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The problems request rewriting given algebraic expressions into equivalent forms by distributing multiplication across addition or combining like terms. Items include expressions such as 30b + 24, 24f + 48, and 6(8 + 7j), plus variable-only sums like g repeated multiple times. The answer section provides the expanded equivalent expressions for each numbered item, supporting self-check and 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does the distributive property mean in these problems?","Question",{"text":112,"@type":113},"Use the distributive property to transform an expression by distributing multiplication over addition, producing an equivalent expression.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How should you solve an item like 6(8 + 7j)?",{"text":117,"@type":113},"Multiply 6 by each term inside the parentheses: 6·8 and 6·7j, then combine the results into an equivalent expression.",{"name":119,"@type":110,"acceptedAnswer":120},"What information does the answer key provide?",{"text":121,"@type":113},"For each numbered problem, the answer key lists the equivalent distributed expression so students can check their work.","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},465762,1790770023,{"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) 30b + 24  \n2) 5 + 5 + 9c + 10c  \n3) 10 + 16d  \n4) 9 + 2e + 8 + 7e  \n5) 24f + 48  \n6) g + g + g + g + g + g + g + g + g  \n7) 8 + 7h + 8 + 7h  \n8) 90i + 80  \n9) 6(8 + 7j)  \n1.  \n2.  \n3.  \n4.  \n5.  \n6.  \n7.  \n8.  \nAnswers  \n10) 10 + 9k + 7k + 2  \n11) 6 + 8m + 8 + 6m  \n12) 5n + 5 + 4n + 3  \n13) 6(4p + 7)  \n14) 4(4r + 10)  \n15) 5(6t + 5)  \n16) 2(4u + 6)  \n17) 10(7v + 4)  \n18) 2(10w + 7)  \n19) 4(5 + 7y)  \n20) 2z + 2z + 2 + 5  \n9.  \n10.  \n11.  \n12.  \n13.  \n14.  \n15.  \n16.  \n17.  \n18.  \n19.  \n20.  \nMath  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n6  \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) 30b + 24 |  | Answers\u003Cbr>1. 6(5b + 4) |\n| --- | --- | --- |\n| 2) 5 + 5 + 9c + 10c |  | 2. 19c+10 |\n| 3) | 10 + 16d | 3. 2(5 + 8d) |\n| 4) | 9 + 2e + 8 + 7e | 4.  9e+17  |\n| 5) | 24f + 48 | 5. 24(1f + 2) |\n| 6) | g + g + g + g + g + g + g + g + g | 6. 9g |\n| 7) | 8 + 7h + 8 + 7h | 7. 14h+16 |\n| 8) | 90i + 80 | 8.  10(9i + 8)  |\n| 9) | 6(8 + 7j) | 9. 48 + 42j |\n| 10) | 10 + 9k + 7k + 2 | 10. 16k+12 |\n| 11) | 6 + 8m + 8 + 6m | 11. 14m+14 |\n| 12) | 5n + 5 + 4n + 3 | 12. 9n+8 |\n| 13) | 6(4p + 7) | 13. 24p + 42 |\n| 14) | 4(4r + 10) | 14. 16r + 40 |\n| 15) | 5(6t + 5) | 15. 30t + 25 |\n| 16) | 2(4u + 6) |  |\n| 17) | 10(7v + 4) | 16.  8u + 12  |\n| 18) | 2(10w + 7) | 17.  70v + 40  |\n| 19) | 4(5 + 7y) | 18.  20w + 14  |\n| 20) | 2z + 2z + 2 + 5 | 19.  20 + 28y \u003Cbr>20. 4z+7 |\n\nMath  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n6  \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.  \n14h+16 16k+12 9e+17 48 + 42j  \n9n+8 6(5b + 4) 19c+10 14m+14  \n10(9i + 8) 24(1f + 2) 2(5 + 8d) 9g  \n24p + 42  \n1) 30b + 24  \n2) 5 + 5 + 9c + 10c  \n3) 10 + 16d  \n4) 9 + 2e + 8 + 7e  \n5) 24f + 48  \n6) g + g + g + g + g + g + g + g + g  \n7) 8 + 7h + 8 + 7h  \n8) 90i + 80  \n9) 6(8 + 7j)  \n10) 10 + 9k + 7k + 2  \n11) 6 + 8m + 8 + 6m  \n12) 5n + 5 + 4n + 3  \n13) 6(4p + 7)  \nAnswers  \n1.  \n2.  \n3.  \n4.  \n5.  \n6.  \n7.  \n8.  \n9.  \n10.  \n11.  \n12.  \n13.  \nMath  \nModified  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n6  \n1-10  \n11-13  \n92  \n15  \n85 77 8 0  \n69 62 54 46 38 31 23","cbCaifFHwATDkOuJ","https://ap.wps.com/l/cbCaifFHwATDkOuJ","pdf",44623,"English","# Apply the distributive property to produce an equivalent expression\n## Problem set (1-20)\n## Answer key","[{\"question\":\"What does the distributive property mean in these problems?\",\"answer\":\"Use the distributive property to transform an expression by distributing multiplication over addition, producing an equivalent expression.\"},{\"question\":\"How should you solve an item like 6(8 + 7j)?\",\"answer\":\"Multiply 6 by each term inside the parentheses: 6·8 and 6·7j, then combine the results into an equivalent expression.\"},{\"question\":\"What information does the answer key provide?\",\"answer\":\"For each numbered problem, the answer key lists the equivalent distributed expression so students can check their work.\"}]","Applying Properties of Operations - Answer Key | PDF"]