[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-366136-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-366136-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":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","lesson-guide-the-properties-of-zero-key-questions","Lesson Guide - The Properties of Zero - Key Questions","","Lesson guide accompanying a video titled “The Properties of Zero,” introducing zero as a special number. Key questions focus on why zero is unique and what properties it has. The guide covers that zero is the additive identity, showing that adding zero leaves a number unchanged, and that zero is the multiplicative absorbing element, showing multiplication by zero yields zero. It also explains the zero product property: if a product equals zero, at least one factor must be zero, with practice prompts and create-your-own examples.",{"@graph":14,"@context":72},[15,34,55],{"@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/lesson-guide-the-properties-of-zero-key-questions/366136/",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/lesson-guide-the-properties-of-zero-key-questions/366136.png","ImageObject",300,407,{"name":42,"@type":43},"anakgang17","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-10","2026-09-23",true,{"@type":52,"interactionType":53,"userInteractionCount":26},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"Why is zero such a special number?","Question",{"text":62,"@type":63},"The guide frames zero as special because it behaves differently in addition and multiplication: it changes nothing when added, and it forces a product to become zero when multiplied.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What is the additive identity property of zero?",{"text":67,"@type":63},"For any real number a, the sum of a and zero equals a. In other words, adding zero leaves the original number unchanged.",{"name":69,"@type":60,"acceptedAnswer":70},"What is the zero product property?",{"text":71,"@type":63},"If a product equals zero, then at least one of the factors must be zero. By the zero product property, for real numbers a and b, if a*b=0 then a=0 or b=0 (or both).","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},366136,1790163947,{"code":4,"msg":81,"data":82},"success",[83,87,91,94,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":92,"slug":93},70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},5,"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"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":95,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"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":26,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"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":79,"read_time":123,"preview_page_count":4},962090883568,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Name:    \nLesson Guide  \nThis lesson guide accompanies the following video lesson:  \nThe Properties of Zero  \nKey Questions  \n• Why is zero such a special number?  \n• What are properties of zero?  \nThe Properties of Zero  \nYou can not   by zero.  \nZero is   positive or negative.  \nZero is  .  \nZero is not  .  \nZero is not  .  \nDid you know that the Ancient Egyptians did not believe that you could have a quantity of nothing?  \nThey did not have a symbol for zero!  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 1  \nThe Additive Identity  \nFor any real number a…  \nThe sum of any number and   equals that same number.  \nExamples:  \n􀀡 + 􀀡 = 􀀡  \n􀀡 , 􀀡􀀢􀀣 + 􀀡 = 􀀡 , 􀀡􀀢􀀣  \n􀀡 + 􀀡 = 􀀡  \nCreate Your Own:  \n_______ + 􀀡 = _______  \nWhy is your example true?  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 2  \nThe Zero Product Property  \nFor any real number a…  \nAnything times   is equal to   .  \nExamples:  \n􀀡􀀢 (􀀡) = 􀀡−􀀡 × 􀀡 = 􀀡􀀡􀀡 (􀀡) = 􀀡  \n􀀡 × 􀀡 = 􀀡  \nCreate Your Own:  \n_______ × 􀀡 = 􀀡  \nWhy is your example true?  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 3  \nFor any real numbers a and b…  \nIf a product is equal to zero, then   one of the terms must equal zero!  \nBy the zero product property, at least one of terms, a or b (or both) must be equal to zero because ANY REAL NUMBER TIMES ZERO EQUALS ZERO!  \nExamples:  \nIf 􀀡 ⋅ −􀀡 = 􀀡 , then 􀀡 = 􀀡  \nIf 􀀡 ⋅ 􀀡 = 􀀡 , then 􀀡 = 􀀡  \nIf 􀀡 ⋅ 􀀡 = 􀀡 , then it is possible that 􀀡 = 􀀡 and 􀀡 = 􀀡 because 􀀡 ⋅ 􀀡 = 􀀡 If 􀀡􀀢􀀡 = 􀀡 , then 􀀡 = 􀀡  \nCreate Your Own:  \nIf   , then   Why is your example true?  \nRemember, the   Ensures that the product of any number and zero is equal to zero  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 4","cbCaidrsBAP3E01D","https://ap.wps.com/l/cbCaidrsBAP3E01D","pdf",2061449,"English","# Key Questions\n# The Properties of Zero\n# The Additive Identity\n# The Zero Product Property","[{\"question\":\"Why is zero such a special number?\",\"answer\":\"The guide frames zero as special because it behaves differently in addition and multiplication: it changes nothing when added, and it forces a product to become zero when multiplied.\"},{\"question\":\"What is the additive identity property of zero?\",\"answer\":\"For any real number a, the sum of a and zero equals a. In other words, adding zero leaves the original number unchanged.\"},{\"question\":\"What is the zero product property?\",\"answer\":\"If a product equals zero, then at least one of the factors must be zero. By the zero product property, for real numbers a and b, if a*b=0 then a=0 or b=0 (or both).\"}]","Lesson Guide - The Properties of Zero - Key Questions | PDF"]