[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-366216-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-366216-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","rational-and-irrational-numbers-lesson-guide","Rational and Irrational Numbers - Lesson Guide","","Lesson guide for the video lesson “Rational and Irrational Numbers Key Questions,” focusing on definitions, properties, and classification of real numbers. It introduces rational numbers as fractions of two integers (with nonzero denominators) and explains them as a ratio of integers, then contrasts irrational numbers as numbers not expressible as such fractions and not terminating or repeating. The guide includes key checks on whether every real number is either rational or irrational, never both, and provides example scenarios for sums and products involving rational and irrational numbers.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/rational-and-irrational-numbers-lesson-guide/366216/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/rational-and-irrational-numbers-lesson-guide/366216.png","ImageObject",300,407,{"name":42,"@type":43},"CatatanPagi","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-06","2026-09-23",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",20,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is a rational number?","Question",{"text":63,"@type":64},"A rational number can be expressed as a fraction of two integers, where the denominator is nonzero. It can also be thought of as a ratio of two integers.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What is an irrational number?",{"text":68,"@type":64},"An irrational number cannot be expressed as a fraction of two integers. Irrational numbers also do not terminate or repeat their decimal expansions.",{"name":70,"@type":61,"acceptedAnswer":71},"Can a real number be both rational and irrational (or neither)?",{"text":72,"@type":64},"Any real number must be either rational or irrational. A number cannot be both, and it cannot be neither.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},366216,1790374660,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":55,"slug":118},9,"Religion & Spirituality","religion-spirituality",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":55,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":106,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":144,"preview_page_count":4},962090894170,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Name:  \n____________________________________  \nLesson Guide  \nThis lesson guide accompanies the following video lesson:  \nRational and Irrational Numbers Key Questions  \n• What is a Rational Number?  \n• What is an Irrational Number?  \nØ Rational Numbers  \nA rational number is any number that can be expressed as a   .  \nEach value, a and b, must be an   and the denominator, b, can not equal    \nA rational number can be thought of as a   of two integers.  \nExamples of Rational Numbers:  \n25 8 16  \nBecause  \na =   b =    \nBecause  \na =   b =    \nBecause  \na =   b =    \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com)  \nØ Irrational Numbers  \nAn irrational number, x, is any number that can not be expressed as a   of two integers.  \nIrrational numbers can not be expressed as terminating or repeating  \n.  \nExample:  \nis irrational because  \nthe value continues forever and never    \nExamples of Irrational Numbers:  \n21 0 . 798316 …  \n􀀡  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com)  \nPART TWO  \nYES NO  \nAny real number must be either rational or irrational. A number can not be both or neither!  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com)  \nPART THREE  \nExample 01 : Rational + Rational  \nConclusion: The sum of two rational numbers is  \n.  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com)  \nExample 02: Rational x Rational  \nConclusion: The product of two rational numbers is    \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com)  \nExample 03: Rational + Irrational  \n(assume that the rational value is not zero)  \nConclusion: The sum of a non-zero rational number and an irrational number is  \n.  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com)  \nExample 04: Rational x Irrational  \n(assume that the rational value is not zero)  \nConclusion: The product of a non-zero rational number and an irrational number is  \n.  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com)","cbCaios0QU7BlGY0","https://ap.wps.com/l/cbCaios0QU7BlGY0","pdf",2277103,"English","# Rational Numbers\n# Irrational Numbers\n# Real Numbers: Rational or Irrational?\n# Examples: Operations With Rational and Irrational Numbers\n## Example 01: Rational + Rational\n## Example 02: Rational × Rational\n## Example 03: Rational + Irrational\n## Example 04: Rational × Irrational","[{\"question\":\"What is a rational number?\",\"answer\":\"A rational number can be expressed as a fraction of two integers, where the denominator is nonzero. It can also be thought of as a ratio of two integers.\"},{\"question\":\"What is an irrational number?\",\"answer\":\"An irrational number cannot be expressed as a fraction of two integers. Irrational numbers also do not terminate or repeat their decimal expansions.\"},{\"question\":\"Can a real number be both rational and irrational (or neither)?\",\"answer\":\"Any real number must be either rational or irrational. A number cannot be both, and it cannot be neither.\"}]","Rational and Irrational Numbers - Lesson Guide | PDF",1790164274,18]