{"id":10350,"date":"2017-05-26T18:42:16","date_gmt":"2017-05-26T18:42:16","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10350"},"modified":"2024-04-30T16:32:53","modified_gmt":"2024-04-30T16:32:53","slug":"adding-and-subtracting-decimals","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/adding-and-subtracting-decimals\/","title":{"raw":"Adding and Subtracting Decimals","rendered":"Adding and Subtracting Decimals"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Add decimals<\/li>\r\n \t<li>Subtract decimals that require borrowing<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Adding Decimals<\/h2>\r\nLet\u2019s take one more look at the lunch order from the start of Decimals, this time noticing how the numbers were added together.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221429\/CNX_BMath_Figure_05_01_002.png\" alt=\"A vertical addition problem is shown. The top line shows $3.45 for a sandwich, the next line shows $1.25 for water, and the last line shows $0.33 for tax. The total is shown to be $5.03.\" \/>\r\nAll three items (sandwich, water, tax) were priced in dollars and cents, so we lined up the dollars under the dollars and the cents under the cents, with the decimal points lined up between them. Then we just added each column, as if we were adding whole numbers. By lining up decimals this way, we can add or subtract the corresponding place values just as we did with whole numbers.\r\n<div class=\"textbox shaded\">\r\n<h3>Add or subtract decimals<\/h3>\r\n<ol id=\"eip-id1168467213800\" class=\"stepwise\">\r\n \t<li>Write the numbers vertically so the decimal points line up.<\/li>\r\n \t<li>Use zeros as place holders, as needed.<\/li>\r\n \t<li>Add or subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<a href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/adding-whole-numbers\/\">Click here to review how to add whole numbers<\/a>.\u00a0 If you would like to review <a href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/subtracting-whole-numbers\/\">how to subtract whole numbers, click here<\/a>.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAdd: [latex]3.7+12.4[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168469591177\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]3.7+12.4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the numbers vertically so the decimal points line up.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill 3.7\\\\ \\hfill \\underset{\\text{_____}}{+12.4}\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Place holders are not needed since both numbers have the same number of decimal places.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill \\stackrel{1}{3}.7\\\\ \\hfill \\underset{\\text{_____}}{+12.4}\\\\ \\hfill 16.1\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146586[\/ohm_question]\r\n\r\n[ohm_question]146587[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAdd: [latex]23.5+41.38[\/latex]\r\n[reveal-answer q=\"920268\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"920268\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468241397\" class=\"unnumbered unstyled\" summary=\"The first line says 23.5 plus 41.38. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]23.5+41.38[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the numbers vertically so the decimal points line up.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221539\/CNX_BMath_Figure_05_02_016_img-01.png\" alt=\"23.5 plus 41.38\" width=\"75\" height=\"48\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Place [latex]0[\/latex] as a place holder after the [latex]5[\/latex] in [latex]23.5[\/latex], so that both numbers have two decimal places.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221540\/CNX_BMath_Figure_05_02_016_img-02.png\" alt=\"23.50, with the 0 highlighted in red, plus 41.38\" width=\"75\" height=\"46\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221541\/CNX_BMath_Figure_05_02_016_img-03.png\" alt=\"23.50 plus 41.38 equals 64.88\" width=\"75\" height=\"62\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146588[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show another example of how to add decimals.\r\n\r\nhttps:\/\/youtu.be\/weTZqwOisDU\r\n<h2>Subtracting decimals<\/h2>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nHow much change would you get if you handed the cashier a [latex]$20[\/latex] bill for a [latex]$14.65[\/latex] purchase? We will show the steps to calculate this in the next example.\r\n\r\nSubtract: [latex]20 - 14.65[\/latex]\r\n[reveal-answer q=\"678104\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"678104\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168467144513\" class=\"unnumbered unstyled\" style=\"width: 859px;\" summary=\"The first line says 20 minus 14.65. The next line says, \">\r\n<tbody>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 625.033px; height: 15px;\"><\/td>\r\n<td style=\"width: 209.967px; height: 15px;\">[latex]20 - 14.65[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 68.2166px;\">\r\n<td style=\"width: 625.033px; height: 68.2166px;\">Write the numbers vertically so the decimal points line up. Remember [latex]20[\/latex] is a whole number, so place the decimal point after the [latex]0[\/latex].<\/td>\r\n<td style=\"width: 209.967px; height: 68.2166px;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221542\/CNX_BMath_Figure_05_02_017_img-01.png\" alt=\"20 minus 14.65\" width=\"113\" height=\"61\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 54px;\">\r\n<td style=\"width: 625.033px; height: 54px;\">Place two zeros after the decimal point in [latex]20[\/latex], as place holders so that both numbers have two decimal places.<\/td>\r\n<td style=\"width: 209.967px; height: 54px;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221543\/CNX_BMath_Figure_05_02_017_img-02.png\" alt=\"20.00, with red zeros to the right of the decimal, minus 14.65\" width=\"117\" height=\"57\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 94px;\">\r\n<td style=\"width: 625.033px; height: 94px;\">Subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.<\/td>\r\n<td style=\"width: 209.967px; height: 94px;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221544\/CNX_BMath_Figure_05_02_017_img-03.png\" alt=\"20.00 minus 14.65 equals 5.35. Carry on the 2 in the tens place down to the ones place. Carry on the ones place to the tenths place. Carry on the tenths place to the hundredths place.\" width=\"132\" height=\"114\" \/><\/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]146590[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSubtract: [latex]2.51 - 7.4[\/latex]\r\n[reveal-answer q=\"743542\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"743542\"]\r\n\r\nSolution\r\nIf we subtract [latex]7.4[\/latex] from [latex]2.51[\/latex], the answer will be negative since [latex]7.4&gt;2.51[\/latex]. To subtract easily, we can subtract [latex]2.51[\/latex] from [latex]7.4[\/latex]. Then we will place the negative sign in the result.\r\n<table id=\"eip-id1168468772855\" class=\"unnumbered unstyled\" summary=\"The first line says 2.51 minus 7.4. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]2.51 - 7.4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the numbers vertically so the decimal points line up.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221545\/CNX_BMath_Figure_05_02_032-01.png\" alt=\"7.4 minus 2.51\" width=\"65\" height=\"50\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Place zero after the [latex]4[\/latex] in [latex]7.4[\/latex] as a place holder, so that both numbers have two decimal places.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221546\/CNX_BMath_Figure_05_02_032-02.png\" alt=\"7.40, with the 0 in red, minus 2.51\" width=\"65\" height=\"49\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract and place the decimal in the answer.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221547\/CNX_BMath_Figure_05_02_032-03.png\" alt=\"7.40 minus 2.51 equals 4.89\" width=\"65\" height=\"68\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remember that we are really subtracting [latex]2.51 - 7.4[\/latex] so the answer is negative<\/td>\r\n<td>[latex]2.51 - 7.4=-4.89[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nFor a refresher on <a href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/notation-and-modeling-subtraction-of-integers\/\">why we subtract integers the way we do, click here<\/a>.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146591[\/ohm_question]\r\n\r\n<\/div>\r\nThis video shows another example of how to subtract one decimal from another.\r\n\r\nhttps:\/\/youtu.be\/t8r-S9Zr41c","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Add decimals<\/li>\n<li>Subtract decimals that require borrowing<\/li>\n<\/ul>\n<\/div>\n<h2>Adding Decimals<\/h2>\n<p>Let\u2019s take one more look at the lunch order from the start of Decimals, this time noticing how the numbers were added together.<\/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\/24221429\/CNX_BMath_Figure_05_01_002.png\" alt=\"A vertical addition problem is shown. The top line shows $3.45 for a sandwich, the next line shows $1.25 for water, and the last line shows $0.33 for tax. The total is shown to be $5.03.\" \/><br \/>\nAll three items (sandwich, water, tax) were priced in dollars and cents, so we lined up the dollars under the dollars and the cents under the cents, with the decimal points lined up between them. Then we just added each column, as if we were adding whole numbers. By lining up decimals this way, we can add or subtract the corresponding place values just as we did with whole numbers.<\/p>\n<div class=\"textbox shaded\">\n<h3>Add or subtract decimals<\/h3>\n<ol id=\"eip-id1168467213800\" class=\"stepwise\">\n<li>Write the numbers vertically so the decimal points line up.<\/li>\n<li>Use zeros as place holders, as needed.<\/li>\n<li>Add or subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.<\/li>\n<\/ol>\n<\/div>\n<p><a href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/adding-whole-numbers\/\">Click here to review how to add whole numbers<\/a>.\u00a0 If you would like to review <a href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/subtracting-whole-numbers\/\">how to subtract whole numbers, click here<\/a>.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Add: [latex]3.7+12.4[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168469591177\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]3.7+12.4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write the numbers vertically so the decimal points line up.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill 3.7\\\\ \\hfill \\underset{\\text{_____}}{+12.4}\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Place holders are not needed since both numbers have the same number of decimal places.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Add the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.<\/td>\n<td>[latex]\\begin{array}{c}\\hfill \\stackrel{1}{3}.7\\\\ \\hfill \\underset{\\text{_____}}{+12.4}\\\\ \\hfill 16.1\\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146586\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146586&theme=oea&iframe_resize_id=ohm146586&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146587\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146587&theme=oea&iframe_resize_id=ohm146587&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]23.5+41.38[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q920268\">Show Solution<\/span><\/p>\n<div id=\"q920268\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468241397\" class=\"unnumbered unstyled\" summary=\"The first line says 23.5 plus 41.38. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]23.5+41.38[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write the numbers vertically so the decimal points line up.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221539\/CNX_BMath_Figure_05_02_016_img-01.png\" alt=\"23.5 plus 41.38\" width=\"75\" height=\"48\" \/><\/td>\n<\/tr>\n<tr>\n<td>Place [latex]0[\/latex] as a place holder after the [latex]5[\/latex] in [latex]23.5[\/latex], so that both numbers have two decimal places.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221540\/CNX_BMath_Figure_05_02_016_img-02.png\" alt=\"23.50, with the 0 highlighted in red, plus 41.38\" width=\"75\" height=\"46\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221541\/CNX_BMath_Figure_05_02_016_img-03.png\" alt=\"23.50 plus 41.38 equals 64.88\" width=\"75\" height=\"62\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146588\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146588&theme=oea&iframe_resize_id=ohm146588&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show another example of how to add decimals.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Examples:  Addition of Decimals\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/weTZqwOisDU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Subtracting decimals<\/h2>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>How much change would you get if you handed the cashier a [latex]$20[\/latex] bill for a [latex]$14.65[\/latex] purchase? We will show the steps to calculate this in the next example.<\/p>\n<p>Subtract: [latex]20 - 14.65[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q678104\">Show Solution<\/span><\/p>\n<div id=\"q678104\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168467144513\" class=\"unnumbered unstyled\" style=\"width: 859px;\" summary=\"The first line says 20 minus 14.65. The next line says,\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 625.033px; height: 15px;\"><\/td>\n<td style=\"width: 209.967px; height: 15px;\">[latex]20 - 14.65[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 68.2166px;\">\n<td style=\"width: 625.033px; height: 68.2166px;\">Write the numbers vertically so the decimal points line up. Remember [latex]20[\/latex] is a whole number, so place the decimal point after the [latex]0[\/latex].<\/td>\n<td style=\"width: 209.967px; height: 68.2166px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221542\/CNX_BMath_Figure_05_02_017_img-01.png\" alt=\"20 minus 14.65\" width=\"113\" height=\"61\" \/><\/td>\n<\/tr>\n<tr style=\"height: 54px;\">\n<td style=\"width: 625.033px; height: 54px;\">Place two zeros after the decimal point in [latex]20[\/latex], as place holders so that both numbers have two decimal places.<\/td>\n<td style=\"width: 209.967px; height: 54px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221543\/CNX_BMath_Figure_05_02_017_img-02.png\" alt=\"20.00, with red zeros to the right of the decimal, minus 14.65\" width=\"117\" height=\"57\" \/><\/td>\n<\/tr>\n<tr style=\"height: 94px;\">\n<td style=\"width: 625.033px; height: 94px;\">Subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.<\/td>\n<td style=\"width: 209.967px; height: 94px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221544\/CNX_BMath_Figure_05_02_017_img-03.png\" alt=\"20.00 minus 14.65 equals 5.35. Carry on the 2 in the tens place down to the ones place. Carry on the ones place to the tenths place. Carry on the tenths place to the hundredths place.\" width=\"132\" height=\"114\" \/><\/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=\"ohm146590\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146590&theme=oea&iframe_resize_id=ohm146590&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>Subtract: [latex]2.51 - 7.4[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q743542\">Show Solution<\/span><\/p>\n<div id=\"q743542\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nIf we subtract [latex]7.4[\/latex] from [latex]2.51[\/latex], the answer will be negative since [latex]7.4>2.51[\/latex]. To subtract easily, we can subtract [latex]2.51[\/latex] from [latex]7.4[\/latex]. Then we will place the negative sign in the result.<\/p>\n<table id=\"eip-id1168468772855\" class=\"unnumbered unstyled\" summary=\"The first line says 2.51 minus 7.4. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]2.51 - 7.4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write the numbers vertically so the decimal points line up.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221545\/CNX_BMath_Figure_05_02_032-01.png\" alt=\"7.4 minus 2.51\" width=\"65\" height=\"50\" \/><\/td>\n<\/tr>\n<tr>\n<td>Place zero after the [latex]4[\/latex] in [latex]7.4[\/latex] as a place holder, so that both numbers have two decimal places.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221546\/CNX_BMath_Figure_05_02_032-02.png\" alt=\"7.40, with the 0 in red, minus 2.51\" width=\"65\" height=\"49\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract and place the decimal in the answer.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221547\/CNX_BMath_Figure_05_02_032-03.png\" alt=\"7.40 minus 2.51 equals 4.89\" width=\"65\" height=\"68\" \/><\/td>\n<\/tr>\n<tr>\n<td>Remember that we are really subtracting [latex]2.51 - 7.4[\/latex] so the answer is negative<\/td>\n<td>[latex]2.51 - 7.4=-4.89[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>For a refresher on <a href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/notation-and-modeling-subtraction-of-integers\/\">why we subtract integers the way we do, click here<\/a>.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146591\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146591&theme=oea&iframe_resize_id=ohm146591&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>This video shows another example of how to subtract one decimal from another.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Examples:  Subtraction of Decimals\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/t8r-S9Zr41c?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-10350\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Examples: Subtraction of Decimals. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/t8r-S9Zr41c\">https:\/\/youtu.be\/t8r-S9Zr41c<\/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 146590, 146591. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <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":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Examples: Subtraction of Decimals\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/t8r-S9Zr41c\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID 146590, 146591\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"0e83969031654ac9b66eb5c3f8703807, 85c102f6992548b9ae9cc1d2aa873030, 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