{"id":323,"date":"2018-04-16T23:51:37","date_gmt":"2018-04-16T23:51:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/?post_type=chapter&#038;p=323"},"modified":"2024-04-26T22:02:38","modified_gmt":"2024-04-26T22:02:38","slug":"adding-and-subtracting-decimals","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/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 Objectives<\/h3>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use addition and subtraction when evaluating expressions with decimals&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:13185,&quot;3&quot;:[null,0],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;,&quot;16&quot;:10}\">Use addition and subtraction when evaluating expressions with decimals<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\nUnderstanding how to work with decimals when making calculations involving money is very important in business. We know that [latex]$1[\/latex] is the same as [latex]$1.00[\/latex]. But the way we write [latex]$1\\text{, or }$1.00[\/latex], depends on the context. In the same way, integers can be written as decimals with as many zeros as needed to the right of the decimal.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{cccc}5=5.0\\hfill &amp; &amp; &amp; -2=-2.0\\hfill \\\\ 5=5.00\\hfill &amp; &amp; &amp; -2=-2.00\\hfill \\\\ 5=5.000\\hfill &amp; &amp; &amp; -2=-2.000\\hfill \\end{array}[\/latex]\r\nand so on [latex]\\dots[\/latex]<\/p>\r\n<p data-type=\"title\">So when making calculations with money, you may have to fill in zeros as place holders to correctly align the values.<\/p>\r\n<p data-type=\"title\">Let's say you stopped by Bouchon Bakery for breakfast this morning: the orange juice was three and a half dollars, the coffee was $1.85, and the scone was $4.\u00a0All three items first need to be represented in dollars in cents so we can correctly add the numbers.<\/p>\r\n<img class=\"aligncenter wp-image-2069\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2985\/2018\/04\/24181617\/Screen-Shot-2018-07-24-at-11.15.49-AM.png\" alt=\"Vertical addition for your purchases at Bouchon Bakery. 3 dollars and 50 cents for juice plus a dollar and 85 cents for coffee plus a 4 dollar scone equals a 9 dollar and 35 cent total. \" width=\"168\" height=\"102\" \/>\r\nWe 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\" data-number-style=\"arabic\">\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\nWe'll practice adding decimals in the example below. Remember \u2014 just like with whole number addition \u2014 you might have to \"carry\" a ten to the next place value as you add each column.\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=\".\" data-label=\"\">\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<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<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAdd: [latex]23.5+41.38[\/latex]\r\n[reveal-answer q=\"920268\"]Show Answer[\/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, \" data-label=\"\">\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=\"Vertical addition for 23.5 plus 41.38.\" width=\"75\" height=\"48\" data-media-type=\"image\/png\" \/><\/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=\"In order to align decimal places, add a trailing 0 to 23.5 such that it becomes 23.50.\" width=\"75\" height=\"46\" data-media-type=\"image\/png\" \/><\/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\" data-media-type=\"image\/png\" \/><\/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\r\nSubtracting decimals follows the same process as adding decimals. Remember \u2014 just like with whole number subtraction \u2014 you may have to \"borrow\" ten from the next place value as you subtract each column.\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 Answer[\/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, \" data-label=\"\">\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=\"Vertical subtraction for 20 minus 14.65\" width=\"113\" height=\"61\" data-media-type=\"image\/png\" \/><\/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=\"In order to align decimal places, add 2 trailing 0's to 20.\" width=\"117\" height=\"57\" data-media-type=\"image\/png\" \/><\/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 14.64 equals 5.35. When subtracting 5 from 0 in the hundredths place, we must borrow from the tenths place. Since we cannot subtract 1 from 0 in the tenths place, we borrow from the ones place, and since we cannot subtract 1 from 0 in the ones place, we borrow from the tens place. Thus, the 2 in 20 is borrowed from such that the ones place becomes 10, and then 9 after being borrowed from. The tenths place becomes 10 and then 9 after being borrowed from. And lastly, the hundredths place becomes 10.\" width=\"109\" height=\"95\" data-media-type=\"image\/png\" \/><\/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]146590[\/ohm_question]\r\n\r\n<\/div>\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 Answer[\/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, \" data-label=\"\">\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=\"Vertical subtraction for 7.4 minus 2.51.\" width=\"65\" height=\"50\" data-media-type=\"image\/png\" \/><\/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=\"In order to align decimal places, add a trailing 0 to 7.4 such that it becomes 7.40\" width=\"65\" height=\"49\" data-media-type=\"image\/png\" \/><\/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\" data-media-type=\"image\/png\" \/><\/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\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 Objectives<\/h3>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use addition and subtraction when evaluating expressions with decimals&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:13185,&quot;3&quot;:[null,0],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;,&quot;16&quot;:10}\">Use addition and subtraction when evaluating expressions with decimals<\/span><\/li>\n<\/ul>\n<\/div>\n<p>Understanding how to work with decimals when making calculations involving money is very important in business. We know that [latex]$1[\/latex] is the same as [latex]$1.00[\/latex]. But the way we write [latex]$1\\text{, or }$1.00[\/latex], depends on the context. In the same way, integers can be written as decimals with as many zeros as needed to the right of the decimal.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{cccc}5=5.0\\hfill & & & -2=-2.0\\hfill \\\\ 5=5.00\\hfill & & & -2=-2.00\\hfill \\\\ 5=5.000\\hfill & & & -2=-2.000\\hfill \\end{array}[\/latex]<br \/>\nand so on [latex]\\dots[\/latex]<\/p>\n<p data-type=\"title\">So when making calculations with money, you may have to fill in zeros as place holders to correctly align the values.<\/p>\n<p data-type=\"title\">Let&#8217;s say you stopped by Bouchon Bakery for breakfast this morning: the orange juice was three and a half dollars, the coffee was $1.85, and the scone was $4.\u00a0All three items first need to be represented in dollars in cents so we can correctly add the numbers.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2069\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2985\/2018\/04\/24181617\/Screen-Shot-2018-07-24-at-11.15.49-AM.png\" alt=\"Vertical addition for your purchases at Bouchon Bakery. 3 dollars and 50 cents for juice plus a dollar and 85 cents for coffee plus a 4 dollar scone equals a 9 dollar and 35 cent total.\" width=\"168\" height=\"102\" \/><br \/>\nWe 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\" data-number-style=\"arabic\">\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>We&#8217;ll practice adding decimals in the example below. Remember \u2014 just like with whole number addition \u2014 you might have to &#8220;carry&#8221; a ten to the next place value as you add each column.<\/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=\".\" data-label=\"\">\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<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<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 Answer<\/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,\" data-label=\"\">\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=\"Vertical addition for 23.5 plus 41.38.\" width=\"75\" height=\"48\" data-media-type=\"image\/png\" \/><\/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=\"In order to align decimal places, add a trailing 0 to 23.5 such that it becomes 23.50.\" width=\"75\" height=\"46\" data-media-type=\"image\/png\" \/><\/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\" data-media-type=\"image\/png\" \/><\/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<p>Subtracting decimals follows the same process as adding decimals. Remember \u2014 just like with whole number subtraction \u2014 you may have to &#8220;borrow&#8221; ten from the next place value as you subtract each column.<\/p>\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 Answer<\/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,\" data-label=\"\">\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=\"Vertical subtraction for 20 minus 14.65\" width=\"113\" height=\"61\" data-media-type=\"image\/png\" \/><\/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=\"In order to align decimal places, add 2 trailing 0's to 20.\" width=\"117\" height=\"57\" data-media-type=\"image\/png\" \/><\/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 14.64 equals 5.35. When subtracting 5 from 0 in the hundredths place, we must borrow from the tenths place. Since we cannot subtract 1 from 0 in the tenths place, we borrow from the ones place, and since we cannot subtract 1 from 0 in the ones place, we borrow from the tens place. Thus, the 2 in 20 is borrowed from such that the ones place becomes 10, and then 9 after being borrowed from. The tenths place becomes 10 and then 9 after being borrowed from. And lastly, the hundredths place becomes 10.\" width=\"109\" height=\"95\" data-media-type=\"image\/png\" \/><\/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=\"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<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 Answer<\/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,\" data-label=\"\">\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=\"Vertical subtraction for 7.4 minus 2.51.\" width=\"65\" height=\"50\" data-media-type=\"image\/png\" \/><\/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=\"In order to align decimal places, add a trailing 0 to 7.4 such that it becomes 7.40\" width=\"65\" height=\"49\" data-media-type=\"image\/png\" \/><\/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\" data-media-type=\"image\/png\" \/><\/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<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-323\">\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>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":12,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"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\"}]","CANDELA_OUTCOMES_GUID":"01e6499a-37ac-4c1c-b810-3012ec1008d9, 453b4e18-695c-4c25-8314-b2364d460ce8","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-323","chapter","type-chapter","status-publish","hentry"],"part":22,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/323","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":12,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/323\/revisions"}],"predecessor-version":[{"id":3985,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/323\/revisions\/3985"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/parts\/22"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/323\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/media?parent=323"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapter-type?post=323"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/contributor?post=323"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/license?post=323"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}