[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-464249-105":59,"doc-detail-464249-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","associative-value-missing-digit-answers","Associative Value (Missing Digit) - Answers","","Worksheet focused on associative property with a missing-digit variable n. Each item rewrites a multiplication expression in an equivalent form, such as (a × b) × c = a × (b × c), to determine the digit that satisfies the equality. An answer section lists the resolved values of n for problems 1 through 20, supporting direct checking of student work.",{"@graph":69,"@context":122},[70,84,105],{"@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/associative-value-missing-digit-answers/464249/",{"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/associative-value-missing-digit-answers/464249.png","ImageObject",300,407,{"name":92,"@type":93},"Lucas Martin","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does each question ask you to do in this worksheet?","Question",{"text":112,"@type":113},"Find the value of n by using the associative property of multiplication.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are the equations structured?",{"text":117,"@type":113},"Each problem shows an equality where parentheses are rearranged, like (a × b) × c = a × (b × c), with n in one side.",{"name":119,"@type":110,"acceptedAnswer":120},"Where can the correct values of n be checked?",{"text":121,"@type":113},"In the Answers section, which provides the value of n for problems 1 through 20.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},464249,1790767917,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":39},8796095360427,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Associative Value (Missing Digit)  \nName:  \nFind the value of n. Answers  \n1) ( 2 × 4 ) × 9 = 2 × ( 4 × n ) 2) ( 3 × n ) × 9 = 3 × ( 2 × 9 )  \n1.  \n2.  \n3) ( 10 × n ) × 5 = 10 × ( 8 × 5 ) 4) ( 4 × n ) × 3 = 4 × ( 5 × 3 )  \n3.  \n4.  \n5) n × ( 5 × 4 ) = ( 3 × 5 ) × 4 6) n × ( 7 × 1 ) = ( 3 × 7 ) × 1  \n5.  \n6.  \n7) 4 × ( n × 2 ) = ( 4 × 6 ) × 2 8) ( 6 × 0 ) × 5 = 6 × ( 0 × n )  \n7.  \n8.  \n9) ( 10 × 1 ) × 3 = 10 × ( 1 × n ) 10) 10 × ( 3 × n ) = ( 10 × 3 ) × 7  \n9.  \n10.  \n11) ( 5 × 4 ) × 3 = 5 × ( 4 × n ) 12) n × ( 4 × 2 ) = ( 5 × 4 ) × 2  \n11.  \n12.  \n13) 5 × ( 10 × 6 ) = ( 5 × 10 ) × n 14) 10 × ( n × 7 ) = ( 10 × 0 ) × 7  \n13.  \n14.  \n15) 1 × ( n × 0 ) = ( 1 × 9 ) × 0 16) 9 × ( n × 4 ) = ( 9 × 2 ) × 4  \n15.  \n16.  \n17) ( 4 × 5 ) × n = 4 × ( 5 × 1 ) 18) 10 × ( 5 × 8 ) = ( 10 × 5 ) × n  \n17.  \n18.  \n19) 0 × ( n × 6 ) = ( 0 × 10 ) × 6 20) ( 9 × 0 ) × 2 = n × ( 0 × 2 )  \n19.  \n20.  \nMath  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n1  \n1-10 11-20  \n95  \n45  \n90  \n40  \n85  \n35  \n80  \n30  \n75  \n25  \n70  \n20  \n65  \n15  \n60  \n10  \n55  \n5  \n50  \n0  \nAssociative Value (Missing Digit)  \nName: Answer Key  \nFind the value of n.  \n1) ( 2 × 4 ) × 9 = 2 × ( 4 × n ) 2) ( 3 × n ) × 9 = 3 × ( 2 × 9 )  \n3) ( 10 × n ) × 5 = 10 × ( 8 × 5 ) 4) ( 4 × n ) × 3 = 4 × ( 5 × 3 )  \n5) n × ( 5 × 4 ) = ( 3 × 5 ) × 4 6) n × ( 7 × 1 ) = ( 3 × 7 ) × 1  \n7) 4 × ( n × 2 ) = ( 4 × 6 ) × 2 8) ( 6 × 0 ) × 5 = 6 × ( 0 × n )  \n9) ( 10 × 1 ) × 3 = 10 × ( 1 × n ) 10) 10 × ( 3 × n ) = ( 10 × 3 ) × 7  \n11) ( 5 × 4 ) × 3 = 5 × ( 4 × n ) 12) n × ( 4 × 2 ) = ( 5 × 4 ) × 2  \n13) 5 × ( 10 × 6 ) = ( 5 × 10 ) × n 14) 10 × ( n × 7 ) = ( 10 × 0 ) × 7  \n15) 1 × ( n × 0 ) = ( 1 × 9 ) × 0 16) 9 × ( n × 4 ) = ( 9 × 2 ) × 4  \n17) ( 4 × 5 ) × n = 4 × ( 5 × 1 ) 18) 10 × ( 5 × 8 ) = ( 10 × 5 ) × n  \n19) 0 × ( n × 6 ) = ( 0 × 10 ) × 6 20) ( 9 × 0 ) × 2 = n × ( 0 × 2 )  \nAnswers  \n1. 9 2. 2 3. 8 4. 5 5. 3 6. 3 7. 6 8. 5 9. 3 10. 7 11. 3 12. 5 13. 6 14. 0 15. 9 16. 2 17. 1 18. 8 19. 10  \n20. 9  \nMath  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n1  \n1-10 11-20  \n95  \n45  \n90  \n40  \n85  \n35  \n80  \n30  \n75  \n25  \n70  \n20  \n65  \n15  \n60  \n10  \n55  \n5  \n50  \n0  \nAssociative Value (Missing Digit)  \nName:  \nFind the value of n.  \n3 5 5 5  \n6 9 2 8  \n7 3 3 3  \n1) ( 2 × 4 ) × 9 = 2 × ( 4 × n ) 2) ( 3 × n ) × 9 = 3 × ( 2 × 9 )  \n3) ( 10 × n ) × 5 = 10 × ( 8 × 5 ) 4) ( 4 × n ) × 3 = 4 × ( 5 × 3 )  \n5) n × ( 5 × 4 ) = ( 3 × 5 ) × 4 6) n × ( 7 × 1 ) = ( 3 × 7 ) × 1  \n7) 4 × ( n × 2 ) = ( 4 × 6 ) × 2 8) ( 6 × 0 ) × 5 = 6 × ( 0 × n )  \nAnswers  \n1.  \n2.  \n3.  \n4.  \n5.  \n6.  \n7.  \n8.  \n9.  \n10.  \n11.  \n12.  \n9) ( 10 × 1 ) × 3 = 10 × ( 1 × n ) 10) 10 × ( 3 × n ) = ( 10 × 3 ) × 7  \n11) ( 5 × 4 ) × 3 = 5 × ( 4 × n ) 12) n × ( 4 × 2 ) = ( 5 × 4 ) × 2  \nMath  \nModified  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n1  \n1-10 92  \n11-12 8  \n83  \n0  \n75 67 58 50 42 33 25 17","cbCaih3ibhdz1nK0","https://ap.wps.com/l/cbCaih3ibhdz1nK0","pdf",44043,"English","# Find the value of n\n## Problem set 1-20\n## Answers","[{\"question\":\"What does each question ask you to do in this worksheet?\",\"answer\":\"Find the value of n by using the associative property of multiplication.\"},{\"question\":\"How are the equations structured?\",\"answer\":\"Each problem shows an equality where parentheses are rearranged, like (a × b) × c = a × (b × c), with n in one side.\"},{\"question\":\"Where can the correct values of n be checked?\",\"answer\":\"In the Answers section, which provides the value of n for problems 1 through 20.\"}]","Associative Value (Missing Digit) - Answers | PDF"]