{"id":4047,"date":"2020-04-05T01:49:28","date_gmt":"2020-04-05T01:49:28","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4047"},"modified":"2024-06-26T18:03:31","modified_gmt":"2024-06-26T18:03:31","slug":"writing-rates-and-calculating-unit-rates","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/writing-rates-and-calculating-unit-rates\/","title":{"raw":"Writing Rates and Calculating Unit Rates","rendered":"Writing Rates and Calculating Unit Rates"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Translate phrases to expressions with fractions<\/li>\r\n \t<li>Write a rate as a fraction<\/li>\r\n \t<li>Calculate a unit rate<\/li>\r\n \t<li>Calculate a unit price<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Write a Rate as a Fraction<\/h2>\r\nFrequently we want to compare two different types of measurements, such as miles to gallons. To make this comparison, we use a rate. Examples of rates are [latex]120[\/latex] miles in [latex]2[\/latex] hours, [latex]160[\/latex] words in [latex]4[\/latex] minutes, and [latex]\\text{\\$5}[\/latex] dollars per [latex]64[\/latex] ounces.\r\n<div class=\"textbox shaded\">\r\n<h3>Rate<\/h3>\r\nA rate compares two quantities of different units. A rate is usually written as a fraction.\r\n\r\n<\/div>\r\nWhen writing a fraction as a rate, we put the first given amount with its units in the numerator and the second amount with its units in the denominator. When rates are simplified, the units remain in the numerator and denominator.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nBob drove his car [latex]525[\/latex] miles in [latex]9[\/latex] hours. Write this rate as a fraction.\r\n\r\nSolution\r\n<table id=\"eip-id1168466124872\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\text{525 miles in 9 hours}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a fraction, with [latex]525[\/latex] miles in the numerator and [latex]9[\/latex] hours in the denominator.<\/td>\r\n<td>[latex]{\\Large\\frac{\\text{525 miles}}{\\text{9 hours}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\Large\\frac{\\text{175 miles}}{\\text{3 hours}}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSo [latex]525[\/latex] miles in [latex]9[\/latex] hours is equivalent to [latex]{\\Large\\frac{\\text{175 miles}}{\\text{3 hours}}}[\/latex]\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]146614[\/ohm_question]\r\n\r\n<\/div>\r\n<h2>Find Unit Rates<\/h2>\r\nIn the last example, we calculated that Bob was driving at a rate of [latex]{\\Large\\frac{\\text{175 miles}}{\\text{3 hours}}}[\/latex]. This tells us that every three hours, Bob will travel [latex]175[\/latex] miles. This is correct, but not very useful. We usually want the rate to reflect the number of miles in one hour. A rate that has a denominator of [latex]1[\/latex] unit is referred to as a unit rate.\r\n<div class=\"textbox shaded\">\r\n<h3>Unit Rate<\/h3>\r\nA unit rate is a rate with denominator of [latex]1[\/latex] unit.\r\n\r\n<\/div>\r\nUnit rates are very common in our lives. For example, when we say that we are driving at a speed of [latex]68[\/latex] miles per hour we mean that we travel [latex]68[\/latex] miles in [latex]1[\/latex] hour. We would write this rate as [latex]68[\/latex] miles\/hour (read [latex]68[\/latex] miles per hour). The common abbreviation for this is [latex]68[\/latex] mph. Note that when no number is written before a unit, it is assumed to be [latex]1[\/latex].\r\n\r\nSo [latex]68[\/latex] miles\/hour really means [latex]\\text{68 miles\/1 hour.}[\/latex]\r\n\r\nTwo rates we often use when driving can be written in different forms, as shown:\r\n<table id=\"fs-id2696361\" class=\"unnumbered\" summary=\"A table is shown with 5 columns and 3 rows. The header row labels the columns: \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Example<\/th>\r\n<th>Rate<\/th>\r\n<th>Write<\/th>\r\n<th>Abbreviate<\/th>\r\n<th>Read<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]68[\/latex] miles in [latex]1[\/latex] hour<\/td>\r\n<td>[latex]\\Large\\frac{\\text{68 miles}}{\\text{1 hour}}[\/latex]<\/td>\r\n<td>[latex]68[\/latex] miles\/hour<\/td>\r\n<td>[latex]68[\/latex] mph<\/td>\r\n<td>[latex]\\text{68 miles per hour}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]36[\/latex] miles to [latex]1[\/latex] gallon<\/td>\r\n<td>[latex]\\Large\\frac{\\text{36 miles}}{\\text{1 gallon}}[\/latex]<\/td>\r\n<td>[latex]36[\/latex] miles\/gallon<\/td>\r\n<td>[latex]36[\/latex] mpg<\/td>\r\n<td>[latex]\\text{36 miles per gallon}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nAnother example of unit rate that you may already know about is hourly pay rate. It is usually expressed as the amount of money earned for one hour of work. For example, if you are paid [latex]\\text{\\$12.50}[\/latex] for each hour you work, you could write that your hourly (unit) pay rate is [latex]\\text{\\$12.50\/hour}[\/latex] (read [latex]\\text{\\$12.50}[\/latex] per hour.)\r\n\r\nTo convert a rate to a unit rate, we divide the numerator by the denominator. This gives us a denominator of [latex]1[\/latex].\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAnita was paid [latex]\\text{\\$384}[\/latex] last week for working [latex]\\text{32 hours}[\/latex]. What is Anita\u2019s hourly pay rate?\r\n[reveal-answer q=\"569163\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"569163\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168467375743\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Start with a rate of dollars to hours. Then divide.<\/td>\r\n<td>[latex]\\text{\\$384}[\/latex] last week for [latex]32[\/latex] hours.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a rate.<\/td>\r\n<td>[latex]{\\Large\\frac{$384}{\\text{32 hours}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide the numerator by the denominator.<\/td>\r\n<td>[latex]{\\Large\\frac{$12}{\\text{1 hour}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as a rate.<\/td>\r\n<td>[latex]$12\/\\text{hour}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nAnita\u2019s hourly pay rate is [latex]\\text{\\$12}[\/latex] per hour.\r\n\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]146615[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSven drives his car [latex]455[\/latex] miles, using [latex]14[\/latex] gallons of gasoline. How many miles per gallon does his car get?\r\n[reveal-answer q=\"888657\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"888657\"]\r\n\r\nSolution\r\nStart with a rate of miles to gallons. Then divide.\r\n<table id=\"eip-id1168468682341\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\text{455 miles to 14 gallons of gas}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a rate.<\/td>\r\n<td>[latex]{\\Large\\frac{\\text{455 miles}}{\\text{14 gallons}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide 455 by 14 to get the unit rate.<\/td>\r\n<td>[latex]{\\Large\\frac{\\text{32.5 miles}}{\\text{1 gallon}}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSven\u2019s car gets [latex]32.5[\/latex] miles\/gallon, or [latex]32.5[\/latex] mpg.\r\n\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]146616[\/ohm_question]\r\n\r\n<\/div>\r\nThe next video shows more examples of how to find rates and unit rates.\r\n\r\nhttps:\/\/youtu.be\/jlEJU-l5DWw\r\n<h2>Calculating Unit Price<\/h2>\r\nSometimes we buy common household items \u2018in bulk\u2019, where several items are packaged together and sold for one price. To compare the prices of different sized packages, we need to find the unit price. To find the unit price, divide the total price by the number of items. A unit price is a unit rate for one item.\r\n<div class=\"textbox shaded\">\r\n<h3>Unit price<\/h3>\r\nA unit price is a unit rate that gives the price of one item.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe grocery store charges [latex]\\text{\\$3.99}[\/latex] for a case of [latex]24[\/latex] bottles of water. What is the unit price?\r\n\r\nSolution\r\nWhat are we asked to find? We are asked to find the unit price, which is the price per bottle.\r\n<table id=\"eip-id1168469868304\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Write as a rate.<\/td>\r\n<td>[latex]{\\Large\\frac{$3.99}{\\text{24 bottles}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide to find the unit price.<\/td>\r\n<td>[latex]{\\Large\\frac{$0.16625}{\\text{1 bottle}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Round the result to the nearest penny.<\/td>\r\n<td>[latex]{\\Large\\frac{$0.17}{\\text{1 bottle}}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe unit price is approximately [latex]\\text{\\$0.17}[\/latex] per bottle. Each bottle costs about [latex]\\text{\\$0.17}[\/latex].\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY\u00a0IT<\/h3>\r\n[ohm_question]146617[\/ohm_question]\r\n\r\n<\/div>\r\nUnit prices are very useful if you comparison shop. The <em>better buy<\/em> is the item with the lower unit price. Most grocery stores list the unit price of each item on the shelves.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nPaul is shopping for laundry detergent. At the grocery store, the liquid detergent is priced at [latex]\\text{\\$14.99}[\/latex] for [latex]64[\/latex] loads of laundry and the same brand of powder detergent is priced at [latex]\\text{\\$15.99}[\/latex] for [latex]80[\/latex] loads.\r\nWhich is the better buy, the liquid or the powder detergent?\r\n[reveal-answer q=\"309277\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"309277\"]\r\n\r\nSolution\r\nTo compare the prices, we first find the unit price for each type of detergent.\r\n<table id=\"fs-id1383623\" class=\"unnumbered\" summary=\"A table is shown with 3 columns and 4 rows. The first column is not labeled. The other columns are labeled as \">\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td><\/td>\r\n<td>Liquid<\/td>\r\n<td>Powder<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>Write as a rate.<\/td>\r\n<td>[latex]{\\Large\\frac{\\text{\\$14.99}}{\\text{64 loads}}}[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{\\text{\\$15.99}}{\\text{80 loads}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>Find the unit price.<\/td>\r\n<td>[latex]{\\Large\\frac{\\text{\\$0.234\\ldots }}{\\text{1 load}}}[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{\\text{\\$0.199\\ldots }}{\\text{1 load}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>Round to the nearest cent.<\/td>\r\n<td>[latex]\\begin{array}{c}\\text{\\$0.23\/load}\\hfill \\\\ \\text{(23 cents per load.)}\\hfill \\end{array}[\/latex]<\/td>\r\n<td>[latex]\\begin{array}{c}\\text{\\$0.20\/load}\\hfill \\\\ \\text{(20 cents per load)}\\hfill \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow we compare the unit prices. The unit price of the liquid detergent is about [latex]\\text{\\$0.23}[\/latex] per load and the unit price of the powder detergent is about [latex]\\text{\\$0.20}[\/latex] per load. The powder is the better buy.\r\n\r\nNotice in the example above\u00a0that we rounded the unit price to the nearest cent. Sometimes we may need to carry the division to one more place to see the difference between the unit prices.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind each unit price and then determine the better buy. Round to the nearest cent if necessary.\r\n\r\nBrand A Storage Bags, [latex]\\text{\\$4.59}[\/latex] for [latex]40[\/latex] count, or Brand B Storage Bags, [latex]\\text{\\$3.99}[\/latex] for [latex]30[\/latex] count\r\n[reveal-answer q=\"610855\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"610855\"]\r\n\r\nBrand A costs [latex]$0.12[\/latex] per bag. Brand B costs [latex]$0.13[\/latex] per bag. Brand A is the better buy.\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nFind each unit price and then determine the better buy. Round to the nearest cent if necessary.\r\nBrand C Chicken Noodle Soup, [latex]\\text{\\$1.89}[\/latex] for [latex]26[\/latex] ounces, or Brand D Chicken Noodle Soup, [latex]\\text{\\$0.95}[\/latex] for [latex]10.75[\/latex] ounces\r\n[reveal-answer q=\"367191\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"367191\"]\r\n\r\nBrand C costs [latex]$0.07[\/latex] per ounce. Brand D costs [latex]$0.09[\/latex] per ounce. Brand C is the better buy.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe follwoing video shows another example of how you can use unit price to compare the value of two products.\r\n\r\nhttps:\/\/youtu.be\/ZI4WaviYNsk","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Translate phrases to expressions with fractions<\/li>\n<li>Write a rate as a fraction<\/li>\n<li>Calculate a unit rate<\/li>\n<li>Calculate a unit price<\/li>\n<\/ul>\n<\/div>\n<h2>Write a Rate as a Fraction<\/h2>\n<p>Frequently we want to compare two different types of measurements, such as miles to gallons. To make this comparison, we use a rate. Examples of rates are [latex]120[\/latex] miles in [latex]2[\/latex] hours, [latex]160[\/latex] words in [latex]4[\/latex] minutes, and [latex]\\text{\\$5}[\/latex] dollars per [latex]64[\/latex] ounces.<\/p>\n<div class=\"textbox shaded\">\n<h3>Rate<\/h3>\n<p>A rate compares two quantities of different units. A rate is usually written as a fraction.<\/p>\n<\/div>\n<p>When writing a fraction as a rate, we put the first given amount with its units in the numerator and the second amount with its units in the denominator. When rates are simplified, the units remain in the numerator and denominator.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Bob drove his car [latex]525[\/latex] miles in [latex]9[\/latex] hours. Write this rate as a fraction.<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168466124872\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\text{525 miles in 9 hours}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a fraction, with [latex]525[\/latex] miles in the numerator and [latex]9[\/latex] hours in the denominator.<\/td>\n<td>[latex]{\\Large\\frac{\\text{525 miles}}{\\text{9 hours}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]{\\Large\\frac{\\text{175 miles}}{\\text{3 hours}}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>So [latex]525[\/latex] miles in [latex]9[\/latex] hours is equivalent to [latex]{\\Large\\frac{\\text{175 miles}}{\\text{3 hours}}}[\/latex]<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146614\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146614&theme=oea&iframe_resize_id=ohm146614&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2>Find Unit Rates<\/h2>\n<p>In the last example, we calculated that Bob was driving at a rate of [latex]{\\Large\\frac{\\text{175 miles}}{\\text{3 hours}}}[\/latex]. This tells us that every three hours, Bob will travel [latex]175[\/latex] miles. This is correct, but not very useful. We usually want the rate to reflect the number of miles in one hour. A rate that has a denominator of [latex]1[\/latex] unit is referred to as a unit rate.<\/p>\n<div class=\"textbox shaded\">\n<h3>Unit Rate<\/h3>\n<p>A unit rate is a rate with denominator of [latex]1[\/latex] unit.<\/p>\n<\/div>\n<p>Unit rates are very common in our lives. For example, when we say that we are driving at a speed of [latex]68[\/latex] miles per hour we mean that we travel [latex]68[\/latex] miles in [latex]1[\/latex] hour. We would write this rate as [latex]68[\/latex] miles\/hour (read [latex]68[\/latex] miles per hour). The common abbreviation for this is [latex]68[\/latex] mph. Note that when no number is written before a unit, it is assumed to be [latex]1[\/latex].<\/p>\n<p>So [latex]68[\/latex] miles\/hour really means [latex]\\text{68 miles\/1 hour.}[\/latex]<\/p>\n<p>Two rates we often use when driving can be written in different forms, as shown:<\/p>\n<table id=\"fs-id2696361\" class=\"unnumbered\" summary=\"A table is shown with 5 columns and 3 rows. The header row labels the columns:\">\n<thead>\n<tr valign=\"top\">\n<th>Example<\/th>\n<th>Rate<\/th>\n<th>Write<\/th>\n<th>Abbreviate<\/th>\n<th>Read<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]68[\/latex] miles in [latex]1[\/latex] hour<\/td>\n<td>[latex]\\Large\\frac{\\text{68 miles}}{\\text{1 hour}}[\/latex]<\/td>\n<td>[latex]68[\/latex] miles\/hour<\/td>\n<td>[latex]68[\/latex] mph<\/td>\n<td>[latex]\\text{68 miles per hour}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]36[\/latex] miles to [latex]1[\/latex] gallon<\/td>\n<td>[latex]\\Large\\frac{\\text{36 miles}}{\\text{1 gallon}}[\/latex]<\/td>\n<td>[latex]36[\/latex] miles\/gallon<\/td>\n<td>[latex]36[\/latex] mpg<\/td>\n<td>[latex]\\text{36 miles per gallon}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Another example of unit rate that you may already know about is hourly pay rate. It is usually expressed as the amount of money earned for one hour of work. For example, if you are paid [latex]\\text{\\$12.50}[\/latex] for each hour you work, you could write that your hourly (unit) pay rate is [latex]\\text{\\$12.50\/hour}[\/latex] (read [latex]\\text{\\$12.50}[\/latex] per hour.)<\/p>\n<p>To convert a rate to a unit rate, we divide the numerator by the denominator. This gives us a denominator of [latex]1[\/latex].<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Anita was paid [latex]\\text{\\$384}[\/latex] last week for working [latex]\\text{32 hours}[\/latex]. What is Anita\u2019s hourly pay rate?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q569163\">Show Solution<\/span><\/p>\n<div id=\"q569163\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168467375743\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Start with a rate of dollars to hours. Then divide.<\/td>\n<td>[latex]\\text{\\$384}[\/latex] last week for [latex]32[\/latex] hours.<\/td>\n<\/tr>\n<tr>\n<td>Write as a rate.<\/td>\n<td>[latex]{\\Large\\frac{$384}{\\text{32 hours}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide the numerator by the denominator.<\/td>\n<td>[latex]{\\Large\\frac{$12}{\\text{1 hour}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as a rate.<\/td>\n<td>[latex]$12\/\\text{hour}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Anita\u2019s hourly pay rate is [latex]\\text{\\$12}[\/latex] per hour.<\/p>\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=\"ohm146615\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146615&theme=oea&iframe_resize_id=ohm146615&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>Sven drives his car [latex]455[\/latex] miles, using [latex]14[\/latex] gallons of gasoline. How many miles per gallon does his car get?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q888657\">Show Solution<\/span><\/p>\n<div id=\"q888657\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nStart with a rate of miles to gallons. Then divide.<\/p>\n<table id=\"eip-id1168468682341\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\text{455 miles to 14 gallons of gas}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a rate.<\/td>\n<td>[latex]{\\Large\\frac{\\text{455 miles}}{\\text{14 gallons}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide 455 by 14 to get the unit rate.<\/td>\n<td>[latex]{\\Large\\frac{\\text{32.5 miles}}{\\text{1 gallon}}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Sven\u2019s car gets [latex]32.5[\/latex] miles\/gallon, or [latex]32.5[\/latex] mpg.<\/p>\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=\"ohm146616\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146616&theme=oea&iframe_resize_id=ohm146616&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The next video shows more examples of how to find rates and unit rates.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Rates and Unit Rates\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/jlEJU-l5DWw?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Calculating Unit Price<\/h2>\n<p>Sometimes we buy common household items \u2018in bulk\u2019, where several items are packaged together and sold for one price. To compare the prices of different sized packages, we need to find the unit price. To find the unit price, divide the total price by the number of items. A unit price is a unit rate for one item.<\/p>\n<div class=\"textbox shaded\">\n<h3>Unit price<\/h3>\n<p>A unit price is a unit rate that gives the price of one item.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The grocery store charges [latex]\\text{\\$3.99}[\/latex] for a case of [latex]24[\/latex] bottles of water. What is the unit price?<\/p>\n<p>Solution<br \/>\nWhat are we asked to find? We are asked to find the unit price, which is the price per bottle.<\/p>\n<table id=\"eip-id1168469868304\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Write as a rate.<\/td>\n<td>[latex]{\\Large\\frac{$3.99}{\\text{24 bottles}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide to find the unit price.<\/td>\n<td>[latex]{\\Large\\frac{$0.16625}{\\text{1 bottle}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Round the result to the nearest penny.<\/td>\n<td>[latex]{\\Large\\frac{$0.17}{\\text{1 bottle}}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The unit price is approximately [latex]\\text{\\$0.17}[\/latex] per bottle. Each bottle costs about [latex]\\text{\\$0.17}[\/latex].<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146617\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146617&theme=oea&iframe_resize_id=ohm146617&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Unit prices are very useful if you comparison shop. The <em>better buy<\/em> is the item with the lower unit price. Most grocery stores list the unit price of each item on the shelves.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Paul is shopping for laundry detergent. At the grocery store, the liquid detergent is priced at [latex]\\text{\\$14.99}[\/latex] for [latex]64[\/latex] loads of laundry and the same brand of powder detergent is priced at [latex]\\text{\\$15.99}[\/latex] for [latex]80[\/latex] loads.<br \/>\nWhich is the better buy, the liquid or the powder detergent?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q309277\">Show Solution<\/span><\/p>\n<div id=\"q309277\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nTo compare the prices, we first find the unit price for each type of detergent.<\/p>\n<table id=\"fs-id1383623\" class=\"unnumbered\" summary=\"A table is shown with 3 columns and 4 rows. The first column is not labeled. The other columns are labeled as\">\n<tbody>\n<tr valign=\"top\">\n<td><\/td>\n<td>Liquid<\/td>\n<td>Powder<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Write as a rate.<\/td>\n<td>[latex]{\\Large\\frac{\\text{\\$14.99}}{\\text{64 loads}}}[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{\\text{\\$15.99}}{\\text{80 loads}}}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Find the unit price.<\/td>\n<td>[latex]{\\Large\\frac{\\text{\\$0.234\\ldots }}{\\text{1 load}}}[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{\\text{\\$0.199\\ldots }}{\\text{1 load}}}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Round to the nearest cent.<\/td>\n<td>[latex]\\begin{array}{c}\\text{\\$0.23\/load}\\hfill \\\\ \\text{(23 cents per load.)}\\hfill \\end{array}[\/latex]<\/td>\n<td>[latex]\\begin{array}{c}\\text{\\$0.20\/load}\\hfill \\\\ \\text{(20 cents per load)}\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Now we compare the unit prices. The unit price of the liquid detergent is about [latex]\\text{\\$0.23}[\/latex] per load and the unit price of the powder detergent is about [latex]\\text{\\$0.20}[\/latex] per load. The powder is the better buy.<\/p>\n<p>Notice in the example above\u00a0that we rounded the unit price to the nearest cent. Sometimes we may need to carry the division to one more place to see the difference between the unit prices.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Find each unit price and then determine the better buy. Round to the nearest cent if necessary.<\/p>\n<p>Brand A Storage Bags, [latex]\\text{\\$4.59}[\/latex] for [latex]40[\/latex] count, or Brand B Storage Bags, [latex]\\text{\\$3.99}[\/latex] for [latex]30[\/latex] count<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q610855\">Show Solution<\/span><\/p>\n<div id=\"q610855\" class=\"hidden-answer\" style=\"display: none\">\n<p>Brand A costs [latex]$0.12[\/latex] per bag. Brand B costs [latex]$0.13[\/latex] per bag. Brand A is the better buy.<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Find each unit price and then determine the better buy. Round to the nearest cent if necessary.<br \/>\nBrand C Chicken Noodle Soup, [latex]\\text{\\$1.89}[\/latex] for [latex]26[\/latex] ounces, or Brand D Chicken Noodle Soup, [latex]\\text{\\$0.95}[\/latex] for [latex]10.75[\/latex] ounces<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q367191\">Show Solution<\/span><\/p>\n<div id=\"q367191\" class=\"hidden-answer\" style=\"display: none\">\n<p>Brand C costs [latex]$0.07[\/latex] per ounce. Brand D costs [latex]$0.09[\/latex] per ounce. Brand C is the better buy.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>The follwoing video shows another example of how you can use unit price to compare the value of two products.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Example:  Determine the Best Buy Using Unit Rate\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/ZI4WaviYNsk?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-4047\">\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>Question ID 146617, 146616, 146615, 146614. <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><li>Revision and Adaptation. <strong>Provided 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, Shared previously<\/div><ul class=\"citation-list\"><li>Rates and Unit Rates. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/jlEJU-l5DWw\">https:\/\/youtu.be\/jlEJU-l5DWw<\/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>Example: Determine the Best Buy Using Unit Rate. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/ZI4WaviYNsk\">https:\/\/youtu.be\/ZI4WaviYNsk<\/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, 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":25777,"menu_order":4,"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\":\"cc\",\"description\":\"Rates and Unit Rates\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/jlEJU-l5DWw\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Example: Determine the Best Buy Using Unit Rate\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/ZI4WaviYNsk\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID 146617, 146616, 146615, 146614\",\"author\":\"Lumen 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