{"id":8533,"date":"2023-10-03T18:09:10","date_gmt":"2023-10-03T18:09:10","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=8533"},"modified":"2024-10-18T20:56:39","modified_gmt":"2024-10-18T20:56:39","slug":"calculations-involving-rational-numbers-learn-it-3","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/calculations-involving-rational-numbers-learn-it-3\/","title":{"raw":"Calculations Involving Rational Numbers: Learn It 3","rendered":"Calculations Involving Rational Numbers: Learn It 3"},"content":{"raw":"<h2>Multiplying Rational Numbers<\/h2>\r\n<p>Just as you add, subtract, multiply, and divide when working with whole numbers, you also use these operations when working with rational numbers. Multiplying rational numbers is less complicated than adding or subtracting rational numbers, as there is no need to find common denominators.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>multiplying rational numbers<\/h3>\r\n<p>To multiply rational numbers, multiply the numerators, then multiply the denominators, and write the numerator product divided by the denominator product. As always, rational numbers should be reduced to lowest terms.<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>Symbolically, we write this as: If [latex]b[\/latex] and [latex]d[\/latex] are non-zero integers, then <center>[latex]\\frac{a}{b} \\times \\frac{c}{d}=\\frac{a \\times c}{b \\times d}[\/latex]<\/center><\/p>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox example\">Calculate [latex]\\frac{12}{25} \\times \\frac{10}{21}[\/latex].[reveal-answer q=\"160936\"]Show Solution[\/reveal-answer] [hidden-answer a=\"160936\"]\r\n\r\n\r\n<p>Multiply the numerators and place that in the numerator, and then multiply the denominators and place that in the denominator.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{12}{25} \\times \\frac{10}{21}=\\frac{12 \\times 10}{25 \\times 21}=\\frac{120}{525}[\/latex]<\/p>\r\n<p>Once we have that result, reduce to lowest terms, which gives <center>[latex]\\frac{120}{525}=\\frac{15 \\times 8}{15 \\times 35}=\\frac{\\cancel{15}\u00d78}{\\cancel{15}\u00d735}=\\frac{8}{35}[\/latex]<\/center><\/p>\r\n\r\n\r\n[\/hidden-answer]<\/section>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]12695[\/ohm2_question]<\/p>\r\n<\/section>\r\n<p>There may be instances where you must multiply more than two rational numbers. This may seem more complicated but in reality you are doing the exact same thing as you did before.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>multiplying more than two rational numbers<\/h3>\r\n<center>[latex] \\frac{a}{b} \\times \\frac{c}{d} \\times \\frac{e}{f}=\\frac{a \\times c \\times e}{b \\times d \\times f}[\/latex]<\/center><\/div>\r\n<\/section>\r\n<section class=\"textbox example\">Calculate [latex]\\frac{2}{3} \\times \\frac{1}{4} \\times \\frac{3}{5}[\/latex].[reveal-answer q=\"160931\"]Show Solution[\/reveal-answer] [hidden-answer a=\"160931\"]\r\n\r\n<p>Multiply the numerators and place that in the numerator, and then multiply the denominators and place that in the denominator.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{2}{3} \\times \\frac{1}{4} \\times \\frac{3}{5}=\\frac{2 \\times 1 \\times 3}{3 \\times 4 \\times 5}=\\frac{6}{60}[\/latex]<\/p>\r\n<p>Once we have that result, reduce to lowest terms, which gives <center>[latex]\\frac{6}{60}=\\frac{6 \\times 1}{6 \\times 10}=\\frac{\\cancel{6}\u00d71}{\\cancel{6}\u00d710}=\\frac{1}{10}[\/latex]<\/center><\/p>\r\n [\/hidden-answer]<\/section>","rendered":"<h2>Multiplying Rational Numbers<\/h2>\n<p>Just as you add, subtract, multiply, and divide when working with whole numbers, you also use these operations when working with rational numbers. Multiplying rational numbers is less complicated than adding or subtracting rational numbers, as there is no need to find common denominators.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>multiplying rational numbers<\/h3>\n<p>To multiply rational numbers, multiply the numerators, then multiply the denominators, and write the numerator product divided by the denominator product. As always, rational numbers should be reduced to lowest terms.<\/p>\n<p>&nbsp;<\/p>\n<p>Symbolically, we write this as: If [latex]b[\/latex] and [latex]d[\/latex] are non-zero integers, then <\/p>\n<div style=\"text-align: center;\">[latex]\\frac{a}{b} \\times \\frac{c}{d}=\\frac{a \\times c}{b \\times d}[\/latex]<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\">Calculate [latex]\\frac{12}{25} \\times \\frac{10}{21}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160936\">Show Solution<\/button> <\/p>\n<div id=\"q160936\" class=\"hidden-answer\" style=\"display: none\">\n<p>Multiply the numerators and place that in the numerator, and then multiply the denominators and place that in the denominator.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{12}{25} \\times \\frac{10}{21}=\\frac{12 \\times 10}{25 \\times 21}=\\frac{120}{525}[\/latex]<\/p>\n<p>Once we have that result, reduce to lowest terms, which gives <\/p>\n<div style=\"text-align: center;\">[latex]\\frac{120}{525}=\\frac{15 \\times 8}{15 \\times 35}=\\frac{\\cancel{15}\u00d78}{\\cancel{15}\u00d735}=\\frac{8}{35}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm12695\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=12695&theme=lumen&iframe_resize_id=ohm12695&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<p>There may be instances where you must multiply more than two rational numbers. This may seem more complicated but in reality you are doing the exact same thing as you did before.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>multiplying more than two rational numbers<\/h3>\n<div style=\"text-align: center;\">[latex]\\frac{a}{b} \\times \\frac{c}{d} \\times \\frac{e}{f}=\\frac{a \\times c \\times e}{b \\times d \\times f}[\/latex]<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\">Calculate [latex]\\frac{2}{3} \\times \\frac{1}{4} \\times \\frac{3}{5}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160931\">Show Solution<\/button> <\/p>\n<div id=\"q160931\" class=\"hidden-answer\" style=\"display: none\">\n<p>Multiply the numerators and place that in the numerator, and then multiply the denominators and place that in the denominator.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2}{3} \\times \\frac{1}{4} \\times \\frac{3}{5}=\\frac{2 \\times 1 \\times 3}{3 \\times 4 \\times 5}=\\frac{6}{60}[\/latex]<\/p>\n<p>Once we have that result, reduce to lowest terms, which gives <\/p>\n<div style=\"text-align: center;\">[latex]\\frac{6}{60}=\\frac{6 \\times 1}{6 \\times 10}=\\frac{\\cancel{6}\u00d71}{\\cancel{6}\u00d710}=\\frac{1}{10}[\/latex]<\/div>\n<\/p><\/div>\n<\/div>\n<\/section>\n","protected":false},"author":15,"menu_order":12,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Contemporary Mathematics\",\"author\":\"Donna Kirk\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/contemporary-mathematics\/pages\/3-4-rational-numbers\",\"project\":\"3.4 Rational Numbers\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/contemporary-mathematics\/pages\/1-introduction\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":53,"module-header":"learn_it","content_attributions":[{"type":"cc-attribution","description":"Contemporary Mathematics","author":"Donna Kirk","organization":"OpenStax","url":"https:\/\/openstax.org\/books\/contemporary-mathematics\/pages\/3-4-rational-numbers","project":"3.4 Rational Numbers","license":"cc-by","license_terms":"Access for free at https:\/\/openstax.org\/books\/contemporary-mathematics\/pages\/1-introduction"}],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8533"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":13,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8533\/revisions"}],"predecessor-version":[{"id":14140,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8533\/revisions\/14140"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/53"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8533\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=8533"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=8533"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=8533"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=8533"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}