{"id":9225,"date":"2017-05-02T19:42:45","date_gmt":"2017-05-02T19:42:45","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9225"},"modified":"2017-09-23T15:11:21","modified_gmt":"2017-09-23T15:11:21","slug":"multiplying-whole-numbers-in-applications","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/multiplying-whole-numbers-in-applications\/","title":{"raw":"Multiplying Whole Numbers in Applications","rendered":"Multiplying Whole Numbers in Applications"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Translate word phrases that represent multiplication into mathematical notation<\/li>\r\n \t<li>Solve word application that involve multiplication<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<h2 data-type=\"title\">Translate Word Phrases to Math Notation<\/h2>\r\nEarlier in this section, we translated math notation into words. Now we\u2019ll reverse the process and translate word phrases into math notation. Some of the words that indicate multiplication are given in the table below.\r\n<table id=\"fs-id1971628\" style=\"width: 75%;\" summary=\"A table with 4 columns and 3 rows. The first column is labeled \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th data-align=\"left\">Operation<\/th>\r\n<th data-align=\"left\">Word Phrase<\/th>\r\n<th data-align=\"left\">Example<\/th>\r\n<th data-align=\"left\">Expression<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Multiplication<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">times\r\n\r\nproduct\r\n\r\ntwice<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">[latex]3[\/latex] times [latex]8[\/latex]\r\n\r\nthe product of [latex]3[\/latex] and [latex]8[\/latex]\r\n\r\ntwice [latex]4[\/latex]<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">[latex]3\\times 8,3\\cdot 8,\\left(3\\right)\\left(8\\right)[\/latex],\r\n\r\n[latex]\\left(3\\right)8,\\text{ or }3\\left(8\\right)[\/latex]\r\n\r\n[latex]2\\cdot 4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate and simplify: the product of [latex]12[\/latex] and [latex]27[\/latex].\r\n\r\nSolution:\r\nThe word <em data-effect=\"italics\">product<\/em> tells us to multiply. The words <em data-effect=\"italics\">of<\/em> [latex]12[\/latex] <em data-effect=\"italics\">and<\/em> [latex]27[\/latex] tell us the two factors.\r\n<table id=\"eip-id1168287170388\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\" \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>the product of [latex]12[\/latex] and [latex]27[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate.<\/td>\r\n<td>[latex]12\\cdot 27[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]324[\/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<iframe id=\"mom1\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144437&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate and simplify: twice two hundred eleven.\r\n\r\n[reveal-answer q=\"44131\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"44131\"]\r\n\r\nSolution:\r\nThe word <em data-effect=\"italics\">twice<\/em> tells us to multiply by [latex]2[\/latex].\r\n<table id=\"eip-id1168289723873\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>twice two hundred eleven<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate.<\/td>\r\n<td>[latex]2(211)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]422[\/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<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144439&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\n&nbsp;\r\n<h2>Multiply Whole Numbers in Applications<\/h2>\r\nWe will use the same strategy we used previously to solve applications of multiplication. First, we need to determine what we are looking for. Then we write a phrase that gives the information to find it. We then translate the phrase into math notation and simplify to get the answer. Finally, we write a sentence to answer the question.\r\n\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nHumberto bought [latex]4[\/latex] sheets of stamps. Each sheet had [latex]20[\/latex] stamps. How many stamps did Humberto buy?\r\n\r\n[reveal-answer q=\"932095\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"932095\"]\r\n\r\nSolution:\r\nWe are asked to find the total number of stamps.\r\n<table id=\"eip-458\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"a\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Write a phrase for the total.<\/td>\r\n<td>the product of [latex]4[\/latex] and [latex]20[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate to math notation.<\/td>\r\n<td>[latex]4\\cdot 20[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215537\/CNX_BMath_Figure_01_04_021_img-01.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence to answer the question.<\/td>\r\n<td>Humberto bought [latex]80[\/latex] stamps.<\/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<iframe id=\"mom3\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144442&amp;theme=oea&amp;iframe_resize_id=mom3\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWhen Rena cooks rice, she uses twice as much water as rice. How much water does she need to cook [latex]4[\/latex] cups of rice?\r\n\r\n[reveal-answer q=\"707137\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"707137\"]\r\n\r\nSolution:\r\nWe are asked to find how much water Rena needs.\r\n<table id=\"eip-id1168288610426\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\" \" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Write as a phrase.<\/td>\r\n<td>twice as much as 4 cups<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate to math notation.<\/td>\r\n<td>[latex]2\\cdot 4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply to simplify.<\/td>\r\n<td>[latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence to answer the question.<\/td>\r\n<td>Rena needs [latex]8[\/latex] cups of water for cups of rice.<\/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<iframe id=\"mom4\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144443&amp;theme=oea&amp;iframe_resize_id=mom4\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nVan is planning to build a patio. He will have [latex]8[\/latex] rows of tiles, with [latex]14[\/latex] tiles in each row. How many tiles does he need for the patio?\r\n\r\n[reveal-answer q=\"76170\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"76170\"]\r\n\r\nSolution:\r\nWe are asked to find the total number of tiles.\r\n<table id=\"eip-842\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"a\">\r\n<tbody>\r\n<tr>\r\n<td>Write a phrase.<\/td>\r\n<td>the product of [latex]8[\/latex] and [latex]14[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate to math notation.<\/td>\r\n<td>[latex]8\\cdot 14[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply to simplify.<\/td>\r\n<td>[latex]\\begin{array}{c}\\\\ \\stackrel{3}{1}4\\hfill \\\\ \\underset{\\text{___}}{\\times 8}\\hfill \\\\ 112\\hfill \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence to answer the question.<\/td>\r\n<td>Van needs [latex]112[\/latex] tiles for his patio.<\/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<iframe id=\"mom5\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144444&amp;theme=oea&amp;iframe_resize_id=mom5\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nIf we want to know the size of a wall that needs to be painted or a floor that needs to be carpeted, we will need to find its area. The area is a measure of the amount of surface that is covered by the shape. Area is measured in square units. We often use square inches, square feet, square centimeters, or square miles to measure area. A square centimeter is a square that is one centimeter (cm.) on a side. A square inch is a square that is one inch on each side, and so on.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215538\/CNX_BMath_Figure_01_04_014.png\" alt=\"An image of two squares, one larger than the other. The smaller square is 1 centimeter by 1 centimeter and has the label \" data-media-type=\"image\/png\" \/>\r\nFor a rectangular figure, the area is the product of the length and the width. The figure below shows a rectangular rug with a length of [latex]2[\/latex] feet and a width of [latex]3[\/latex] feet. Each square is [latex]1[\/latex] foot wide by [latex]1[\/latex] foot long, or [latex]1[\/latex] square foot. The rug is made of [latex]6[\/latex] squares. The area of the rug is [latex]6[\/latex] square feet.\r\n\r\nThe area of a rectangle is the product of its length and its width, or [latex]6[\/latex] square feet.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215540\/CNX_BMath_Figure_01_04_013.png\" alt=\"An image of a rectangle containing 6 blocks, 2 feet tall and 3 feet wide. This image has the label \" data-media-type=\"image\/png\" \/>\r\n\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nJen\u2019s kitchen ceiling is a rectangle that measures [latex]9[\/latex] feet long by [latex]12[\/latex] feet wide. What is the area of Jen\u2019s kitchen ceiling?\r\n\r\n[reveal-answer q=\"947398\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"947398\"]\r\n\r\nSolution:\r\nWe are asked to find the area of the kitchen ceiling.\r\n<table id=\"eip-430\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"a\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Write a phrase for the area.<\/td>\r\n<td>the product of [latex]9[\/latex] and [latex]12[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate to math notation.<\/td>\r\n<td>[latex]9\\cdot 12[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]\\begin{array}{c}\\\\ \\stackrel{1}{1}2\\hfill \\\\ \\underset{\\text{___}}{\\times 9}\\hfill \\\\ 108\\hfill \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Answer with a sentence.<\/td>\r\n<td>The area of Jen's kitchen ceiling is [latex]108[\/latex] square feet.<\/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<iframe id=\"mom6\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144445&amp;theme=oea&amp;iframe_resize_id=mom6\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nIn the following video we show another example of using multiplication to solve application problems.\r\nhttps:\/\/youtu.be\/xTX4pVOblnA","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Translate word phrases that represent multiplication into mathematical notation<\/li>\n<li>Solve word application that involve multiplication<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<h2 data-type=\"title\">Translate Word Phrases to Math Notation<\/h2>\n<p>Earlier in this section, we translated math notation into words. Now we\u2019ll reverse the process and translate word phrases into math notation. Some of the words that indicate multiplication are given in the table below.<\/p>\n<table id=\"fs-id1971628\" style=\"width: 75%;\" summary=\"A table with 4 columns and 3 rows. The first column is labeled\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"left\">Operation<\/th>\n<th data-align=\"left\">Word Phrase<\/th>\n<th data-align=\"left\">Example<\/th>\n<th data-align=\"left\">Expression<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Multiplication<\/td>\n<td data-valign=\"top\" data-align=\"left\">times<\/p>\n<p>product<\/p>\n<p>twice<\/td>\n<td data-valign=\"top\" data-align=\"left\">[latex]3[\/latex] times [latex]8[\/latex]<\/p>\n<p>the product of [latex]3[\/latex] and [latex]8[\/latex]<\/p>\n<p>twice [latex]4[\/latex]<\/td>\n<td data-valign=\"top\" data-align=\"left\">[latex]3\\times 8,3\\cdot 8,\\left(3\\right)\\left(8\\right)[\/latex],<\/p>\n<p>[latex]\\left(3\\right)8,\\text{ or }3\\left(8\\right)[\/latex]<\/p>\n<p>[latex]2\\cdot 4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate and simplify: the product of [latex]12[\/latex] and [latex]27[\/latex].<\/p>\n<p>Solution:<br \/>\nThe word <em data-effect=\"italics\">product<\/em> tells us to multiply. The words <em data-effect=\"italics\">of<\/em> [latex]12[\/latex] <em data-effect=\"italics\">and<\/em> [latex]27[\/latex] tell us the two factors.<\/p>\n<table id=\"eip-id1168287170388\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>the product of [latex]12[\/latex] and [latex]27[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td>[latex]12\\cdot 27[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]324[\/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=\"mom1\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144437&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate and simplify: twice two hundred eleven.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q44131\">Show Solution<\/span><\/p>\n<div id=\"q44131\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nThe word <em data-effect=\"italics\">twice<\/em> tells us to multiply by [latex]2[\/latex].<\/p>\n<table id=\"eip-id1168289723873\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>twice two hundred eleven<\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td>[latex]2(211)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]422[\/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=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144439&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Multiply Whole Numbers in Applications<\/h2>\n<p>We will use the same strategy we used previously to solve applications of multiplication. First, we need to determine what we are looking for. Then we write a phrase that gives the information to find it. We then translate the phrase into math notation and simplify to get the answer. Finally, we write a sentence to answer the question.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Humberto bought [latex]4[\/latex] sheets of stamps. Each sheet had [latex]20[\/latex] stamps. How many stamps did Humberto buy?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q932095\">Show Solution<\/span><\/p>\n<div id=\"q932095\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nWe are asked to find the total number of stamps.<\/p>\n<table id=\"eip-458\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"a\" data-label=\"\">\n<tbody>\n<tr>\n<td>Write a phrase for the total.<\/td>\n<td>the product of [latex]4[\/latex] and [latex]20[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Translate to math notation.<\/td>\n<td>[latex]4\\cdot 20[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215537\/CNX_BMath_Figure_01_04_021_img-01.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write a sentence to answer the question.<\/td>\n<td>Humberto bought [latex]80[\/latex] stamps.<\/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=\"mom3\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144442&amp;theme=oea&amp;iframe_resize_id=mom3\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>When Rena cooks rice, she uses twice as much water as rice. How much water does she need to cook [latex]4[\/latex] cups of rice?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q707137\">Show Solution<\/span><\/p>\n<div id=\"q707137\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nWe are asked to find how much water Rena needs.<\/p>\n<table id=\"eip-id1168288610426\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"\" data-label=\"\">\n<tbody>\n<tr>\n<td>Write as a phrase.<\/td>\n<td>twice as much as 4 cups<\/td>\n<\/tr>\n<tr>\n<td>Translate to math notation.<\/td>\n<td>[latex]2\\cdot 4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply to simplify.<\/td>\n<td>[latex]8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence to answer the question.<\/td>\n<td>Rena needs [latex]8[\/latex] cups of water for cups of rice.<\/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=\"mom4\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144443&amp;theme=oea&amp;iframe_resize_id=mom4\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Van is planning to build a patio. He will have [latex]8[\/latex] rows of tiles, with [latex]14[\/latex] tiles in each row. How many tiles does he need for the patio?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q76170\">Show Solution<\/span><\/p>\n<div id=\"q76170\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nWe are asked to find the total number of tiles.<\/p>\n<table id=\"eip-842\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"a\">\n<tbody>\n<tr>\n<td>Write a phrase.<\/td>\n<td>the product of [latex]8[\/latex] and [latex]14[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Translate to math notation.<\/td>\n<td>[latex]8\\cdot 14[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply to simplify.<\/td>\n<td>[latex]\\begin{array}{c}\\\\ \\stackrel{3}{1}4\\hfill \\\\ \\underset{\\text{___}}{\\times 8}\\hfill \\\\ 112\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence to answer the question.<\/td>\n<td>Van needs [latex]112[\/latex] tiles for his patio.<\/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=\"mom5\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144444&amp;theme=oea&amp;iframe_resize_id=mom5\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>If we want to know the size of a wall that needs to be painted or a floor that needs to be carpeted, we will need to find its area. The area is a measure of the amount of surface that is covered by the shape. Area is measured in square units. We often use square inches, square feet, square centimeters, or square miles to measure area. A square centimeter is a square that is one centimeter (cm.) on a side. A square inch is a square that is one inch on each side, and so on.<\/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\/24215538\/CNX_BMath_Figure_01_04_014.png\" alt=\"An image of two squares, one larger than the other. The smaller square is 1 centimeter by 1 centimeter and has the label\" data-media-type=\"image\/png\" \/><br \/>\nFor a rectangular figure, the area is the product of the length and the width. The figure below shows a rectangular rug with a length of [latex]2[\/latex] feet and a width of [latex]3[\/latex] feet. Each square is [latex]1[\/latex] foot wide by [latex]1[\/latex] foot long, or [latex]1[\/latex] square foot. The rug is made of [latex]6[\/latex] squares. The area of the rug is [latex]6[\/latex] square feet.<\/p>\n<p>The area of a rectangle is the product of its length and its width, or [latex]6[\/latex] square feet.<\/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\/24215540\/CNX_BMath_Figure_01_04_013.png\" alt=\"An image of a rectangle containing 6 blocks, 2 feet tall and 3 feet wide. This image has the label\" data-media-type=\"image\/png\" \/><\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Jen\u2019s kitchen ceiling is a rectangle that measures [latex]9[\/latex] feet long by [latex]12[\/latex] feet wide. What is the area of Jen\u2019s kitchen ceiling?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q947398\">Show Solution<\/span><\/p>\n<div id=\"q947398\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nWe are asked to find the area of the kitchen ceiling.<\/p>\n<table id=\"eip-430\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"a\" data-label=\"\">\n<tbody>\n<tr>\n<td>Write a phrase for the area.<\/td>\n<td>the product of [latex]9[\/latex] and [latex]12[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Translate to math notation.<\/td>\n<td>[latex]9\\cdot 12[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]\\begin{array}{c}\\\\ \\stackrel{1}{1}2\\hfill \\\\ \\underset{\\text{___}}{\\times 9}\\hfill \\\\ 108\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Answer with a sentence.<\/td>\n<td>The area of Jen&#8217;s kitchen ceiling is [latex]108[\/latex] square feet.<\/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=\"mom6\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144445&amp;theme=oea&amp;iframe_resize_id=mom6\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>In the following video we show another example of using multiplication to solve application problems.<br \/>\n<iframe loading=\"lazy\" id=\"oembed-1\" title=\"Multiply Whole Numbers to Solve Applications\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/xTX4pVOblnA?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-9225\">\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>Multiply Whole Numbers to Solve Applications. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/xTX4pVOblnA\">https:\/\/youtu.be\/xTX4pVOblnA<\/a>. <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, Shared previously<\/div><ul class=\"citation-list\"><li>Question ID: 144437, 144439, 144442, 144443, 144444, 144445. <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>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":20,"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\":\"Multiply Whole Numbers to Solve Applications\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/xTX4pVOblnA\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Question ID: 144437, 144439, 144442, 144443, 144444, 144445\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + 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