[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-480379-105":59,"doc-detail-480379-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","","Worksheet practice focused on multiplying rational numbers using the commutative property. Each item rewrites a product to rearrange factors and group terms into easier combinations of numerators and denominators. Problems include both positive and negative rationals, requiring correct sign handling, simplification of fractions, and consistent factor reordering across multiple expressions. An answer key provides the final computed values for all listed 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includes an answer key that lists the final values for each problem.","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},480379,1792860492,{"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":29,"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) 7 × 1⁄7 × 15 × 1⁄5 × 14 =\u003Cbr>3) 2 × -1⁄2 × 9 × 1⁄3 × 4 =\u003Cbr>5) 4⁄5 × 21 × -5⁄7 × 10 × 8 =\u003Cbr>7) 1⁄2 × 21 × 5⁄7 × 4 × 5 = | 2)\u003Cbr>4)\u003Cbr>6)\u003Cbr>8) | 1⁄2 × 4 × 4 =\u003Cbr>8 × 1⁄5 × 9 × 2⁄3 × 10 =\u003Cbr>2⁄7 × 8 × 21 =\u003Cbr>6⁄7 × 15 × -3⁄5 × 14 × 7 = |  |  |  |  | 1.\u003Cbr>2.\u003Cbr>3.\u003Cbr>4.\u003Cbr>5.\u003Cbr>6.\u003Cbr>7.\u003Cbr>8.\u003Cbr>9.\u003Cbr>10. |  | Answers |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| 9) 3⁄5 × 10 × 10 = | 10) | -1⁄2 × 14 × -4⁄7 × 6 × 6 = |  |  |  |  |  |  |  |  |  |  |  |\n| 1-10 |  |  | 90 | 80 | 70 | 60 | 50 | 40 |  | 30 | 20 | 10 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 9)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 9)[ 9](Math www.CommonCoreSheets.com 9)  \n Multiplication of Rational Numbers with Commutative Property Name: Answer Key  \n\n| Solve each problem.\u003Cbr>1) 7 × 1⁄7 × 15 × 1⁄5 × 14 = 7 × ( 1⁄5 × 15) × ( 1⁄7 × 14)\u003Cbr>7 × 3 × 2\u003Cbr>3) 2 × -1⁄2 × 9 × 1⁄3 × 4 = 2 × ( 1⁄3 × 9) × (-1⁄2 × 4)\u003Cbr>2 × 3 × -2\u003Cbr>5) 4⁄5 × 21 × -5⁄7 × 10 × 8 =(-5⁄7 × 21) × (4⁄5 × 10) × 8\u003Cbr>-15 × 8 × 8\u003Cbr>7) 1⁄2 × 21 × 5⁄7 × 4 × 5 =( 5⁄7 × 21) × ( 1⁄2 × 4) × 5\u003Cbr>15 × 2 × 5 | 2)\u003Cbr>4)\u003Cbr>6)\u003Cbr>8) | 1⁄2 × 4 × 4 =( 1⁄2 × 4) × 4\u003Cbr>2 × 4\u003Cbr>8 × 1⁄5 × 9 × 2⁄3 × 10 = 8 × (2⁄3 × 9) × ( 1⁄5 × 10)\u003Cbr>8 × 6 × 2\u003Cbr>2⁄7 × 8 × 21 =(2⁄7 × 21) × 8\u003Cbr>6 × 8\u003Cbr>6⁄7 × 15 × -3⁄5 × 14 × 7 =(-3⁄5 × 15) × (6⁄7 × 14) × 7\u003Cbr>-9 × 12 × 7 |  |  |  |  | 1.\u003Cbr>2.\u003Cbr>3.\u003Cbr>4.\u003Cbr>5.\u003Cbr>6.\u003Cbr>7.\u003Cbr>8.\u003Cbr>9.\u003Cbr>10. |  | Answers\u003Cbr>42 |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  | 8 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  | -12 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  | 96 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  | -960 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  | 48 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  | 150 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  | -756 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  | 60 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  | 144 |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| 9) 3⁄5 × 10 × 10 =(3⁄5 × 10) × 10\u003Cbr>6 × 10 | 10) | -1⁄2 × 14 × -4⁄7 × 6 × 6 =(-4⁄7 × 14) × (-1⁄2 × 6) × 6\u003Cbr>-8 × -3 × 6 |  |  |  |  |  |  |  |  |  |  |  |\n| 1-10 |  |  | 90 | 80 | 70 | 60 | 50 | 40 |  | 30 | 20 | 10 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 9)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 9)[ 9](Math www.CommonCoreSheets.com 9)  \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| -960 96 48 42\u003Cbr>8 -12 |  |  |  |  |  |  |\n| 1) 7 × 1⁄7 × 15 × 1⁄5 × 14 = 2) 1⁄2 × 4 × 4 =\u003Cbr>3) 2 × -1⁄2 × 9 × 1⁄3 × 4 = 4) 8 × 1⁄5 × 9 × 2⁄3 × 10 =\u003Cbr>5) 4⁄5 × 21 × -5⁄7 × 10 × 8 = 6) 2⁄7 × 8 × 21 = |  |  |  |  |  |  |\n| 1-6 | 83 | 67 | 50 | 33 | 17 | 0 |\n\nMath  \nModified  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n9","cbCaipdJT9bnOR1E","https://ap.wps.com/l/cbCaipdJT9bnOR1E","pdf",46119,"English","# Solve each problem\n## Factor rearrangement using commutative property\n# Answers","[{\"question\":\"What property is used to simplify the rational number multiplication problems?\",\"answer\":\"The problems use the commutative property to rearrange factors in multiplication so the products can be grouped more conveniently.\"},{\"question\":\"How are negative rational numbers handled in these multiplications?\",\"answer\":\"Negative signs are treated according to multiplication rules; the final sign depends on the number of negative factors in each expression.\"},{\"question\":\"Where can the final results be found?\",\"answer\":\"The document includes an answer key that lists the final values for each problem.\"}]","Multiplication of Rational Numbers with Commutative Property | PDF",1790794892]