{"id":1393,"date":"2022-04-19T07:54:40","date_gmt":"2022-04-19T07:54:40","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=1393"},"modified":"2024-01-01T15:15:36","modified_gmt":"2024-01-01T15:15:36","slug":"multiplicative-inverse-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/multiplicative-inverse","title":{"rendered":"Multiplicative Inverse &#8211; Definition, Examples, Practice Problems"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-89726b47-5b75-4cbd-9b20-cf2554255294\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/multiplicative-inverse#0-what-is-multiplicative-inverse>What Is Multiplicative Inverse?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/multiplicative-inverse#1-multiplicative-inverse-property>Multiplicative Inverse Property<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/multiplicative-inverse#6-unit-fractions>Unit Fractions<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/multiplicative-inverse#10-solved-examples-on-multiplicative-inverse>Solved Examples on Multiplicative Inverse<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/multiplicative-inverse#11-practice-problems-on-multiplicative-inverse>Practice Problems on Multiplicative Inverse<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/multiplicative-inverse#12-frequently-asked-questions-on-multiplicative-inverse>Frequently Asked Questions on Multiplicative Inverse<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-multiplicative-inverse\">What Is Multiplicative Inverse?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The meaning of the word \u201cinverse\u201d is something opposite in effect. The multiplicative inverse of a number is a number that, when multiplied by the given number, gives 1 as the product. By multiplicative inverse definition, it is the reciprocal of a number.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>The multiplicative inverse of a number \u201ca\u201d is represented as a<sup>-1 <\/sup>or $\\frac{1}{a}$.&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-decimal-fractions-using-equivalence\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/decimals_convert_to_equi_frac_to_add_pt.png\" alt=\"Add Decimal Fractions Using Equivalence Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Decimal Fractions Using Equivalence Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-fractions-using-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_add_unlike_models_pt.png\" alt=\"Add Fractions using Models Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Fractions using Models Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-fractions-with-the-aid-of-a-number-line\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_add_like_frac_sum_greater_than_1_nl_pt.png\" alt=\"Add Fractions WIth the Aid of a Number LIne Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Fractions WIth the Aid of a Number LIne Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-like-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_add_like_frac_sum_upto_1_pt.png\" alt=\"Add Like Fractions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Like Fractions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-like-fractions-greater-than-1\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_find_sum_pt.png\" alt=\"Add Like Fractions Greater than 1 Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Like Fractions Greater than 1 Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-like-fractions-to-get-a-sum-greater-than-1\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_add_like_frac_sum_greater_than_1_pt.png\" alt=\"Add Like Fractions to Get a Sum Greater than 1 Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Like Fractions to Get a Sum Greater than 1 Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-like-fractions-using-number-lines\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_add_like_frac_sum_upto_1_nl_pt.png\" alt=\"Add Like Fractions using Number Lines Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Like Fractions using Number Lines Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-unlike-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_add_unlike_pt.png\" alt=\"Add Unlike Fractions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Unlike Fractions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/are-the-fractions-equivalent\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_identify_equi_visual_model_pt.png\" alt=\"Are the Fractions Equivalent Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Are the Fractions Equivalent Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/area-word-problems-on-product-of-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_real_life_prob_area_pt.png\" alt=\"Area Word Problems on Product of Fractions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Area Word Problems on Product of Fractions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    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         }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-multiplicative-inverse-property\">Multiplicative Inverse Property<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The multiplicative inverse property states that if we multiply a number with its reciprocal, the product is always equal to 1. The image given below shows that $\\frac{1}{a}$ is the reciprocal of the number \u201ca\u201d.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"402\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/multiplicative-inverse-property.png\" alt=\"Multiplicative Inverse Property\" class=\"wp-image-37031\" title=\"Multiplicative Inverse Property\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/multiplicative-inverse-property.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/multiplicative-inverse-property-300x195.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">A pair of numbers, when multiplied to give product 1, are said to be multiplicative inverses of each other. Here, a and $\\frac{1}{a}$ are reciprocals of each other.&nbsp;<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-decimal-fractions-to-write-decimal-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-decimal-fractions-to-write-decimal-number.jpeg\" alt=\"Add Decimal Fractions to Write Decimal Number Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-fractions-using-area-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-fractions-using-area-models.jpeg\" alt=\"Add Fractions using Area Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-fractions-using-fraction-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-fractions-using-fraction-models.jpeg\" alt=\"Add Fractions Using Fraction Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-fractions-using-visual-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-fractions-using-visual-models.jpeg\" alt=\"Add Fractions Using Visual Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-like-fractions-using-area-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-like-fractions-using-area-models.jpeg\" alt=\"Add Like Fractions using Area Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-mixed-numbers-and-fractions-using-area-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-mixed-numbers-and-fractions-using-area-models.jpeg\" alt=\"Add Mixed Numbers and Fractions using Area Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-mixed-numbers-and-fractions-using-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-mixed-numbers-and-fractions-using-models.jpeg\" alt=\"Add Mixed Numbers and Fractions using Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/adding-fractions-mixed-numbers-word-problems\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/adding-fractions-mixed-numbers-word-problems.jpeg\" alt=\"Adding Fractions & Mixed Numbers Word Problems Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/adding-fractions-using-fraction-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/adding-fractions-using-fraction-models.jpeg\" alt=\"Adding Fractions Using Fraction Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/adding-fractions-using-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/adding-fractions-using-models.jpeg\" alt=\"Adding Fractions Using Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const 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maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-how-to-find-the-multiplicative-inverse\">How to Find the Multiplicative Inverse?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Consider that we have seven apples. To make them into groups of 1 each, we need to divide them by 7. Since division is the reverse process of <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication\" title=\"\">multiplication<\/a>, dividing by a number is equivalent to multiplying by the reciprocal of the number.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, 7 \u00f7 7 = 7 \u00d7 $\\frac{1}{7}$ = 1<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, $\\frac{1}{7}$ is called the multiplicative inverse of 7.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us understand the multiplicative inverse of different types of numbers like natural numbers, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/integers\" title=\"\">integers<\/a> and <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/fraction\" title=\"\">fractions<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-natural-numbers\">Natural Numbers<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The numbers that are used for counting, such as 1, 2, 3, and so on, are known as <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/natural-numbers\" title=\"\">natural numbers<\/a>. The reciprocal of \u201ca\u201d is $\\frac{1}{a}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example, if we multiply 7 by $\\frac{1}{7}$, we get $7\\frac{1}{7}=1$. So, the multiplicative inverse of 7 is $\\frac{1}{7}$.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-integers\">Integers<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The reciprocal of a positive integer \u201ca\u201d is $\\frac{1}{a}$. Negative integers lie on the left side of zero on a number line and their value is always less than 0. Negative integers have minus (-) sign in front of them. The product of any integer and its reciprocal must be 1. The reciprocal of a negative number will be a negative number. For example: If the number is -2, then its reciprocal will be $-\\frac{1}{2}$ not $\\frac{1}{2}$, as&nbsp; $-2 \\times \\left[-\\frac{1}{2}\\right] = 1$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-fractions\">Fractions<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">To find the reciprocal of a fraction we can just flip it over. The reciprocal of any fraction $\\frac{a}{b}$ is $\\frac{b}{a}$, because $\\frac{a}{b}\\times\\frac{b}{a}=1$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-unit-fractions\">Unit Fractions<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/unit-fraction\" title=\"\">Unit fraction<\/a> is the fraction in which the numerator is 1 irrespective of the number in the denominator. The reciprocal of unit fraction $\\frac{1}{x}$ is x, a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/whole-numbers\" title=\"\">whole number<\/a>. For example, reciprocal or multiplicative inverse of \u00bc is 4.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-mixed-fraction\">Mixed Fraction<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/mixed-number\" title=\"\">mixed fraction<\/a> is a combination of a whole number and a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/proper-fraction\" title=\"\">proper fraction<\/a>. For example: $2\\frac{3}{7},5\\frac{4}{5}$, etc.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In order to find the reciprocal of a mixed fraction, we convert it to an <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/improper-fraction\" title=\"\">improper fraction<\/a> and then find its reciprocal.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example, to find the reciprocal of $2\\frac{3}{7}$,&nbsp; we convert $2\\frac{3}{7}$ to improper fraction, that is $\\frac{17}{7}$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since the reciprocal of $2\\frac{3}{7}$ or $\\frac{17}{7}$ is $\\frac{7}{17}$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-fun-facts\">Fun Facts<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>The word \u201creciprocal\u201d comes from the Latin word \u201creciprocus\u201d, which means back and forth.&nbsp;<\/li>\n\n\n\n<li>The multiplicative inverse of a proper fraction is an improper fraction.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we learned about the reciprocal of different types of numbers. To read more such informative articles on other concepts, do visit our <a href=\"https:\/\/www.splashlearn.com\/features\/parents\" title=\"\">website<\/a>. We, at SplashLearn, are on a mission to make learning fun and interactive for all students.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-solved-examples-on-multiplicative-inverse\">Solved Examples on Multiplicative Inverse<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1: What is the multiplicative inverse of -100?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution<\/strong>: The multiplicative inverse of -100 is -$\\frac{1}{100}$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2: The reciprocal of a number is <\/strong>$2\\frac{3}{5}$<strong>. Find the number.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution<\/strong>: A pair of numbers when multiplied to give product as 1, they are said to be reciprocals of each other.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, the reciprocal of $2\\frac{3}{5}$ or $\\frac{13}{5}$ is the original number. Since the reciprocal of $\\frac{13}{5}$ is $\\frac{5}{13}$, the original number is $\\frac{5}{13}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 3: What is the multiplicative inverse of <\/strong>$\\frac{2}{3} + \\frac{3}{2}$<strong>?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution<\/strong>: To find the reciprocal, we need to simplify the expression first.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{2}{3} + \\frac{3}{2} = \\frac{13}{6}$The reciprocal of $\\frac{13}{6}$<strong> <\/strong>is $\\frac{6}{13}$<strong>.<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-practice-problems-on-multiplicative-inverse\">Practice Problems on Multiplicative Inverse<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Multiplicative Inverse - Definition with Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Which of the following will be the multiplicative inverse of $\\frac{1}{10}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">10<\/div><div class=\"spq_answer_block\" data-value=\"1\">-10<\/div><div class=\"spq_answer_block\" data-value=\"2\">$-\\frac{1}{10}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 10<br\/> The reciprocal of $\\frac{1}{10}$ is 10.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The multiplicative inverse of a mixed fraction is a:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">improper fraction<\/div><div class=\"spq_answer_block\" data-value=\"1\">proper fraction<\/div><div class=\"spq_answer_block\" data-value=\"2\">mixed fraction<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: proper fraction<br\/>Mixed fractions can be converted into improper fractions. Since the reciprocal of an improper fraction is a proper fraction, the multiplicative inverse of a mixed fraction is a proper fraction.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which number does not have a multiplicative inverse?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">- 3<\/div><div class=\"spq_answer_block\" data-value=\"1\">2<\/div><div class=\"spq_answer_block\" data-value=\"2\">1<\/div><div class=\"spq_answer_block\" data-value=\"3\">0<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 0<br\/>The multiplicative inverse of 0 is $\\frac{1}{0}$, which is not defined.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Multiplicative Inverse - 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Since the reciprocal of an improper fraction is a proper fraction, the multiplicative inverse of a mixed fraction is a proper fraction.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"mixed fraction\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Mixed fractions can be converted into improper fractions. Since the reciprocal of an improper fraction is a proper fraction, the multiplicative inverse of a mixed fraction is a proper fraction.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of these\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Mixed fractions can be converted into improper fractions. 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For example: Additive inverse of 5 is -5.&nbsp;On the other hand, the multiplicative inverse of a number is the number that, when multiplied by the original number, gives 1 as the result. For example: Multiplicative inverse of 5 is $\\frac{1}{5}$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-5ada89c9-fdc7-47da-bf08-dda350c5082d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-5ada89c9-fdc7-47da-bf08-dda350c5082d\"><strong>What is the multiplicative inverse of 0?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-5ada89c9-fdc7-47da-bf08-dda350c5082d\">\n\n<p>As per the definition of multiplicative inverse of a number is a number that, when multiplied by the given number, yields the product as 1. Since the product of any number with zero is always zero. So we can say that zero doesn\u2019t have a reciprocal.&nbsp;<\/p>\n\n\n\n<p>Since division by zero is not defined, the reciprocal of zero, which is 1\/0, is undefined. So, it does not exist.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-5ada89c9-fdc7-47da-bf08-dda350c5082d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-5ada89c9-fdc7-47da-bf08-dda350c5082d\"><strong>What is multiplicative identity?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-5ada89c9-fdc7-47da-bf08-dda350c5082d\">\n\n<p>The multiplicative identity is a number, which when multiplied to any number \u201ca\u201d, gives a product as \u201ca\u201d. Multiplicative identity is a real number is 1, because&nbsp;$a\\times1=a$<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-5ada89c9-fdc7-47da-bf08-dda350c5082d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-5ada89c9-fdc7-47da-bf08-dda350c5082d\"><strong>What is the use of multiplicative inverse?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-5ada89c9-fdc7-47da-bf08-dda350c5082d\">\n\n<p>The multiplicative inverse is used to simplify the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/expression\" title=\"\">expressions<\/a>. One application of multiplicative inverse is when we solve the division problems. While dividing two numbers, we multiply the reciprocal of the divisor to the dividend. For example,&nbsp;5 \u00f7 10 = 5 \u00d7 $\\frac{1}{10} = \\frac{1}{2}$.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>What Is Multiplicative Inverse? The meaning of the word \u201cinverse\u201d is something opposite in effect. The multiplicative inverse of a number is a number that, when multiplied by the given number, gives 1 as the product. By multiplicative inverse definition, it is the reciprocal of a number.&nbsp; The multiplicative inverse of a number \u201ca\u201d is &#8230; <a title=\"Multiplicative Inverse &#8211; Definition, Examples, Practice Problems\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/multiplicative-inverse\" aria-label=\"More on Multiplicative Inverse &#8211; Definition, Examples, Practice Problems\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-1393","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1393","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=1393"}],"version-history":[{"count":35,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1393\/revisions"}],"predecessor-version":[{"id":37032,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1393\/revisions\/37032"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=1393"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=1393"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=1393"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}