[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-480388-105":59,"doc-detail-480388-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","multiplication-of-rational-numbers-with-commutative-property","Multiplication of Rational Numbers with Commutative Property","","Worksheets and answer key for practicing multiplication of rational numbers using the commutative property. Problems require evaluating products of fractions and negative rational factors, then comparing results based on rearranging the order of multiplication. The answer key provides stepwise factorizations and final numeric solutions for each problem, supporting checking and targeted remediation.",{"@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/multiplication-of-rational-numbers-with-commutative-property/480388/",{"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/multiplication-of-rational-numbers-with-commutative-property/480388.png","ImageObject",300,407,{"name":92,"@type":93},"Ben ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","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 skill do these problems practice?","Question",{"text":112,"@type":113},"They practice multiplying rational numbers, including products with negative fractions, using the commutative property to reorder factors.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are answers provided in the document?",{"text":117,"@type":113},"An answer key includes worked rearrangements and the final simplified results for each numbered problem.",{"name":119,"@type":110,"acceptedAnswer":120},"Do all problems follow the same format?",{"text":121,"@type":113},"Yes. Each item asks to solve a multiplication expression of rational numbers, then match it to its corresponding final answer in the key.","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},480388,1792922379,{"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":143,"read_time":39},2336478951081,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Multiplication of Rational Numbers with Commutative Property Name:  \n\n| Solve each problem.\u003Cbr>1) 4 × 1⁄7 × 4 × -1⁄2 × 21 =\u003Cbr>3) 4 × 1⁄5 × 21 × -3⁄7 × 15 =\u003Cbr>5) 1⁄2 × 6 × 4 =\u003Cbr>7) 5 × -3⁄5 × 21 × 3⁄7 × 10 = | 2)\u003Cbr>4)\u003Cbr>6)\u003Cbr>8) | 9 × 1⁄7 × 9 × -1⁄3 × 14 =\u003Cbr>3⁄5 × 6 × -2⁄3 × 10 × 2 =\u003Cbr>-6⁄7 × 4 × -1⁄2 × 21 × 6 =\u003Cbr>2⁄3 × 6 × 6 = |  |  |  |  | Answers\u003Cbr>1.  \u003Cbr>2.  \u003Cbr>3.  \u003Cbr>4.  \u003Cbr>5.  \u003Cbr>6.  \u003Cbr>7.  \u003Cbr>8.  \u003Cbr>9.  \u003Cbr>10.   |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 9) 1⁄5 × 5 × 15 = | 10) | -3⁄5 × 4 × -1⁄2 × 15 × 10 = |  |  |  |  |  |  |  |  |  |  |  |\n| 1-10 |  |  | 90 | 80 | 70 | 60 |  | 50 | 40 | 30 | 20 | 10 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 7)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 7)[ 7](Math www.CommonCoreSheets.com 7)  \n Multiplication of Rational Numbers with Commutative Property Name: Answer Key  \n\n| Solve each problem.\u003Cbr>1) 4 × 1⁄7 × 4 × -1⁄2 × 21 = 4 × (-1⁄2 × 4) × ( 1⁄7 × 21)\u003Cbr>4 × -2 × 3\u003Cbr>3) 4 × 1⁄5 × 21 × -3⁄7 × 15 = 4 × (-3⁄7 × 21) × ( 1⁄5 × 15)\u003Cbr>4 × -9 × 3\u003Cbr>5) 1⁄2 × 6 × 4 =( 1⁄2 × 4) × 6\u003Cbr>2 × 6\u003Cbr>7) 5 × -3⁄5 × 21 × 3⁄7 × 10 = 5 × (3⁄7 × 21) × (-3⁄5 × 10)\u003Cbr>5 × 9 × -6 | 2)\u003Cbr>4)\u003Cbr>6)\u003Cbr>8) | 9 × 1⁄7 × 9 × -1⁄3 × 14 = 9 × (-1⁄3 × 9) × ( 1⁄7 × 14)\u003Cbr>9 × -3 × 2\u003Cbr>3⁄5 × 6 × -2⁄3 × 10 × 2 =(-2⁄3 × 6) × (3⁄5 × 10) × 2\u003Cbr>-4 × 6 × 2\u003Cbr>-6⁄7 × 4 × -1⁄2 × 21 × 6 =(-1⁄2 × 4) × (-6⁄7 × 21) × 6\u003Cbr>-2 × -18 × 6\u003Cbr>2⁄3 × 6 × 6 =(2⁄3 × 6) × 6\u003Cbr>4 × 6 |  |  |  |  | 1.\u003Cbr>2.\u003Cbr>3.\u003Cbr>4.\u003Cbr>5.\u003Cbr>6.\u003Cbr>7.\u003Cbr>8.\u003Cbr>9.\u003Cbr>10. |  | Answers\u003Cbr>-24 |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  | -54 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  | -108 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  | -48 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  | 12 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  | 216 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  | -270 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  | 24 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  | 15 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  | 180 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| 9) 1⁄5 × 5 × 15 =( 1⁄5 × 15) × 5\u003Cbr>3 × 5 | 10) | -3⁄5 × 4 × -1⁄2 × 15 × 10 =(-1⁄2 × 4) × (-3⁄5 × 15) × 10\u003Cbr>-2 × -9 × 10 |  |  |  |  |  |  |  |  |  |  |  |\n| 1-10 |  |  | 90 | 80 | 70 | 60 | 50 | 40 |  | 30 | 20 | 10 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 7)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 7)[ 7](Math www.CommonCoreSheets.com 7)  \n Multiplication of Rational Numbers with Commutative Property Name:  \n\n| Solve each problem. | Answers\u003Cbr>1.  \u003Cbr>2.  \u003Cbr>3.  \u003Cbr>4.  \u003Cbr>5.  \u003Cbr>6.   |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| -108 -48 216 -54\u003Cbr>-24 12 |  |  |  |  |  |  |  |\n| 1) 4 × 1⁄7 × 4 × -1⁄2 × 21 = 2) 9 × 1⁄7 × 9 × -1⁄3 × 14 =\u003Cbr>3) 4 × 1⁄5 × 21 × -3⁄7 × 15 = 4) 3⁄5 × 6 × -2⁄3 × 10 × 2 =\u003Cbr>5) 1⁄2 × 6 × 4 = 6) -6⁄7 × 4 × -1⁄2 × 21 × 6 = |  |  |  |  |  |  |  |\n| 1-6 |  | 83 | 67 | 50 | 33 | 17 | 0 |\n\nMath  \nModified  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n7","cbCaijxesYsVQVKj","https://ap.wps.com/l/cbCaijxesYsVQVKj","pdf",46060,"English","# Solve each problem\n## Practice set\n## Answer key solutions","[{\"question\":\"What skill do these problems practice?\",\"answer\":\"They practice multiplying rational numbers, including products with negative fractions, using the commutative property to reorder factors.\"},{\"question\":\"How are answers provided in the document?\",\"answer\":\"An answer key includes worked rearrangements and the final simplified results for each numbered problem.\"},{\"question\":\"Do all problems follow the same format?\",\"answer\":\"Yes. Each item asks to solve a multiplication expression of rational numbers, then match it to its corresponding final answer in the key.\"}]","Multiplication of Rational Numbers with Commutative Property | PDF",1790794907]