<tbody>\n<tr>\n<td>[latex]2+3=5[\/latex]<\/td>\n<td>[latex]3+2=5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]4+7=11[\/latex]<\/td>\n<td>[latex]7+4=11[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]8+9=17[\/latex]<\/td>\n<td>[latex]9+8=17[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that when the order of the addends is reversed, the sum does not change. This property is called the Commutative Property of Addition, which states that changing the order of the addends does not change their sum.<\/p>\n<div class=\"textbox shaded\">\n<h3>Commutative Property of Addition<\/h3>\n<p>Changing the order of the addends [latex]a[\/latex] and [latex]b[\/latex] does not change their sum.<\/p>\n<p>[latex]a+b=b+a[\/latex]<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Add:<\/p>\n<ol id=\"eip-id1168288474909\" class=\"circled\">\n<li>[latex]8+7[\/latex]<\/li>\n<li>[latex]7+8[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q203214\">Show Solution<\/span><\/p>\n<div id=\"q203214\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<p>&nbsp;<\/p>\n<table id=\"eip-id1168288224694\" class=\"unnumbered unstyled aligncenter\" style=\"width: 60%;\" summary=\"\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td style=\"text-align: left;\">[latex]8+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]15[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id11688224694\" class=\"unnumbered unstyled aligncenter\" style=\"width: 60%;\" summary=\"\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]7+8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]15[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: left;\"><\/div>\n<\/div>\n<\/div>\n<p>Did you notice that changing the order of the addends did not change their sum? We could have immediately known the sum from part 2 just by recognizing that the addends were the same as in part 1, but in the reverse order. As a result, both sums are the same.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm143191\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143191&theme=oea&iframe_resize_id=ohm143191&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Add: [latex]28+61[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q775723\">Show Solution<\/span><\/p>\n<div id=\"q775723\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nTo add numbers with more than one digit, it is often easier to write the numbers vertically in columns.<\/p>\n<table id=\"eip-id1168288293873\" class=\"unnumbered unstyled\" style=\"width: 70%;\" summary=\"a\">\n<tbody>\n<tr>\n<td>Write the numbers so the ones and tens digits line up vertically.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill 28\\\\ \\\\ \\hfill \\underset{\\text{____}}{+61}\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Then add the digits in each place value.<\/p>\n<p>Add the ones: [latex]8+1=9[\/latex]<\/p>\n<p>Add the tens: [latex]2+6=8[\/latex]<\/td>\n<td>[latex]\\begin{array}{c}\\hfill 28\\\\ \\\\ \\hfill \\underset{\\text{____}}{+61}\\\\ \\hfill 89\\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm143196\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143196&theme=oea&iframe_resize_id=ohm143196&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>In the previous example, the sum of the ones and the sum of the tens were both less than [latex]10[\/latex]. But what happens if the sum is [latex]10[\/latex] or more? Let\u2019s use our [latex]\\text{base - 10}[\/latex] model to find out.<\/p>\n<p>The graphic below\u00a0shows the addition of [latex]17[\/latex] and [latex]26[\/latex] again.<\/p>\n<p>&nbsp;<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215337\/CNX_BMath_Figure_01_02_001.png\" alt=\"An image containing two groups of items. The left group includes 1 horizontal rod with 10 blocks and 7 individual blocks 2 horizontal rods with 10 blocks each and 6 individual blocks. The label to the left of this group of items is\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>When we add the ones, [latex]7+6[\/latex], we get [latex]13[\/latex] ones. Because we have more than [latex]10[\/latex] ones, we can exchange [latex]10[\/latex] of the ones for [latex]1[\/latex] ten. Now we have [latex]4[\/latex] tens and [latex]3[\/latex] ones. Without using the model, we show this as a small red [latex]1[\/latex] above the digits in the tens place.<\/p>\n<p>When the sum in a place value column is greater than [latex]9[\/latex], we carry over to the next column to the left. Carrying is the same as regrouping by exchanging. For example, [latex]10[\/latex] ones for [latex]1[\/latex] ten or [latex]10[\/latex] tens for [latex]1[\/latex] hundred.<\/p>\n<div class=\"textbox shaded\">\n<h3>Add whole numbers<\/h3>\n<ol id=\"eip-id1168288474750\" class=\"stepwise\">\n<li>Write the numbers so each place value lines up vertically.<\/li>\n<li>Add the digits in each place value. Work from right to left starting with the ones place. If a sum in a place value is more than [latex]9[\/latex], carry to the next place value.<\/li>\n<li>Continue adding each place value from right to left, adding each place value and carrying if needed.<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Add: [latex]43+69[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q61333\">Show Solution<\/span><\/p>\n<div id=\"q61333\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168287505854\" class=\"unnumbered unstyled\" style=\"width: 70%;\" summary=\"a\">\n<tbody>\n<tr>\n<td>Write the numbers so the digits line up vertically.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill 43\\\\ \\\\ \\hfill \\underset{\\text{____}}{+69}\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the digits in each place.<\/p>\n<p>Add the ones: [latex]3+9=12[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write the [latex]2[\/latex] in the ones place in the sum.<\/p>\n<p>Add the [latex]1[\/latex] ten to the tens place.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill \\stackrel{1}{4}3\\\\ \\hfill \\underset{\\text{____}}{+69}\\\\ \\hfill 2\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Now add the tens: [latex]1+4+6=11[\/latex]<\/p>\n<p>Write the<\/p>\n<p>[latex]11[\/latex] in the sum.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill \\stackrel{1}{4}3\\\\ \\hfill \\underset{\\text{____}}{+69}\\\\ \\hfill 112\\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm147154\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=147154&theme=oea&iframe_resize_id=ohm147154&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Add: [latex]324+586[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q390190\">Show Solution<\/span><\/p>\n<div id=\"q390190\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168287251210\" class=\"unnumbered unstyled\" style=\"width: 80%;\" summary=\"a\">\n<tbody>\n<tr>\n<td>Write the numbers so the digits line up vertically.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215338\/CNX_BMath_Figure_01_02_020-01.png\" alt=\"...\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add the digits in each place value.<\/p>\n<p>Add the ones: [latex]4+6=10[\/latex]<\/p>\n<p>Write the [latex]0[\/latex] in the ones place in the sum and carry the [latex]1[\/latex] ten to the tens place.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215339\/CNX_BMath_Figure_01_02_020-02.png\" alt=\"...\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add the tens: [latex]1+2+8=11[\/latex]<\/p>\n<p>Write the [latex]1[\/latex] in the tens place in the sum and carry the [latex]1[\/latex] hundred to the hundreds<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215340\/CNX_BMath_Figure_01_02_020-03.png\" alt=\"...\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add the hundreds: [latex]1+3+5=9[\/latex]<\/p>\n<p>Write the [latex]9[\/latex] in the hundreds place.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215341\/CNX_BMath_Figure_01_02_020-04.png\" alt=\"...\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm147156\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=147156&theme=oea&iframe_resize_id=ohm147156&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Add: [latex]1,683+479[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q603010\">Show Solution<\/span><\/p>\n<div id=\"q603010\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168288687380\" class=\"unnumbered unstyled\" style=\"width: 80%;\" summary=\"a\">\n<tbody>\n<tr>\n<td>Write the numbers so the digits line up vertically.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill 1,683\\\\ \\\\ \\hfill \\underset{\\text{______}}{+479}\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the digits in each place value.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Add the ones: [latex]3+9=12[\/latex].<\/p>\n<p>Write the [latex]2[\/latex] in the ones place of the sum and carry the [latex]1[\/latex] ten to the tens place.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill 1,6\\stackrel{1}{8}3\\\\ \\\\ \\hfill \\underset{\\text{______}}{+479}\\\\ \\hfill 2\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the tens: [latex]1+7+8=16[\/latex]<\/p>\n<p>Write the [latex]6[\/latex] in the tens place and carry the [latex]1[\/latex] hundred to the hundreds place.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill 1,\\stackrel{1}{6}\\stackrel{1}{8}3\\\\ \\\\ \\hfill \\underset{\\text{______}}{+479}\\\\ \\hfill 62\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the hundreds: [latex]1+6+4=11[\/latex]<\/p>\n<p>Write the [latex]1[\/latex] in the hundreds place and carry the [latex]1[\/latex] thousand to the thousands place.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill \\stackrel{1}{1},\\stackrel{1}{6}\\stackrel{1}{8}3\\\\ \\\\ \\hfill \\underset{\\text{______}}{+479}\\\\ \\hfill 162\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the thousands [latex]1+1=2[\/latex] .<\/p>\n<p>Write the [latex]2[\/latex] in the thousands place of the sum.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill \\stackrel{1}{1},\\stackrel{1}{6}\\stackrel{1}{8}3\\\\ \\\\ \\hfill \\underset{\\text{______}}{+479}\\\\ \\hfill 2,162\\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>When the addends have different numbers of digits, be careful to line up the corresponding place values starting with the ones and moving toward the left.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm143197\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143197&theme=oea&iframe_resize_id=ohm143197&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Add: [latex]21,357+861+8,596[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q725487\">Show Solution<\/span><\/p>\n<div id=\"q725487\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168288531101\" class=\"unnumbered unstyled\" style=\"width: 80%;\" summary=\"a\">\n<tbody>\n<tr>\n<td>Write the numbers so the place values line up vertically.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill 21,357\\\\ \\hfill 861\\\\ \\\\ \\hfill \\underset{\\text{_______}}{+8,596}\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the digits in each place value.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Add the ones: [latex]7+1+6=14[\/latex]<\/p>\n<p>Write the [latex]4[\/latex] in the ones place of the sum and carry the [latex]1[\/latex] to the tens place.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill 21,3\\stackrel{1}{5}7\\\\ \\hfill 861\\\\ \\\\ \\hfill \\underset{\\text{_______}}{+8,596}\\\\ \\hfill 4\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the tens: [latex]1+5+6+9=21[\/latex]<\/p>\n<p>Write the [latex]1[\/latex] in the tens place and carry the [latex]2[\/latex] to the hundreds place.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill 21,\\stackrel{2}{3}\\stackrel{1}{5}7\\\\ \\hfill 861\\\\ \\\\ \\hfill \\underset{\\text{_______}}{+8,596}\\\\ \\hfill 14\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the hundreds: [latex]2+3+8+5=18[\/latex]<\/p>\n<p>Write the [latex]8[\/latex] in the hundreds place and carry the [latex]1[\/latex] to the thousands place.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill 2\\stackrel{1}{1,}\\stackrel{2}{3}\\stackrel{1}{5}7\\\\ \\hfill 861\\\\ \\\\ \\hfill \\underset{\\text{_______}}{+8,596}\\\\ \\hfill 814\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the thousands [latex]1+1+8=10[\/latex] .<\/p>\n<p>Write the [latex]0[\/latex] in the thousands place and carry the [latex]1[\/latex] to the ten thousands place.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill \\stackrel{1}{2}\\stackrel{1}{1,}\\stackrel{2}{3}\\stackrel{1}{5}7\\\\ \\hfill 861\\\\ \\\\ \\hfill \\underset{\\text{_______}}{+8,596}\\\\ \\hfill 0814\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the ten-thousands [latex]1+2=3[\/latex] .<\/p>\n<p>Write the [latex]3[\/latex] in the ten thousands place in the sum.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill \\stackrel{1}{2}\\stackrel{1}{1,}\\stackrel{2}{3}\\stackrel{1}{5}7\\\\ \\hfill 861\\\\ \\\\ \\hfill \\underset{\\text{_______}}{+8,596}\\\\ \\hfill 30,814\\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>This example had three addends. We can add any number of addends using the same process as long as we are careful to line up the place values correctly.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm143204\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143204&theme=oea&iframe_resize_id=ohm143204&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Watch the video below for another example of how to add three whole numbers by lining up place values.<br \/>\n<iframe loading=\"lazy\" id=\"oembed-1\" title=\"Example:  Adding Whole Numbers\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/N3I6OiO5mKI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-4595\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Example: Adding Whole Numbers. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/N3I6OiO5mKI\">https:\/\/youtu.be\/N3I6OiO5mKI<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID: 143190, 143191, 143196, 143197, 143204. <strong>Authored by<\/strong>: Alyson Day. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Example: Adding Whole Numbers\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/N3I6OiO5mKI\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at 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