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Problems involve simplifying products and sums using variables represented by letters such as b, c, d, e, f, g, h, i, j, k, m, n, p, r, t, u, v, w, y, and z. It provides both the original expression prompts and the corresponding expanded or regrouped results, covering items 1 through 20 with numbered solution entries.",{"@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/applying-properties-of-operations-answer-key/465744/",{"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/applying-properties-of-operations-answer-key/465744.png","ImageObject",300,407,{"name":92,"@type":93},"Hazel","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-02","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What skill does this answer key practice?","Question",{"text":112,"@type":113},"It practices applying the distributive property to produce equivalent expressions by rewriting products of sums into expanded forms.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are the answers presented?",{"text":117,"@type":113},"Each problem is numbered and matched with its equivalent rewritten expression, including terms with variables like b, c, and others.",{"name":119,"@type":110,"acceptedAnswer":120},"What types of algebraic expressions are included?",{"text":121,"@type":113},"The problems include expressions such as a single product with parentheses (e.g., 5(2 + 7c)) and repeated addition terms (e.g., f + f + f + f) that can be rewritten using multiplication.","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},465744,1790770002,{"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":8,"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},137441390410,"https://ap-avatar.wpscdn.com/avatar/2000252f4ab5702993?_k=1776741390130283984","Applying Properties of Operations  \nName:  \nApply the distributive property to produce an equivalent expression.  \n1) 36b + 63  \n2) 5(2 + 7c)  \n3) 2(7d + 3)  \n4) 4(6e + 7)  \n5) f + f + f + f  \n6) g + g + g + g + g + g  \n7) 9h + 7 + 7 + 8h  \n8) 3i + 9i + 5 + 10  \n9) 70j + 42  \n1.  \n2.  \n3.  \n4.  \n5.  \n6.  \n7.  \n8.  \nAnswers  \n10) 8(9k + 5)  \n11) m + m + m + m + m  \n12) 24 + 40n  \n13) 2(7p + 5)  \n14) r + r + r + r + r  \n15) 3(9t + 3)  \n16) 27u + 72  \n17) v + v + v + v + v + v + v  \n18) 54 + 54w  \n19) 8(5y + 2)  \n20) 21 + 24z  \n9.  \n10.  \n11.  \n12.  \n13.  \n14.  \n15.  \n16.  \n17.  \n18.  \n19.  \n20.  \nMath  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n10  \n1-10 11-20  \n95  \n45  \n90  \n40  \n85  \n35  \n80  \n30  \n75  \n25  \n70  \n20  \n65  \n15  \n60  \n10  \n55  \n5  \n50  \n0  \nApplying Properties of Operations  \nName: Answer Key  \n\n| Apply the distributive property to produce an equivalent expression.\u003Cbr>1) 36b + 63 | Answers\u003Cbr>1. 9(4b + 7) |\n| --- | --- |\n| 2) 5(2 + 7c) | 2. 10 + 35c |\n| 3) 2(7d + 3) | 3. 14d + 6 |\n| 4) 4(6e + 7) | 4.  24e + 28  |\n| 5) f + f + f + f | 5. 4f |\n| 6) g + g + g + g + g + g | 6. 6g |\n| 7) 9h + 7 + 7 + 8h | 7. 17h+14 |\n| 8) 3i + 9i + 5 + 10 | 8. 12i+15 |\n| 9) 70j + 42 | 9. 14(5j + 3) |\n| 10) 8(9k + 5) | 10. 72k + 40 |\n| 11) m + m + m + m + m | 11. 5m |\n| 12) 24 + 40n |  |\n| 13) 2(7p + 5) | 12.  8(3 + 5n) \u003Cbr>13. 14p + 10 |\n| 14) r + r + r + r + r |  |\n| 15) 3(9t + 3) | 14.  5r \u003Cbr>15. 27t + 9 |\n| 16) 27u + 72 |  |\n| 17) v + v + v + v + v + v + v | 16.  9(3u + 8)  |\n| 18) 54 + 54w | 17.  7v  |\n| 19) 8(5y + 2) | 18.  54(1 + 1w)  |\n| 20) 21 + 24z | 19.  40y + 16 \u003Cbr>20. 3(7 + 8z) |\n\nMath  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n10  \n1-10 11-20  \n95  \n45  \n90  \n40  \n85  \n35  \n80  \n30  \n75  \n25  \n70  \n20  \n65  \n15  \n60  \n10  \n55  \n5  \n50  \n0  \nApplying Properties of Operations  \nName:  \nApply the distributive property to produce an equivalent expression.  \n14d + 6 10 + 35c 17h+14 6g  \n14(5j + 3) 4f 8(3 + 5n) 14p + 10  \n72k + 40 24e + 28 5m 9(4b + 7)  \n12i+15  \nAnswers  \n1) 36b + 63  \n2) 5(2 + 7c)  \n3) 2(7d + 3)  \n4) 4(6e + 7)  \n5) f + f + f + f  \n6) g + g + g + g + g + g  \n7) 9h + 7 + 7 + 8h  \n8) 3i + 9i + 5 + 10  \n9) 70j + 42  \n10) 8(9k + 5)  \n11) m + m + m + m + m  \n12) 24 + 40n  \n13) 2(7p + 5)  \n1.  \n2.  \n3.    \n4.    \n5.    \n6.    \n7.    \n8.    \n9.    \n10.    \n11.    \n12.    \n13.    \n\n| \u003Cbr>Math | Modified\u003Cbr>[www.CommonCoreSheets.com](www.CommonCoreSheets.com) | 10 | 1-10\u003Cbr>11-13 | 92 | 85 | 77 | 69 | 62 | 54 | 46 | 38 | 31 | 23 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  | 15 | 8 | 0 |  |  |  |  |  |  |  |","cbCaioLk73NWhQGH","https://ap.wps.com/l/cbCaioLk73NWhQGH","pdf",44572,"English","# Apply the distributive property to produce an equivalent expression\n## Questions 1-10\n## Questions 10-20","[{\"question\":\"What skill does this answer key practice?\",\"answer\":\"It practices applying the distributive property to produce equivalent expressions by rewriting products of sums into expanded forms.\"},{\"question\":\"How are the answers presented?\",\"answer\":\"Each problem is numbered and matched with its equivalent rewritten expression, including terms with variables like b, c, and others.\"},{\"question\":\"What types of algebraic expressions are included?\",\"answer\":\"The problems include expressions such as a single product with parentheses (e.g., 5(2 + 7c)) and repeated addition terms (e.g., f + f + f + f) that can be rewritten using multiplication.\"}]","Applying Properties of Operations - Answer Key | PDF"]