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An answer key provides simplified equivalents for each item.",{"@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/applying-properties-of-operations-answer-key/463712/",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/applying-properties-of-operations-answer-key/463712.png","ImageObject",300,407,{"name":42,"@type":43},"Patrick","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",5,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What does the distributive property require in these problems?","Question",{"text":63,"@type":64},"Rewrite expressions of the form a(b + c) as a·b + a·c to form an equivalent expression. The worksheet focuses on producing simplified sums that match the distributive expansion.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are repeated terms like f + f + f + f + f handled?",{"text":68,"@type":64},"Combine the repeated additions into a multiplication form (e.g., 5f) and keep it equivalent to the original sum.",{"name":70,"@type":61,"acceptedAnswer":71},"Are expressions with multiple like terms, such as 5 + 10i + 2i + 9, simplified by combining coefficients?",{"text":72,"@type":64},"Yes. Combine the like terms with the same variable (10i + 2i) into a single term (12i) while keeping the constants together.","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},463712,1790767003,{"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 & 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expression.\u003Cbr>1) 3(10 + 5b) |  |  |  |  |  |  |  | Answers\u003Cbr>1. |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 2) 2(9 + 2c) |  |  |  |  |  |  |  | 2. |  |  |  |  |  |  |\n| 3) 4(2 + 3d) |  |  |  |  |  |  |  | 3. |  |  |  |  |  |  |\n| 4) 5(8 + 4e) |  |  |  |  |  |  |  | 4.   |  |  |  |  |  |  |\n| 5) f + f + f + f + f |  |  |  |  |  |  |  | 5. |  |  |  |  |  |  |\n| 6) g + g + g + g + g + g + g + g + g |  |  |  |  |  |  |  | 6. |  |  |  |  |  |  |\n| 7) 36h + 12 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| 8) 5 + 10i + 2i + 9 |  |  |  |  |  |  |  | 7.   |  |  |  |  |  |  |\n| 9) 48 + 12j |  |  |  |  |  |  |  | 8.   |  |  |  |  |  |  |\n| 10) 3(3k + 8) |  |  |  |  |  |  |  | 9.   |  |  |  |  |  |  |\n| 11) 6(7 + 2m) |  |  |  |  |  |  |  | 10.   |  |  |  |  |  |  |\n| 12) 36n + 81 |  |  |  |  |  |  |  | 11.   |  |  |  |  |  |  |\n| 13) 2(8p + 3) |  |  |  |  |  |  |  | 12.   |  |  |  |  |  |  |\n| 14) 3(4r + 4) |  |  |  |  |  |  |  | 13.   |  |  |  |  |  |  |\n| 15) 90t + 40 |  |  |  |  |  |  |  | 14.   |  |  |  |  |  |  |\n| 16) 60u + 70 |  |  |  |  |  |  |  | 15.   |  |  |  |  |  |  |\n| 17) 72 + 72v |  |  |  |  |  |  |  | 16.   |  |  |  |  |  |  |\n| 18) 56w + 21 |  |  |  |  |  |  |  | 17.   |  |  |  |  |  |  |\n| 19) 70y + 63 |  |  |  |  |  |  |  | 18.   |  |  |  |  |  |  |\n| 20) 6 + 8 + 3z + 3z |  |  |  |  |  |  |  | 19.  \u003Cbr>20. |  |  |  |  |  |  |\n| \u003Cbr>Math | [www.CommonCoreSheets.com](www.CommonCoreSheets.com) | 1 | 1-10\u003Cbr>11-20 | 95 | 90 | 85 | 80 |  | 75 | 70 | 65 | 60 | 55 | 50 |\n|  |  |  |  | 45 | 40 | 35 | 30 |  | 25 | 20 | 15 | 10 | 5 | 0 |\n\nApplying Properties of Operations  \nName: Answer Key  \n\n| Apply the distributive property to produce an equivalent expression.\u003Cbr>1) 3(10 + 5b) |  | Answers\u003Cbr>1. 30 + 15b |\n| --- | --- | --- |\n| 2) | 2(9 + 2c) | 2. 18 + 4c |\n| 3) | 4(2 + 3d) | 3. 8 + 12d |\n| 4) | 5(8 + 4e) | 4. 40 + 20e |\n| 5) | f + f + f + f + f | 5. 5f |\n| 6) | g + g + g + g + g + g + g + g + g | 6. 9g |\n| 7) | 36h + 12 | 7. 12(3h + 1) |\n| 8) | 5 + 10i + 2i + 9 | 8. 12i+14 |\n| 9) | 48 + 12j | 9. 12(4 + 1j) |\n| 10) | 3(3k + 8) | 10. 9k + 24 |\n| 11) | 6(7 + 2m) | 11. 42 + 12m |\n| 12) | 36n + 81 |  |\n| 13) | 2(8p + 3) | 12.  9(4n + 9) \u003Cbr>13. 16p + 6 |\n| 14) | 3(4r + 4) | 14. 12r + 12 |\n| 15) | 90t + 40 |  |\n| 16) | 60u + 70 | 15.  10(9t + 4)  |\n| 17) | 72 + 72v | 16.  10(6u + 7)  |\n| 18) | 56w + 21 | 17.  72(1 + 1v)  |\n| 19) | 70y + 63 | 18.  7(8w + 3)  |\n| 20) | 6 + 8 + 3z + 3z | 19.  7(10y + 9) \u003Cbr>20. 6z+14 |\n\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  \nApplying Properties of Operations  \nName:  \nApply the distributive property to produce an equivalent expression.  \n8 + 12d 12(4 + 1j) 30 + 15b 9k + 24  \n16p + 6 42 + 12m 12i+14 9(4n + 9)  \n18 + 4c 9g 5f 12(3h + 1)  \n40 + 20e  \n1) 3(10 + 5b)  \n2) 2(9 + 2c)  \n3) 4(2 + 3d)  \n4) 5(8 + 4e)  \n5) f + f + f + f + f  \n6) g + g + g + g + g + g + g + g + g  \n7) 36h + 12  \n8) 5 + 10i + 2i + 9  \n9) 48 + 12j  \n10) 3(3k + 8)  \n11) 6(7 + 2m)  \n12) 36n + 81  \n13) 2(8p + 3)  \nAnswers  \n1.  \n2.  \n3.  \n4.  \n5.  \n6.  \n7.  \n8.  \n9.  \n10.  \n11.  \n12.  \n13.  \nMath  \nModified  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n1  \n1-10  \n11-13  \n92  \n15  \n85 77 8 0  \n69 62 54 46 38 31 23","cbCain4fmvGu2CQn","https://ap.wps.com/l/cbCain4fmvGu2CQn","pdf",44563,"English","# Apply the distributive property\n## Problems (1-20)\n## Answer key","[{\"question\":\"What does the distributive property require in these problems?\",\"answer\":\"Rewrite expressions of the form a(b + c) as a·b + a·c to form an equivalent expression. The worksheet focuses on producing simplified sums that match the distributive expansion.\"},{\"question\":\"How are repeated terms like f + f + f + f + f handled?\",\"answer\":\"Combine the repeated additions into a multiplication form (e.g., 5f) and keep it equivalent to the original sum.\"},{\"question\":\"Are expressions with multiple like terms, such as 5 + 10i + 2i + 9, simplified by combining coefficients?\",\"answer\":\"Yes. Combine the like terms with the same variable (10i + 2i) into a single term (12i) while keeping the constants together.\"}]","Applying Properties of Operations - Answer Key | PDF"]