[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-360709-105":59,"doc-detail-360709-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","identifying-properties-of-operations-part-1-3","Identifying Properties of Operations - Part 1-3","","Practice worksheet for identifying and applying core properties of operations in math. Students distinguish commutative, associative, distributive, and identity properties by examining changes in order, changes in grouping, multiplying across sums, and using zero or one to preserve values. The worksheet includes guided sections to match equations to property names and choose the property that justifies steps, including a challenge problem requiring explanation of which properties are used.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/identifying-properties-of-operations-part-1-3/360709/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/identifying-properties-of-operations-part-1-3/360709.png","ImageObject",300,407,{"name":92,"@type":93},"Bintang","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-08","2026-09-23",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",16,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What do the commutative and associative properties change in an equation?","Question",{"text":113,"@type":114},"Commutative property changes the order of addends or factors (a+b=b+a). Associative property changes the grouping of terms (a+b)+c=a+(b+c).","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How is the distributive property used on sums and products?",{"text":118,"@type":114},"Distributive property multiplies across a sum, such as a×(b+c)=(a×b)+(a×c).",{"name":120,"@type":111,"acceptedAnswer":121},"Which properties justify the challenge equation (x + 0) + 5 = 5 + x?",{"text":122,"@type":114},"The identity property shows x+0=x, and then the commutative property allows switching the order to get 5+x. Logan’s reasoning is incomplete because it doesn’t include both properties.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},360709,1790285388,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":39,"preview_page_count":4},962085564381,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Name:    \nIdentifying Properties of Operations  \nDirections: For each problem below, identify the property of operations being used.  \nChoose from:  \n| (A) Commutative\u003Cbr>Property | (B) Associative\u003Cbr>Property | (C) Distributive\u003Cbr>Property | (D) Identity Property |\n| --- | --- | --- | --- |\n| Changing the order:\u003Cbr>4 + 6 = 6 + 4 | Changing grouping:(2 + 3) + 4 = 2 + (3 + 4) | Multiply across a sum:\u003Cbr>3 × (2 + 5) = (3 × 2) + (3 × 5) | Zero or one keeps the value:\u003Cbr>9 + 0 = 9 or 7 × 1 = 7 |\n\nPart 1: Identify the Property (1–6)  \nWrite the correct letter (A, B, C, or D) next to each expression.  \n1.) 3 + 10 = 10 + 3 →    \n2.) (5 + 2) + 4 = 5 + (2 + 4) →    \n3.) 8 × (2 + 1) = (8 × 2) + (8 × 1) →    \n4.) 0 + 15 = 15 →    \n5.) 9 × (6 × 1) = (9 × 6) × 1 →    \n6.) 12 + (3 + 0) = (12 + 3) + 0 →    \nPart 2: Match the Equation to the Property (7–9) Write the correct property name for each example. 7.) (2 + 5) + 8 = 2 + (5 + 8) → ________________________  \n8.) 4 × (6 + 3) = (4 × 6) + (4 × 3) → ________________________  \n9.) 11 + 7 = 7 + 11 → ________________________  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 1  \nPart 3: Apply the Property (10–12)  \nChoose the correct property that would help you solve or simplify the expression.  \n10.) Which property allows you to solve 18 × 0 = 0 quickly?  \nAnswer:    \n11.) Which property justifies the step:  \n7 + (9 + 1) = (7 + 9) + 1?  \nAnswer:    \n12.) Which property tells you that 4 × 3 = 3 × 4?  \nAnswer:    \nChallenge Problem: Logan thinks that the equation (x + 0) + 5 = 5 + x  \nuses the commutative property.  \nIs he right? If not, which property (or properties) are being used, and how would you explain it?  \nYour Answer:  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 2  \nAnswer Key  \nPart 1: Identify the Property 1.) A – Commutative Property 2.) B – Associative Property  \n3.) C – Distributive Property  \n4.) D – Identity Property  \n5.) B – Associative Property  \n6.) B – Associative Property  \nPart 2: Match the Equation to the Property 7.) Associative Property  \n8.) Distributive Property  \n9.) Commutative Property  \nPart 3: Apply the Property 10.) Identity Property  \n11.) Associative Property  \n12.) Commutative Property  \nChallenge Problem:  \nLogan is partially correct, but his reasoning is incomplete.  \nThe equation (x + 0) + 5 = 5 + x uses both the Identity Property (x + 0 = x) and the Commutative Property (x + 5 = 5 + x) .  \nA good explanation:  \n“First, the identity property tells us that x + 0 is just x. Then, the commutative property lets us switch the order to get 5 + x.”  \nLet me know if you’d like a B version of the answer key formatted for printing!  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 3","cbCaigBro0yJG4E0","https://ap.wps.com/l/cbCaigBro0yJG4E0","pdf",651321,"English","# Part 1: Identify the Property\n## Expressions 1–6\n# Part 2: Match the Equation to the Property\n## Equations 7–9\n# Part 3: Apply the Property\n## Questions 10–12\n## Challenge Problem","[{\"question\":\"What do the commutative and associative properties change in an equation?\",\"answer\":\"Commutative property changes the order of addends or factors (a+b=b+a). Associative property changes the grouping of terms (a+b)+c=a+(b+c).\"},{\"question\":\"How is the distributive property used on sums and products?\",\"answer\":\"Distributive property multiplies across a sum, such as a×(b+c)=(a×b)+(a×c).\"},{\"question\":\"Which properties justify the challenge equation (x + 0) + 5 = 5 + x?\",\"answer\":\"The identity property shows x+0=x, and then the commutative property allows switching the order to get 5+x. Logan’s reasoning is incomplete because it doesn’t include both properties.\"}]","Identifying Properties of Operations - Part 1-3 | PDF",1790141285]