[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-480296-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-480296-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","finding-associative-property-of-multiplication-answer-key","Finding Associative Property of Multiplication - Answer Key","","Worksheet and answer key practice associativity in multiplication by selecting equivalent expressions. Students compare expressions using the same factors grouped in different ways, such as (a × b) × c versus a × (b × c), and decide which option preserves equality. Problems include cases using 0 and 1 to test understanding of multiplicative identity and zero, with multiple-choice selections and a corresponding set of correct answers.",{"@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/finding-associative-property-of-multiplication-answer-key/480296/",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/finding-associative-property-of-multiplication-answer-key/480296.png","ImageObject",300,407,{"name":42,"@type":43},"Aldword","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-03","2026-09-30",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",7,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What concept do the problems practice?","Question",{"text":63,"@type":64},"The problems practice the associative property of multiplication by matching equivalent expressions formed by regrouping factors.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do students decide which choice is correct?",{"text":68,"@type":64},"Students select the expression that is equal to the target expression after regrouping multiplication factors.",{"name":70,"@type":61,"acceptedAnswer":71},"Why do some items include 0 and 1?",{"text":72,"@type":64},"Items use 0 and 1 to confirm multiplication behavior such as producing 0 when a factor is 0 and preserving values when a factor is 1.","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},480296,1792997208,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,109,114,119,122,126],{"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":55,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},"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":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":30,"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":110},2336478940917,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Finding Associative Property of Multiplication  \nName:  \n\n| Determine which choice is an equivalent equation. |  |  |  |  |  |  |  |  |  | Answers |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1) Which expression is equal to 2) Which expression is equal to ( 4 × 6 ) × 8 ( 7 × 3 ) × 2\u003Cbr>A. ( 4 + 6 ) + 8 A. ( 7 + 3 ) × 2\u003Cbr>B. ( 4 + 6 ) × 8 B. 7 × ( 3 + 2 )\u003Cbr>C. 4 × ( 6 × 8 ) C. 7 × ( 3 × 2 )\u003Cbr>D. 4 + ( 6 × 8 ) D. 7 + ( 3 + 2 )\u003Cbr>3) Which expression is equal to 4) Which expression is equal to\u003Cbr>8 × ( 6 × 1 ) ( 10 × 2 ) × 7\u003Cbr>A. ( 8 × 6 ) × 1 A. ( 10 + 2 ) × 7\u003Cbr>B. ( 8 × 6 ) + 1 B. 10 × ( 2 × 7 ) |  |  |  |  |  |  |  |  |  | 1.  \u003Cbr>2.  \u003Cbr>3.  \u003Cbr>4.  \u003Cbr>5.   |  |  |  |\n| C. ( 8 + 6 ) + 1\u003Cbr>D. 8 + ( 6 × 1 )\u003Cbr>5) Which expression is equal to 6)\u003Cbr>7 × ( 0 × 5 )\u003Cbr>A. ( 7 × 0 ) × 5\u003Cbr>B. 7 + ( 0 × 5 )\u003Cbr>C. ( 7 + 0 ) × 5\u003Cbr>D. 7 + ( 0 + 5 )\u003Cbr>7) Which expression is equal to 8)( 1 × 3 ) × 9\u003Cbr>A. 1 × ( 3 × 9 ) |  | C. 10 + ( 2 + 7 )\u003Cbr>D. ( 10 × 2 ) + 7\u003Cbr>Which expression is equal to ( 7 × 0 ) × 6\u003Cbr>A. ( 7 + 0 ) + 6\u003Cbr>B. 7 × ( 0 + 6 )\u003Cbr>C. 7 × ( 0 × 6 )\u003Cbr>D. ( 7 × 0 ) + 6\u003Cbr>Which expression is equal to ( 3 × 9 ) × 8\u003Cbr>A. ( 3 + 9 ) + 8 |  |  |  |  |  |  |  | 6.  \u003Cbr>7.  \u003Cbr>8.  \u003Cbr>9.  \u003Cbr>10.  \u003Cbr>11.   |  |  |  |\n| B. 1 + ( 3 × 9 )\u003Cbr>C. ( 1 + 3 ) × 9 |  | B. 3 + ( 9 + 8 )\u003Cbr>C. 3 × ( 9 × 8 ) |  |  |  |  |  |  |  | 12.   |  |  |  |\n| D. ( 1 × 3 ) + 9 |  | D. 3 + ( 9 × 8 ) |  |  |  |  |  |  |  |  |  |  |  |\n| 9) Which expression is equal to 10) |  | Which expression is equal to |  |  |  |  |  |  |  |  |  |  |  |\n| 5 × ( 10 × 8 ) |  | 1 × ( 8 × 5 ) |  |  |  |  |  |  |  |  |  |  |  |\n| A. ( 5 × 10 ) × 8 |  | A. ( 1 × 8 ) × 5 |  |  |  |  |  |  |  |  |  |  |  |\n| B. ( 5 × 10 ) + 8 |  | B. 1 × ( 8 + 5 ) |  |  |  |  |  |  |  |  |  |  |  |\n| C. 5 + ( 10 + 8 ) |  | C. ( 1 + 8 ) × 5 |  |  |  |  |  |  |  |  |  |  |  |\n| D. ( 5 + 10 ) × 8 |  | D. 1 + ( 8 × 5 ) |  |  |  |  |  |  |  |  |  |  |  |\n| 11) Which expression is equal to 12) |  | Which expression is equal to |  |  |  |  |  |  |  |  |  |  |  |\n| 2 × ( 7 × 1 ) |  | ( 7 × 5 ) × 10 |  |  |  |  |  |  |  |  |  |  |  |\n| A. ( 2 + 7 ) + 1 |  | A. 7 + ( 5 + 10 ) |  |  |  |  |  |  |  |  |  |  |  |\n| B. ( 2 × 7 ) × 1 |  | B. 7 × ( 5 + 10 ) |  |  |  |  |  |  |  |  |  |  |  |\n| C. 2 + ( 7 + 1 ) |  | C. 7 × ( 5 × 10 ) |  |  |  |  |  |  |  |  |  |  |  |\n| D. ( 2 × 7 ) + 1 |  | D. ( 7 + 5 ) + 10 |  |  |  |  |  |  |  |  |  |  |  |\n| \u003Cbr>Math | [www.CommonCoreSheets.com](www.CommonCoreSheets.com) | 5 | 1-10\u003Cbr>11-12 | 92 | 83 | 75 | 67 | 58 | 50 | 42 | 33 | 25 | 17 |\n|  |  |  |  | 8 | 0 |  |  |  |  |  |  |  |  |\n\nFinding Associative Property of Multiplication  \nName: Answer Key  \n\n| Determine which choice is an equivalent equation. |  |  |  |  |  |  |  |  |  | Answers |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1) Which expression is equal to 2) Which expression is equal to ( 4 × 6 ) × 8 ( 7 × 3 ) × 2\u003Cbr>A. ( 4 + 6 ) + 8 A. ( 7 + 3 ) × 2\u003Cbr>B. ( 4 + 6 ) × 8 B. 7 × ( 3 + 2 )\u003Cbr>C. 4 × ( 6 × 8 ) C. 7 × ( 3 × 2 )\u003Cbr>D. 4 + ( 6 × 8 ) D. 7 + ( 3 + 2 )\u003Cbr>3) Which expression is equal to 4) Which expression is equal to\u003Cbr>8 × ( 6 × 1 ) ( 10 × 2 ) × 7\u003Cbr>A. ( 8 × 6 ) × 1 A. ( 10 + 2 ) × 7\u003Cbr>B. ( 8 × 6 ) + 1 B. 10 × ( 2 × 7 ) |  |  |  |  |  |  |  |  |  | 1.  C \u003Cbr>2.  C \u003Cbr>3.  A \u003Cbr>4.  B \u003Cbr>5.  A  |  |  |  |\n| C. ( 8 + 6 ) + 1\u003Cbr>D. 8 + ( 6 × 1 )\u003Cbr>5) Which expression is equal to 6)\u003Cbr>7 × ( 0 × 5 )\u003Cbr>A. ( 7 × 0 ) × 5\u003Cbr>B. 7 + ( 0 × 5 )\u003Cbr>C. ( 7 + 0 ) × 5\u003Cbr>D. 7 + ( 0 + 5 )\u003Cbr>7) Which expression is equal to 8)( 1 × 3 ) × 9\u003Cbr>A. 1 × ( 3 × 9 ) |  | C. 10 + ( 2 + 7 )\u003Cbr>D. ( 10 × 2 ) + 7\u003Cbr>Which expression is equal to ( 7 × 0 ) × 6\u003Cbr>A. ( 7 + 0 ) + 6\u003Cbr>B. 7 × ( 0 + 6 )\u003Cbr>C. 7 × ( 0 × 6 )\u003Cbr>D. ( 7 × 0 ) + 6\u003Cbr>Which expression is equal to ( 3 × 9 ) × 8\u003Cbr>A. ( 3 + 9 ) + 8 |  |  |  |  |  |  |  | 6.  C \u003Cbr>7.  A \u003Cbr>8.  C \u003Cbr>9.  A \u003Cbr>10.  A \u003Cbr>11.  B  |  |  |  |\n| B. 1 + ( 3","cbCaip0FgKuWRAEB","https://ap.wps.com/l/cbCaip0FgKuWRAEB","pdf",43511,"English","# Determine Equivalent Equations\n## Multiple-Choice Items\n## Answer Key","[{\"question\":\"What concept do the problems practice?\",\"answer\":\"The problems practice the associative property of multiplication by matching equivalent expressions formed by regrouping factors.\"},{\"question\":\"How do students decide which choice is correct?\",\"answer\":\"Students select the expression that is equal to the target expression after regrouping multiplication factors.\"},{\"question\":\"Why do some items include 0 and 1?\",\"answer\":\"Items use 0 and 1 to confirm multiplication behavior such as producing 0 when a factor is 0 and preserving values when a factor is 1.\"}]","Finding Associative Property of Multiplication - Answer Key | PDF",1790794764]