{"id":34742,"date":"2023-10-06T09:06:18","date_gmt":"2023-10-06T09:06:18","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=34742"},"modified":"2024-02-05T16:18:53","modified_gmt":"2024-02-05T16:18:53","slug":"reciprocal-formula-definition-examples-practice-problems-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal-formula","title":{"rendered":"Reciprocal Formula &#8211; Definition, Examples, Practice Problems, FAQs"},"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-6a765cb6-1166-4564-b5ca-a1f3ddb0c8a7\" 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\/reciprocal-formula#0-what-is-the-reciprocal-formula>What Is the Reciprocal Formula?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal-formula#1-reciprocal-formula>Reciprocal Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal-formula#2-how-to-find-reciprocal>How to Find Reciprocal<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal-formula#5-solved-examples-on-the-reciprocal-formula>Solved Examples on the Reciprocal Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal-formula#6-practice-problems-on-the-reciprocal-formula>Practice Problems on the Reciprocal Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal-formula#7-frequently-asked-questions-about-the-reciprocal-formula>Frequently Asked Questions about the Reciprocal Formula<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-reciprocal-formula\">What Is the Reciprocal Formula?<\/h2>\n\n\n\n<p><strong>The reciprocal formula calculates the <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal\"><strong>reciprocal<\/strong><\/a><strong> of a given number. The reciprocal of a non-zero number &#8220;a&#8221; is \u201c1 divided by a.&#8221; <\/strong>It is expressed as $\\frac{1}{a}$ and represents the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/multiplicative-inverse\">multiplicative inverse<\/a> of the number. In other words, when a number and its reciprocal are multiplied together, the result is 1.<\/p>\n\n\n\n<p>Reciprocal is defined as the multiplicative inverse of a number. If \u2018n\u2019 is any non-zero number, the reciprocal will be $\\frac{1}{n}$. This means we have to convert the original number to the upside-down form. If the number is multiplied by its reciprocal, the product is equal to one.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"476\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/reciprocal-of-a-number-1.png\" alt=\"Reciprocal of a number\" class=\"wp-image-34745\" title=\"Reciprocal of a number\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/reciprocal-of-a-number-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/reciprocal-of-a-number-1-300x230.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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\/find-volume-using-the-formula\" 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\/geo_meas_vol_formula_pt.png\" alt=\"Find Volume using the Formula 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\">Find Volume using the Formula 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                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const 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\" id=\"1-reciprocal-formula\">Reciprocal Formula<\/h2>\n\n\n\n<p>Reciprocal of a non-zero real number $= \\frac{1}{Number}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2-how-to-find-reciprocal\">How to Find Reciprocal<\/h2>\n\n\n\n<p>To find the reciprocal of a number, just flip its fraction form.<\/p>\n\n\n\n<p><strong>Example 1<\/strong>: Find the reciprocal of 7.<\/p>\n\n\n\n<p>The given number is 7. In fraction form, we can write it as $\\frac{7}{1}$.<\/p>\n\n\n\n<p>Flipping $\\frac{7}{1}$ (interchanging the numerator and denominator), we get $\\frac{1}{7}$.<\/p>\n\n\n\n<p>Thus, the reciprocal of 7 will be $\\frac{1}{7}$.<\/p>\n\n\n\n<p>Similarly, the reciprocal of a fraction can be written by interchanging the values of the numerator and the denominator.<\/p>\n\n\n\n<p><strong>Example 2:<\/strong> Find the reciprocal of $\\frac{5}{3}$.<\/p>\n\n\n\n<p>To find the answers, follow the below steps:<\/p>\n\n\n\n<p>Reciprocal formula: $x = \\frac{1}{x}$<\/p>\n\n\n\n<p>Here, $x = \\frac{5}{3}$<\/p>\n\n\n\n<p>Reciprocal of $\\frac{5}{3} = \\frac{1}{\\frac{5}{3}} = \\frac{3}{5}$.<\/p>\n\n\n\n<p>Thus, the reciprocal of the fraction&nbsp;$\\frac{5}{3}&nbsp; =&nbsp;\\frac{3}{5}$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-facts-about-the-reciprocal-formula\">Facts about the Reciprocal Formula<\/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>Except zero, all the numbers have reciprocal.<\/li>\n\n\n\n<li>On multiplying a number and its reciprocal, the product is always one.<\/li>\n\n\n\n<li>In mathematics, the term &#8220;reciprocal&#8221; is often used to describe the multiplicative inverse of a number.<\/li>\n\n\n\n<li>The reciprocal of -1 is -1.<\/li>\n\n\n\n<li>The reciprocal of 1 is 1.<\/li>\n\n\n\n<li>Reciprocal of a proper fraction is an improper fraction, and vice-versa.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we explored the concept of reciprocals and how they are obtained by flipping the fraction form of a number. Understanding reciprocals is essential in various mathematical applications. To reinforce our understanding, let&#8217;s work through some examples and test our knowledge with practice MCQs.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-solved-examples-on-the-reciprocal-formula\">Solved Examples on the Reciprocal Formula<\/h2>\n\n\n\n<p><strong>Example 1: What is the reciprocal of 5 and 8?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>The given numbers are 5 and 8. To find the solution, we have to use <strong>reciprocal formula<\/strong>:<\/p>\n\n\n\n<p>Reciprocal formula: Reciprocal of $x = \\frac{1}{x}$.<\/p>\n\n\n\n<p>Reciprocal of $5 = \\frac{1}{5}$<\/p>\n\n\n\n<p>Reciprocal of $8 = \\frac{1}{8}$<\/p>\n\n\n\n<p>Thus, the reciprocal of 5 is, $\\frac{1}{5}$ and the reciprocal of 8 is $\\frac{1}{8}$.<\/p>\n\n\n\n<p><strong>Example 2: What is the reciprocal of <\/strong>$\\frac{7}{2}$<strong>?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>The given fraction is $\\frac{7}{2}$ . To find the solution, we have to use the <strong>reciprocal formula<\/strong>:<\/p>\n\n\n\n<p>Reciprocal formula: Reciprocal of $x = \\frac{1}{x}$<\/p>\n\n\n\n<p>Here, $x = \\frac{7}{2}$<\/p>\n\n\n\n<p>Reciprocal of $\\frac{7}{2} = \\frac{1}{\\frac{7}{2}} = \\frac{2}{7}$.<\/p>\n\n\n\n<p>Thus, the reciprocal of the fraction $\\frac{7}{2} =&nbsp;\\frac{2}{7}$.<\/p>\n\n\n\n<p><strong>Example 3: Find the reciprocal of <\/strong>$-\\;\\frac{1}{3}$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>The given fraction is $-\\;\\frac{1}{3}$ . To find the solution, we have to use the <strong>reciprocal formula<\/strong>:<\/p>\n\n\n\n<p>Reciprocal formula: Reciprocal of $x = \\frac{1}{x}$.<\/p>\n\n\n\n<p>Here, $x = -\\;\\frac{1}{3}$<\/p>\n\n\n\n<p>Reciprocal of $\\frac{-\\;1}{3} = \\frac{1}{-\\;\\frac{1}{3}} = -\\;\\frac{3}{1}$<\/p>\n\n\n\n<p>Thus, the reciprocal of the fraction $-\\;\\frac{1}{3}$ is&nbsp; $-\\;3$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-practice-problems-on-the-reciprocal-formula\">Practice Problems on the Reciprocal Formula<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Reciprocal Formula - Definition, Examples, Practice Problems, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the reciprocal of 6 and $\\frac{1}{6}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$6, \\frac{1}{6}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{1}{6} ,\\; 6$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{1}{6} ,\\; \\frac{-\\;1}{6}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$6,\\; -\\;6$<\/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: $\\frac{1}{6} ,\\; 6$<br\/>Reciprocal of $6 = \\frac{1}{6}$<br>\r\nReciprocal of $\\frac{1}{6} = 6$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the reciprocal of $\\frac{5}{2}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{5}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$-\\;\\frac{5}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{2}{5}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$-\\;\\frac{2}{5}$<\/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: $\\frac{2}{5}$<br\/>The given fraction is $\\frac{5}{2}$ . To find the solution, we have to use the reciprocal formula:<br>\r\nReciprocal of $x = \\frac{1}{x}$.<br>\r\nHere, $x = \\frac{5}{2}$<br>\r\nReciprocal of $\\frac{5}{2} =  \\frac{1}{\\frac{5}{2}} = \\frac{2}{5}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Find the reciprocal of $-\\;\\frac{1}{9}$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{1}{9}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$-\\;\\frac{1}{9}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$-\\;9$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$9$<\/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: $-\\;9$<br\/>Reciprocal formula: Reciprocal of $x = \\frac{1}{x}$.<br>\r\nHere, $x = -\\;\\frac{1}{9}$<br>\r\nReciprocal of $-\\;\\frac{1}{9} = \\frac{1}{-\\;\\frac{1}{9}} = -\\;\\frac{9}{1} = -\\;9$<\/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\": \"Reciprocal Formula - Definition, Examples, Practice Problems, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Reciprocal Formula\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the reciprocal of 6 and $$\\\\frac{1}{6}$$?\",\n                    \"text\": \"What is the reciprocal of 6 and $$\\\\frac{1}{6}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Reciprocal of $$6 = \\\\frac{1}{6}$$<br>\r\nReciprocal of $$\\\\frac{1}{6} = 6$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$6, \\\\frac{1}{6}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Reciprocal of $$6 = \\\\frac{1}{6}$$<br>\r\nReciprocal of $$\\\\frac{1}{6} = 6$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{6} ,\\\\; \\\\frac{-\\\\;1}{6}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Reciprocal of $$6 = \\\\frac{1}{6}$$<br>\r\nReciprocal of $$\\\\frac{1}{6} = 6$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$6,\\\\; -\\\\;6$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Reciprocal of $$6 = \\\\frac{1}{6}$$<br>\r\nReciprocal of $$\\\\frac{1}{6} = 6$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{1}{6} ,\\\\; 6$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Reciprocal of $$6 = \\\\frac{1}{6}$$<br>\r\nReciprocal of $$\\\\frac{1}{6} = 6$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Reciprocal of $$6 = \\\\frac{1}{6}$$<br>\r\nReciprocal of $$\\\\frac{1}{6} = 6$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the reciprocal of $$\\\\frac{5}{2}$$?\",\n                    \"text\": \"What is the reciprocal of $$\\\\frac{5}{2}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The given fraction is $$\\\\frac{5}{2}$$ . To find the solution, we have to use the reciprocal formula:<br>\r\nReciprocal of $$x = \\\\frac{1}{x}$$.<br>\r\nHere, $$x = \\\\frac{5}{2}$$<br>\r\nReciprocal of $$\\\\frac{5}{2} =  \\\\frac{1}{\\\\frac{5}{2}} = \\\\frac{2}{5}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{5}{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The given fraction is $$\\\\frac{5}{2}$$ . To find the solution, we have to use the reciprocal formula:<br>\r\nReciprocal of $$x = \\\\frac{1}{x}$$.<br>\r\nHere, $$x = \\\\frac{5}{2}$$<br>\r\nReciprocal of $$\\\\frac{5}{2} =  \\\\frac{1}{\\\\frac{5}{2}} = \\\\frac{2}{5}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-\\\\;\\\\frac{5}{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The given fraction is $$\\\\frac{5}{2}$$ . To find the solution, we have to use the reciprocal formula:<br>\r\nReciprocal of $$x = \\\\frac{1}{x}$$.<br>\r\nHere, $$x = \\\\frac{5}{2}$$<br>\r\nReciprocal of $$\\\\frac{5}{2} =  \\\\frac{1}{\\\\frac{5}{2}} = \\\\frac{2}{5}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-\\\\;\\\\frac{2}{5}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The given fraction is $$\\\\frac{5}{2}$$ . To find the solution, we have to use the reciprocal formula:<br>\r\nReciprocal of $$x = \\\\frac{1}{x}$$.<br>\r\nHere, $$x = \\\\frac{5}{2}$$<br>\r\nReciprocal of $$\\\\frac{5}{2} =  \\\\frac{1}{\\\\frac{5}{2}} = \\\\frac{2}{5}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{2}{5}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The given fraction is $$\\\\frac{5}{2}$$ . To find the solution, we have to use the reciprocal formula:<br>\r\nReciprocal of $$x = \\\\frac{1}{x}$$.<br>\r\nHere, $$x = \\\\frac{5}{2}$$<br>\r\nReciprocal of $$\\\\frac{5}{2} =  \\\\frac{1}{\\\\frac{5}{2}} = \\\\frac{2}{5}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The given fraction is $$\\\\frac{5}{2}$$ . To find the solution, we have to use the reciprocal formula:<br>\r\nReciprocal of $$x = \\\\frac{1}{x}$$.<br>\r\nHere, $$x = \\\\frac{5}{2}$$<br>\r\nReciprocal of $$\\\\frac{5}{2} =  \\\\frac{1}{\\\\frac{5}{2}} = \\\\frac{2}{5}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the reciprocal of $$-\\\\;\\\\frac{1}{9}$$.\",\n                    \"text\": \"Find the reciprocal of $$-\\\\;\\\\frac{1}{9}$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Reciprocal formula: Reciprocal of $$x = \\\\frac{1}{x}$$.<br>\r\nHere, $$x = -\\\\;\\\\frac{1}{9}$$<br>\r\nReciprocal of $$-\\\\;\\\\frac{1}{9} = \\\\frac{1}{-\\\\;\\\\frac{1}{9}} = -\\\\;\\\\frac{9}{1} = -\\\\;9$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{9}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Reciprocal formula: Reciprocal of $$x = \\\\frac{1}{x}$$.<br>\r\nHere, $$x = -\\\\;\\\\frac{1}{9}$$<br>\r\nReciprocal of $$-\\\\;\\\\frac{1}{9} = \\\\frac{1}{-\\\\;\\\\frac{1}{9}} = -\\\\;\\\\frac{9}{1} = -\\\\;9$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-\\\\;\\\\frac{1}{9}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Reciprocal formula: Reciprocal of $$x = \\\\frac{1}{x}$$.<br>\r\nHere, $$x = -\\\\;\\\\frac{1}{9}$$<br>\r\nReciprocal of $$-\\\\;\\\\frac{1}{9} = \\\\frac{1}{-\\\\;\\\\frac{1}{9}} = -\\\\;\\\\frac{9}{1} = -\\\\;9$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$9$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Reciprocal formula: Reciprocal of $$x = \\\\frac{1}{x}$$.<br>\r\nHere, $$x = -\\\\;\\\\frac{1}{9}$$<br>\r\nReciprocal of $$-\\\\;\\\\frac{1}{9} = \\\\frac{1}{-\\\\;\\\\frac{1}{9}} = -\\\\;\\\\frac{9}{1} = -\\\\;9$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$-\\\\;9$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Reciprocal formula: Reciprocal of $$x = \\\\frac{1}{x}$$.<br>\r\nHere, $$x = -\\\\;\\\\frac{1}{9}$$<br>\r\nReciprocal of $$-\\\\;\\\\frac{1}{9} = \\\\frac{1}{-\\\\;\\\\frac{1}{9}} = -\\\\;\\\\frac{9}{1} = -\\\\;9$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Reciprocal formula: Reciprocal of $$x = \\\\frac{1}{x}$$.<br>\r\nHere, $$x = -\\\\;\\\\frac{1}{9}$$<br>\r\nReciprocal of $$-\\\\;\\\\frac{1}{9} = \\\\frac{1}{-\\\\;\\\\frac{1}{9}} = -\\\\;\\\\frac{9}{1} = -\\\\;9$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-frequently-asked-questions-about-the-reciprocal-formula\">Frequently Asked Questions about the Reciprocal Formula<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-c4cd5f6e-1741-4b1e-b52c-a72eeab0b84e\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\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-0-c4cd5f6e-1741-4b1e-b52c-a72eeab0b84e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c4cd5f6e-1741-4b1e-b52c-a72eeab0b84e\"><strong>How to find the reciprocal of a mixed fraction?<\/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-0-c4cd5f6e-1741-4b1e-b52c-a72eeab0b84e\">\n\n<p>To find the reciprocal of a mixed fraction, convert it into an improper fraction. Then take the reciprocal of the improper fraction. For example: $4\\frac{3}{2}$ is a mixed fraction. Converting it into an improper fraction will be&nbsp; $4\\frac{3}{2} = \\frac{11}{2}$. Now, find the reciprocal by interchanging the denominator and numerator $\\frac{2}{11}$ . The reciprocal of $4\\frac{3}{2}$ is $\\frac{2}{11}$ .<\/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-c4cd5f6e-1741-4b1e-b52c-a72eeab0b84e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c4cd5f6e-1741-4b1e-b52c-a72eeab0b84e\"><strong>What is finding unity?<\/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-c4cd5f6e-1741-4b1e-b52c-a72eeab0b84e\">\n\n<p>If the reciprocal of the number is multiplied by itself, the value will result in unity which is one. For example, $2 \\times \\frac{1}{2} = 1$.<\/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-c4cd5f6e-1741-4b1e-b52c-a72eeab0b84e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c4cd5f6e-1741-4b1e-b52c-a72eeab0b84e\"><strong>What is the reciprocal of a negative number?<\/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-c4cd5f6e-1741-4b1e-b52c-a72eeab0b84e\">\n\n<p>The reciprocal of any negative number -x will be the inverse of the number along with the negative sign $-\\frac{1}{x}$ . For example, the reciprocal of -5 will be $-\\frac{1}{5}$ .<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Reciprocal Formula? The reciprocal formula calculates the reciprocal of a given number. The reciprocal of a non-zero number &#8220;a&#8221; is \u201c1 divided by a.&#8221; It is expressed as $\\frac{1}{a}$ and represents the multiplicative inverse of the number. In other words, when a number and its reciprocal are multiplied together, the result is &#8230; <a title=\"Reciprocal Formula &#8211; Definition, Examples, Practice Problems, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal-formula\" aria-label=\"More on Reciprocal Formula &#8211; Definition, Examples, Practice Problems, FAQs\">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-34742","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\/34742","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=34742"}],"version-history":[{"count":9,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34742\/revisions"}],"predecessor-version":[{"id":39975,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34742\/revisions\/39975"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=34742"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=34742"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=34742"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}