[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-480319-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-480319-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","associative-value-missing-digit-find-the-value-of-n","Associative Value (Missing Digit) - Find the Value of n","","A math worksheet on the associative property of multiplication, focusing on equations with a missing digit n. It provides multiple problems in the form (a × b) × c = a × (b × n) or similar rearrangements, requiring students to compute the value of n that makes both sides equal. An answer section and key are included for checking results, covering a range of factor combinations including zeros.",{"@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/associative-value-missing-digit-find-the-value-of-n/480319/",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/associative-value-missing-digit-find-the-value-of-n/480319.png","ImageObject",300,407,{"name":42,"@type":43},"Aldword","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-01","2026-09-30",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",5,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What does the missing digit n represent in these problems?","Question",{"text":63,"@type":64},"n is the unknown digit that must be found so that the two multiplication expressions on each equation are equal.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are the problems structured?",{"text":68,"@type":64},"Each problem rewrites multiplication using the associative property, comparing a product grouped one way versus grouped another way with n inserted.",{"name":70,"@type":61,"acceptedAnswer":71},"Is there an answer key included?",{"text":72,"@type":64},"Yes. The document provides an Answers/Answer Key section listing the values of n for the problems.","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},480319,1791413570,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,99,104,109,114,119,122,126],{"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":55,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},"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":55,"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":112,"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},2336478940917,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","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  \nAssociative Value (Missing Digit)  \nName:  \nFind the value of n. Answers  \n1) ( 10 × 7 ) × 4 = 10 × ( n × 4 ) 2) ( 4 × 7 ) × 0 = n × ( 7 × 0 )  \n1.  \n2.  \n3) 5 × ( 4 × 7 ) = ( 5 × 4 ) × n 4) n × ( 5 × 2 ) = ( 9 × 5 ) × 2  \n3.  \n4.  \n5) 10 × ( 2 × n ) = ( 10 × 2 ) × 9 6) 10 × ( 5 × 6 ) = ( n × 5 ) × 6  \n5.  \n6.  \n7) ( n × 5 ) × 3 = 9 × ( 5 × 3 ) 8) ( n × 7 ) × 3 = 6 × ( 7 × 3 )  \n7.  \n8.  \n9) 5 × ( 7 × 2 ) = ( 5 × n ) × 2 10) 2 × ( 3 × 9 ) = ( n × 3 ) × 9  \n9.  \n10.  \n11) ( 6 × n ) × 1 = 6 × ( 8 × 1 ) 12) ( 10 × 1 ) × n = 10 × ( 1 × 7 )  \n11.  \n12.  \n13) 9 × ( 10 × 8 ) = ( 9 × n ) × 8 14) ( 9 × n ) × 6 = 9 × ( 7 × 6 )  \n13.  \n14.  \n15) ( 8 × 9 ) × 2 = 8 × ( 9 × n ) 16) ( 0 × 1 ) × 9 = 0 × ( 1 × n )  \n15.  \n16.  \n17) ( 8 × 3 ) × 6 = 8 × ( n × 6 ) 18) 4 × ( n × 9 ) = ( 4 × 0 ) × 9  \n17.  \n18.  \n19) 4 × ( 9 × 5 ) = ( n × 9 ) × 5 20) 3 × ( n × 1 ) = ( 3 × 8 ) × 1  \n19.  \n20.  \nMath  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n2  \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 val","cbCaivMprQnsDQ4V","https://ap.wps.com/l/cbCaivMprQnsDQ4V","pdf",448052,"English","# Problems\n## Find the value of n\n# Answer Key","[{\"question\":\"What does the missing digit n represent in these problems?\",\"answer\":\"n is the unknown digit that must be found so that the two multiplication expressions on each equation are equal.\"},{\"question\":\"How are the problems structured?\",\"answer\":\"Each problem rewrites multiplication using the associative property, comparing a product grouped one way versus grouped another way with n inserted.\"},{\"question\":\"Is there an answer key included?\",\"answer\":\"Yes. The document provides an Answers/Answer Key section listing the values of n for the problems.\"}]","Associative Value (Missing Digit) - Find the Value of n | PDF",1790794795,76]