{"id":4416,"date":"2020-04-13T12:55:12","date_gmt":"2020-04-13T12:55:12","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4416"},"modified":"2020-04-27T19:55:22","modified_gmt":"2020-04-27T19:55:22","slug":"finding-the-reciprocal-of-a-number","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/finding-the-reciprocal-of-a-number\/","title":{"raw":"Finding the Reciprocal of a Number","rendered":"Finding the Reciprocal of a Number"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Find the reciprocal of a fraction<\/li>\r\n \t<li>Recognize the difference between absolute value, reciprocal and opposite of a fraction or number<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p>The fractions [latex]\\Large\\frac{2}{3}[\/latex] and [latex]\\Large\\frac{3}{2}[\/latex] are related to each other in a special way. So are [latex]\\Large-\\frac{10}{7}[\/latex] and [latex]\\Large-\\frac{7}{10}[\/latex]. Do you see how? Besides looking like upside-down versions of one another, if we were to multiply these pairs of fractions, the product would be [latex]1[\/latex].<\/p>\r\n<p style=\"text-align: center\">[latex]\\Large\\frac{2}{3}\\cdot \\frac{3}{2}\\normalsize=1\\text{ and }-\\Large\\frac{10}{7}\\left(-\\frac{7}{10}\\right)\\normalsize=1[\/latex]<\/p>\r\n<p style=\"text-align: left\">Such pairs of numbers are called reciprocals.<\/p>\r\n\r\n<div class=\"textbox shaded\">\r\n<h3>Reciprocal<\/h3>\r\nThe reciprocal of the fraction [latex]\\Large\\frac{a}{b}[\/latex] is [latex]\\Large\\frac{b}{a}[\/latex], where [latex]a\\ne 0[\/latex] and [latex]b\\ne 0[\/latex],\r\nA number and its reciprocal have a product of [latex]1[\/latex].\r\n<p style=\"text-align: center\">[latex]\\Large\\frac{a}{b}\\cdot \\frac{b}{a}\\normalsize=1[\/latex]<\/p>\r\n\r\n<\/div>\r\nTo find the reciprocal of a fraction, we invert the fraction. This means that we place the numerator in the denominator and the denominator in the numerator.\r\n\r\nTo get a positive result when multiplying two numbers, the numbers must have the same sign. So reciprocals must have the same sign.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220923\/CNX_BMath_Figure_04_02_035_img.png\" alt=\"\" \/>\r\nTo find the reciprocal, keep the same sign and invert the fraction. The number zero does not have a reciprocal. Why? A number and its reciprocal multiply to [latex]1[\/latex]. Is there any number [latex]r[\/latex] so that [latex]0\\cdot r=1?[\/latex] No. So, the number [latex]0[\/latex] does not have a reciprocal.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the reciprocal of each number. Then check that the product of each number and its reciprocal is [latex]1[\/latex].\r\n<ol id=\"eip-id1168469776775\" class=\"circled\">\r\n \t<li>[latex]\\Large\\frac{4}{9}[\/latex]<\/li>\r\n \t<li>[latex]\\Large-\\frac{1}{6}[\/latex]<\/li>\r\n \t<li>[latex]\\Large-\\frac{14}{5}[\/latex]<\/li>\r\n \t<li>[latex]7[\/latex]<\/li>\r\n<\/ol>\r\nSolution:\r\nTo find the reciprocals, we keep the sign and invert the fractions.\r\n<table id=\"eip-374\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the reciprocal of [latex]\\Large\\frac{4}{9}[\/latex]<\/td>\r\n<td>The reciprocal of [latex]\\Large\\frac{4}{9}[\/latex] is [latex]\\Large\\frac{9}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check:<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the number and its reciprocal.<\/td>\r\n<td>[latex]\\Large\\frac{4}{9}\\cdot \\frac{9}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply numerators and denominators.<\/td>\r\n<td>[latex]\\Large\\frac{36}{36}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]1\\quad\\checkmark [\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-37774\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the reciprocal of [latex]\\Large-\\frac{1}{6}[\/latex]<\/td>\r\n<td>[latex]\\Large-\\frac{6}{1}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]-6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check:<\/td>\r\n<td>[latex]\\Large-\\frac{1}{6}\\normalsize\\cdot \\left(-6\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]1\\quad\\checkmark [\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1170196522976\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the reciprocal of [latex]\\Large-\\frac{14}{5}[\/latex]<\/td>\r\n<td>[latex]\\Large-\\frac{5}{14}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check:<\/td>\r\n<td>[latex]\\Large-\\frac{14}{5}\\cdot \\left(-\\frac{5}{14}\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\Large\\frac{70}{70}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]1\\quad\\checkmark [\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1170195508737\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>4.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the reciprocal of [latex]7[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write [latex]7[\/latex] as a fraction.<\/td>\r\n<td>[latex]\\Large\\frac{7}{1}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the reciprocal of [latex]\\Large\\frac{7}{1}[\/latex]<\/td>\r\n<td>[latex]\\Large\\frac{1}{7}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check:<\/td>\r\n<td>[latex]7\\cdot\\Large\\left(\\frac{1}{7}\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]1\\quad\\checkmark [\/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 height=\"400\"]141842[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we will show more examples of how to find the reciprocal of integers, fractions and mixed numbers.\r\n\r\nhttps:\/\/youtu.be\/IM991IqCi44\r\n\r\nIn a previous chapter, we worked with opposites and absolute values. The table below compares opposites, absolute values, and reciprocals.\r\n<table id=\"fs-id1394345\" class=\"unnumbered\" style=\"width: 85%\" summary=\"A table is shown with 2 rows and 3 columns. The first row is a header row labeling each column. The first column is \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Opposite<\/th>\r\n<th>Absolute Value<\/th>\r\n<th>Reciprocal<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>has opposite sign<\/td>\r\n<td>is never negative<\/td>\r\n<td>has same sign, fraction inverts<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFill in the chart for each fraction in the left column:\r\n<table id=\"fs-id1179454\" class=\"unnumbered\" style=\"width: 85%\" summary=\"A table is shown with 5 rows and 4 columns. The first row is a header row labeling each column. The first column is \">\r\n<thead>\r\n<tr>\r\n<th>Number<\/th>\r\n<th>Opposite<\/th>\r\n<th>Absolute Value<\/th>\r\n<th>Reciprocal<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]\\Large-\\frac{3}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\Large\\frac{1}{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\Large\\frac{9}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]-5[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[reveal-answer q=\"72832\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"72832\"]\r\n\r\nSolution:\r\nTo find the opposite, change the sign. To find the absolute value, leave the positive numbers the same, but take the opposite of the negative numbers. To find the reciprocal, keep the sign the same and invert the fraction.\r\n<table id=\"fs-id1722688\" class=\"unnumbered\" style=\"width: 85%\" summary=\"A table is shown with 5 rows and 4 columns. The first row is a header row labeling each column. The first column is \">\r\n<thead>\r\n<tr>\r\n<th>Number<\/th>\r\n<th>Opposite<\/th>\r\n<th>Absolute Value<\/th>\r\n<th>Reciprocal<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]\\Large-\\frac{3}{8}[\/latex]<\/td>\r\n<td>[latex]\\Large\\frac{3}{8}[\/latex]<\/td>\r\n<td>[latex]\\Large\\frac{3}{8}[\/latex]<\/td>\r\n<td>[latex]\\Large-\\frac{8}{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\Large\\frac{1}{2}[\/latex]<\/td>\r\n<td>[latex]\\Large-\\frac{1}{2}[\/latex]<\/td>\r\n<td>[latex]\\Large\\frac{1}{2}[\/latex]<\/td>\r\n<td>[latex]2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\Large\\frac{9}{5}[\/latex]<\/td>\r\n<td>[latex]\\Large-\\frac{9}{5}[\/latex]<\/td>\r\n<td>[latex]\\Large\\frac{9}{5}[\/latex]<\/td>\r\n<td>[latex]\\Large\\frac{5}{9}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]-5[\/latex]<\/td>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>[latex]\\Large-\\frac{1}{5}[\/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\nFill in the chart for each number given:\r\n<table id=\"fs-id2657895\" class=\"unnumbered\" style=\"width: 85%\" summary=\"A table is shown with 5 rows and 4 columns. The first row is a header row labeling each column. The first column is \">\r\n<thead>\r\n<tr>\r\n<th>Number<\/th>\r\n<th>Opposite<\/th>\r\n<th>Absolute Value<\/th>\r\n<th>Reciprocal<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]\\Large-\\frac{5}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\Large\\frac{1}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\Large\\frac{8}{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]-8[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[reveal-answer q=\"718627\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"718627\"]\r\n<table id=\"fs-id1722656\" class=\"unnumbered\" style=\"width: 85%\" summary=\"A table is shown with 5 rows and 4 columns. The first row is a header row labeling each column. The first column is \">\r\n<thead>\r\n<tr>\r\n<th>Number<\/th>\r\n<th>Opposite<\/th>\r\n<th>Absolute Value<\/th>\r\n<th>Reciprocal<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]-\\Large\\frac{5}{8}[\/latex]<\/td>\r\n<td>[latex]\\Large\\frac{5}{8}[\/latex]<\/td>\r\n<td>[latex]\\Large\\frac{5}{8}[\/latex]<\/td>\r\n<td>[latex]-\\Large\\frac{8}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\Large\\frac{1}{4}[\/latex]<\/td>\r\n<td>[latex]-\\Large\\frac{1}{4}[\/latex]<\/td>\r\n<td>[latex]\\Large\\frac{1}{4}[\/latex]<\/td>\r\n<td>[latex]4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\Large\\frac{8}{3}[\/latex]<\/td>\r\n<td>[latex]-\\Large\\frac{8}{3}[\/latex]<\/td>\r\n<td>[latex]\\Large\\frac{8}{3}[\/latex]<\/td>\r\n<td>[latex]\\Large\\frac{3}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]-8[\/latex]<\/td>\r\n<td>[latex]8[\/latex]<\/td>\r\n<td>[latex]8[\/latex]<\/td>\r\n<td>[latex]-\\Large\\frac{1}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try it<\/h3>\r\n[ohm_question height=\"400\"]146026[\/ohm_question]\r\n\r\n<\/div>\r\nThe following video provides more examples of finding the opposite of a number.\r\n\r\nhttps:\/\/youtu.be\/suk9KMzOKkU\r\n\r\nThe next video shows how to find the absolute value of an integer.\r\n\r\nhttps:\/\/youtu.be\/lY5ksjix5Kg","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Find the reciprocal of a fraction<\/li>\n<li>Recognize the difference between absolute value, reciprocal and opposite of a fraction or number<\/li>\n<\/ul>\n<\/div>\n<p>The fractions [latex]\\Large\\frac{2}{3}[\/latex] and [latex]\\Large\\frac{3}{2}[\/latex] are related to each other in a special way. So are [latex]\\Large-\\frac{10}{7}[\/latex] and [latex]\\Large-\\frac{7}{10}[\/latex]. Do you see how? Besides looking like upside-down versions of one another, if we were to multiply these pairs of fractions, the product would be [latex]1[\/latex].<\/p>\n<p style=\"text-align: center\">[latex]\\Large\\frac{2}{3}\\cdot \\frac{3}{2}\\normalsize=1\\text{ and }-\\Large\\frac{10}{7}\\left(-\\frac{7}{10}\\right)\\normalsize=1[\/latex]<\/p>\n<p style=\"text-align: left\">Such pairs of numbers are called reciprocals.<\/p>\n<div class=\"textbox shaded\">\n<h3>Reciprocal<\/h3>\n<p>The reciprocal of the fraction [latex]\\Large\\frac{a}{b}[\/latex] is [latex]\\Large\\frac{b}{a}[\/latex], where [latex]a\\ne 0[\/latex] and [latex]b\\ne 0[\/latex],<br \/>\nA number and its reciprocal have a product of [latex]1[\/latex].<\/p>\n<p style=\"text-align: center\">[latex]\\Large\\frac{a}{b}\\cdot \\frac{b}{a}\\normalsize=1[\/latex]<\/p>\n<\/div>\n<p>To find the reciprocal of a fraction, we invert the fraction. This means that we place the numerator in the denominator and the denominator in the numerator.<\/p>\n<p>To get a positive result when multiplying two numbers, the numbers must have the same sign. So reciprocals must have the same sign.<\/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\/24220923\/CNX_BMath_Figure_04_02_035_img.png\" alt=\"\" \/><br \/>\nTo find the reciprocal, keep the same sign and invert the fraction. The number zero does not have a reciprocal. Why? A number and its reciprocal multiply to [latex]1[\/latex]. Is there any number [latex]r[\/latex] so that [latex]0\\cdot r=1?[\/latex] No. So, the number [latex]0[\/latex] does not have a reciprocal.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Find the reciprocal of each number. Then check that the product of each number and its reciprocal is [latex]1[\/latex].<\/p>\n<ol id=\"eip-id1168469776775\" class=\"circled\">\n<li>[latex]\\Large\\frac{4}{9}[\/latex]<\/li>\n<li>[latex]\\Large-\\frac{1}{6}[\/latex]<\/li>\n<li>[latex]\\Large-\\frac{14}{5}[\/latex]<\/li>\n<li>[latex]7[\/latex]<\/li>\n<\/ol>\n<p>Solution:<br \/>\nTo find the reciprocals, we keep the sign and invert the fractions.<\/p>\n<table id=\"eip-374\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Find the reciprocal of [latex]\\Large\\frac{4}{9}[\/latex]<\/td>\n<td>The reciprocal of [latex]\\Large\\frac{4}{9}[\/latex] is [latex]\\Large\\frac{9}{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply the number and its reciprocal.<\/td>\n<td>[latex]\\Large\\frac{4}{9}\\cdot \\frac{9}{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply numerators and denominators.<\/td>\n<td>[latex]\\Large\\frac{36}{36}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]1\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-37774\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Find the reciprocal of [latex]\\Large-\\frac{1}{6}[\/latex]<\/td>\n<td>[latex]\\Large-\\frac{6}{1}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]-6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td>[latex]\\Large-\\frac{1}{6}\\normalsize\\cdot \\left(-6\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]1\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1170196522976\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Find the reciprocal of [latex]\\Large-\\frac{14}{5}[\/latex]<\/td>\n<td>[latex]\\Large-\\frac{5}{14}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td>[latex]\\Large-\\frac{14}{5}\\cdot \\left(-\\frac{5}{14}\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]\\Large\\frac{70}{70}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]1\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1170195508737\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td>4.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Find the reciprocal of [latex]7[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write [latex]7[\/latex] as a fraction.<\/td>\n<td>[latex]\\Large\\frac{7}{1}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write the reciprocal of [latex]\\Large\\frac{7}{1}[\/latex]<\/td>\n<td>[latex]\\Large\\frac{1}{7}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td>[latex]7\\cdot\\Large\\left(\\frac{1}{7}\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]1\\quad\\checkmark[\/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=\"ohm141842\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141842&theme=oea&iframe_resize_id=ohm141842&show_question_numbers\" width=\"100%\" height=\"400\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we will show more examples of how to find the reciprocal of integers, fractions and mixed numbers.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex: Determine the Reciprocal of Integers, Fractions, and Mixed Numbers\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/IM991IqCi44?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>In a previous chapter, we worked with opposites and absolute values. The table below compares opposites, absolute values, and reciprocals.<\/p>\n<table id=\"fs-id1394345\" class=\"unnumbered\" style=\"width: 85%\" summary=\"A table is shown with 2 rows and 3 columns. The first row is a header row labeling each column. The first column is\">\n<thead>\n<tr valign=\"top\">\n<th>Opposite<\/th>\n<th>Absolute Value<\/th>\n<th>Reciprocal<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>has opposite sign<\/td>\n<td>is never negative<\/td>\n<td>has same sign, fraction inverts<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Fill in the chart for each fraction in the left column:<\/p>\n<table id=\"fs-id1179454\" class=\"unnumbered\" style=\"width: 85%\" summary=\"A table is shown with 5 rows and 4 columns. The first row is a header row labeling each column. The first column is\">\n<thead>\n<tr>\n<th>Number<\/th>\n<th>Opposite<\/th>\n<th>Absolute Value<\/th>\n<th>Reciprocal<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]\\Large-\\frac{3}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\Large\\frac{1}{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\Large\\frac{9}{5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]-5[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q72832\">Show Solution<\/span><\/p>\n<div id=\"q72832\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nTo find the opposite, change the sign. To find the absolute value, leave the positive numbers the same, but take the opposite of the negative numbers. To find the reciprocal, keep the sign the same and invert the fraction.<\/p>\n<table id=\"fs-id1722688\" class=\"unnumbered\" style=\"width: 85%\" summary=\"A table is shown with 5 rows and 4 columns. The first row is a header row labeling each column. The first column is\">\n<thead>\n<tr>\n<th>Number<\/th>\n<th>Opposite<\/th>\n<th>Absolute Value<\/th>\n<th>Reciprocal<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]\\Large-\\frac{3}{8}[\/latex]<\/td>\n<td>[latex]\\Large\\frac{3}{8}[\/latex]<\/td>\n<td>[latex]\\Large\\frac{3}{8}[\/latex]<\/td>\n<td>[latex]\\Large-\\frac{8}{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\Large\\frac{1}{2}[\/latex]<\/td>\n<td>[latex]\\Large-\\frac{1}{2}[\/latex]<\/td>\n<td>[latex]\\Large\\frac{1}{2}[\/latex]<\/td>\n<td>[latex]2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\Large\\frac{9}{5}[\/latex]<\/td>\n<td>[latex]\\Large-\\frac{9}{5}[\/latex]<\/td>\n<td>[latex]\\Large\\frac{9}{5}[\/latex]<\/td>\n<td>[latex]\\Large\\frac{5}{9}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]-5[\/latex]<\/td>\n<td>[latex]5[\/latex]<\/td>\n<td>[latex]5[\/latex]<\/td>\n<td>[latex]\\Large-\\frac{1}{5}[\/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>Fill in the chart for each number given:<\/p>\n<table id=\"fs-id2657895\" class=\"unnumbered\" style=\"width: 85%\" summary=\"A table is shown with 5 rows and 4 columns. The first row is a header row labeling each column. The first column is\">\n<thead>\n<tr>\n<th>Number<\/th>\n<th>Opposite<\/th>\n<th>Absolute Value<\/th>\n<th>Reciprocal<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]\\Large-\\frac{5}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\Large\\frac{1}{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\Large\\frac{8}{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]-8[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q718627\">Show Solution<\/span><\/p>\n<div id=\"q718627\" class=\"hidden-answer\" style=\"display: none\">\n<table id=\"fs-id1722656\" class=\"unnumbered\" style=\"width: 85%\" summary=\"A table is shown with 5 rows and 4 columns. The first row is a header row labeling each column. The first column is\">\n<thead>\n<tr>\n<th>Number<\/th>\n<th>Opposite<\/th>\n<th>Absolute Value<\/th>\n<th>Reciprocal<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]-\\Large\\frac{5}{8}[\/latex]<\/td>\n<td>[latex]\\Large\\frac{5}{8}[\/latex]<\/td>\n<td>[latex]\\Large\\frac{5}{8}[\/latex]<\/td>\n<td>[latex]-\\Large\\frac{8}{5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\Large\\frac{1}{4}[\/latex]<\/td>\n<td>[latex]-\\Large\\frac{1}{4}[\/latex]<\/td>\n<td>[latex]\\Large\\frac{1}{4}[\/latex]<\/td>\n<td>[latex]4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\Large\\frac{8}{3}[\/latex]<\/td>\n<td>[latex]-\\Large\\frac{8}{3}[\/latex]<\/td>\n<td>[latex]\\Large\\frac{8}{3}[\/latex]<\/td>\n<td>[latex]\\Large\\frac{3}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]-8[\/latex]<\/td>\n<td>[latex]8[\/latex]<\/td>\n<td>[latex]8[\/latex]<\/td>\n<td>[latex]-\\Large\\frac{1}{8}[\/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=\"ohm146026\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146026&theme=oea&iframe_resize_id=ohm146026&show_question_numbers\" width=\"100%\" height=\"400\"><\/iframe><\/p>\n<\/div>\n<p>The following video provides more examples of finding the opposite of a number.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex:  Determine the Opposites of Integers\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/suk9KMzOKkU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>The next video shows how to find the absolute value of an integer.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Ex 2: Determine the Absolute Value of an Integer\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/lY5ksjix5Kg?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-4416\">\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>Ex: Determine the Reciprocal of Integers, Fractions, and Mixed Numbers. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/IM991IqCi44\">https:\/\/youtu.be\/IM991IqCi44<\/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: 141842, 146026. <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, Shared previously<\/div><ul class=\"citation-list\"><li>Ex 2: Determine the Absolute Value of an Integer. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/lY5ksjix5Kg\">https:\/\/youtu.be\/lY5ksjix5Kg<\/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":1,"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\":\"Ex: Determine the Reciprocal of Integers, Fractions, and Mixed Numbers\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/IM991IqCi44\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex 2: 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