{"id":70,"date":"2022-04-12T12:01:14","date_gmt":"2022-04-12T12:01:14","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=70"},"modified":"2025-02-22T15:37:39","modified_gmt":"2025-02-22T15:37:39","slug":"e-1-reciprocals-and-multiplicative-inverses","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/e-1-reciprocals-and-multiplicative-inverses\/","title":{"rendered":"E.1 Reciprocals and multiplicative inverses"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#071267;text-transform:uppercase\"><strong>Reciprocals and multiplicative inverses<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-f79afd6ea8b322268468366b8e5f7cc7\" style=\"color:#74008b\"><strong>Key Notes:<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-b84aee8610edd3071511333d025ab178\" style=\"color:#000060\"><strong>Understanding Reciprocals<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Definition: The reciprocal of a number a is 1\/a It&#8217;s the number that, when multiplied by a , gives 1.<\/li>\n\n\n\n<li>Examples: For example, the reciprocal of 2 is 1\/2 \u200b, because 2 \u00d7 12 = 1.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-8af6f741de736700f69fd56ad91563af\" style=\"color:#000060\"><strong>Multiplicative Inverses<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Definition: The multiplicative inverse of a number a is another number b such that a \u00d7 b = 1.<\/li>\n\n\n\n<li>Connection to reciprocals: The multiplicative inverse of a is 1\/a\u200b.<\/li>\n\n\n\n<li>Example: For example, the multiplicative inverse of 3 is 1\/3\u200b, because 3 \u00d7 1\/3 = 1.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-9c6edf6940df51ddbb7001591130b76a\" style=\"color:#000060\"><strong>Finding Reciprocals and Inverses<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Practice exercises: Provide examples where students find reciprocals of integers and fractions.<\/li>\n\n\n\n<li>Checking answers: Emphasize checking by multiplication to ensure correctness (e.g., 1\/4 \u00d7 4 = 1).<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-43614c14933b4068e1fe62a30a8c912e\" style=\"color:#000060\"><strong>Properties and Applications<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Reciprocal property: a\u00d71\/a=1 for any nonzero number a.<\/li>\n\n\n\n<li>Solving equations: Use reciprocals to solve equations involving fractions and multiplicative inverses.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-f615e44dc58be295fbc69c0149596912\" style=\"color:#000060\"><strong>Graphical Representation<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Show reciprocals on a number line.<\/li>\n\n\n\n<li>Visualize how the product of a number and its reciprocal is always 1.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-59bd64ff6f5ea7b26d9f134c5fac3a34\" style=\"color:#000060\"><strong>Real-life Examples<\/strong>:<\/p>\n\n\n\n<p class=\"has-large-font-size\">Applications in everyday life: Discuss scenarios where understanding reciprocals (e.g., cooking recipes, proportions) and multiplicative inverses (e.g., scaling measurements) are important.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#e3ccfc\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-bbd6c7a25a1a948a9c2141f60af94b8f\" style=\"color:#b00012\"><strong>\ud83c\udfaf What is the multiplicative inverse of -5\/9 ?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Switch the numerator and denominator.<\/p>\n\n\n\n<p>\u20135\/9 \u2192 9\/\u20135<\/p>\n\n\n\n<p>Move the negative sign to the numerator. This will not change the value of the fraction.<\/p>\n\n\n\n<p>9\/-5 = -9\/5<\/p>\n\n\n\n<p>The multiplicative inverse of<\/p>\n\n\n\n<p>\u20135\/9 is -9\/5<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#dcfed5\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-7b8e7f8250b93c474209300f999fe6db\" style=\"color:#b00012\"><strong>\ud83c\udfaf What is the reciprocal of 5\/9?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Switch the numerator and denominator.<\/p>\n\n\n\n<p>5\/9 \u2192&nbsp;9\/5<\/p>\n\n\n\n<p>The reciprocal of 5\/9 is 9\/5 .<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f8cece\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-1bc2481ebf9c0bc3f36fbfc8839e4fba\" style=\"color:#b00012\"><strong>\ud83c\udfaf What is the multiplicative inverse of 10\/9 ?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Switch the numerator and denominator.<\/p>\n\n\n\n<p>10\/9 \u2192&nbsp;9\/10<\/p>\n\n\n\n<p>The multiplicative inverse of 10\/9 is 9\/10 .<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-columns are-vertically-aligned-center has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#ffef76\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Pink_Modern_Minimalist_Microphone_Talk_Podcast_Cover-removebg-preview.png\" alt=\"\" class=\"wp-image-11304\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Pink_Modern_Minimalist_Microphone_Talk_Podcast_Cover-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Pink_Modern_Minimalist_Microphone_Talk_Podcast_Cover-removebg-preview-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Pink_Modern_Minimalist_Microphone_Talk_Podcast_Cover-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/16941474600225lryhxyj-voicemaker.in-speech.mp3\"><\/audio><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/strong><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/80681\/159\/762\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-287.png\" alt=\"\" class=\"wp-image-9539\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-287.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-287-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-287-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full is-resized\"><a href=\"https:\/\/wordwall.net\/play\/85059\/282\/310\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-294.png\" alt=\"\" class=\"wp-image-9540\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-294.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-294-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-294-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Reciprocals and multiplicative inverses Key Notes: Understanding Reciprocals: Multiplicative Inverses: Finding Reciprocals and Inverses: Properties and Applications: Graphical Representation: Real-life Examples: Applications in everyday life: Discuss scenarios where understanding reciprocals (e.g., cooking recipes, proportions) and multiplicative inverses (e.g., scaling measurements) are important. Learn with an example \ud83c\udfaf What is the multiplicative inverse of -5\/9 ?<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/e-1-reciprocals-and-multiplicative-inverses\/\">Continue reading <span class=\"screen-reader-text\">&#8220;E.1 Reciprocals and multiplicative inverses&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-70","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/70","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=70"}],"version-history":[{"count":23,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/70\/revisions"}],"predecessor-version":[{"id":19904,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/70\/revisions\/19904"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=70"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}