[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-465929-105":59,"doc-detail-465929-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","proportional-ratios-quick-review-and-helpful-hints","Proportional Ratios - Quick Review and Helpful Hints","","Practice-focused math worksheet on proportional ratios, defining when two ratios are proportional and stating the equality relationship. Presents a quick method for solving proportions using cross-multiplication, including how to find a missing value by isolating a variable after multiplying cross-products. Includes a worked example and word problems about distance, scale/canvas enlargement, and cost using proportional reasoning. Concludes with answer keys and step-by-step explanations for each item.",{"@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/proportional-ratios-quick-review-and-helpful-hints/465929/",{"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/proportional-ratios-quick-review-and-helpful-hints/465929.png","ImageObject",300,407,{"name":92,"@type":93},"Mafia Boss","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},"When are two ratios proportional?","Question",{"text":112,"@type":113},"Two ratios are proportional when they are equal, like ab = cd in the proportion setup.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the fastest method to solve a proportion?",{"text":117,"@type":113},"Use cross-multiplication: multiply each numerator by the other denominator. Then divide to isolate the variable and get the missing value.",{"name":119,"@type":110,"acceptedAnswer":120},"How do you solve a missing value in a proportion when you have a variable?",{"text":121,"@type":113},"Cross-multiply to form an equation, then divide both sides to isolate the variable. The worksheet emphasizes isolating the variable after simplifying the cross-products.","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},465929,1790770278,{"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},962090760730,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Practice 􀀏 Progress 􀀏 Succeed | ASTB Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nProportional Ratios  \n\n| Name:   | D | ate:   | S | core:   / 18 |\n| --- | --- | --- | --- | --- |\n\nQuick Review and Helpful Hints  \nTwo ratios are proportional when they are equal, like ab = ~~ ~~cd . The fastest way to work with a proportion is cross-multiplication: multiply each numerator by the other denominator. To 􀀂nd a missing value, cross-multiply and then divide to isolate the variable.  \n▷ Example: Solve the proportion 34 = x20 . Work: Cross-multiply: 4 􀀁 x = 3 􀀁 20, which gives 4x = 60 . Divide both sides by 4: x = 604 = 15 . ⋆ Answer: x = 15  \n♦ Word Problems  \n15. A car travels 150 miles on 5 gallons of gas. At the same rate, how far can it travel on 8 gallons?  \n16. A photo 4 inches wide and 6 inches tall is enlarged so its width becomes 10 inches. Keeping the same proportions, what is the new height?  \n17. If 3 notebooks cost $7 .50, how much do 7 notebooks cost at the same price?  \n18. On a map, 2 inches represents 30 miles. How many miles do 5 inches represent?  \n\n|  |\n| --- |\n|  |\n\n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n1  \nScan Me  \nPractice 􀀏 Progress 􀀏 Succeed | ASTB Math  \nAnswer Keys  \n [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n1. x = 6 7. x = 5 13. x = 4  \n2. x = 10 8. x = 21 14. x = 25  \n3. x = 3 9. x = 8 15. 240 miles  \n4.  x = 5  10. x = 12 16. 15 inches  \n5.  x = 20  11. x = 10 17. $17 .50  \n6.  x = 12  12. x = 6 18. 75 miles  \nStep-by-Step Explanations  \n1. Start by naming the process: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is Multiply diagonally – equal fractions always have equal crossproducts: 3x = 2 􀀁 9 = 18, so x = 6 . So the 􀀂nal answer is x = 6 .  \n2. A good way to think about this is: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is Set the cross-products equal: 6x = 5 􀀁 12 = 60, then divide by 6 to 􀀂nd x = 10 . So the 􀀂nal answer is x = 10 .  \n3. Step by step: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is Even with x on top, the rule is the same: 12x = 4 􀀁 9 = 36, so x = 3 . So the 􀀂nal answer is x = 3 .  \n4. Take it one move at a time: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is When x sits in a denominator, cross-multiply anyway: 14x = 7 􀀁 10 = 70, giving x = 5 . So the 􀀂nal answer is x = 5 .  \n5. Start by naming the process: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is Cross-multiply and solve: 3x = 5 􀀁 12 = 60, so x = 20 . So the  \n􀀂nal answer is x = 20 .  \n6. A ","cbCair0MYWTIOO97","https://ap.wps.com/l/cbCair0MYWTIOO97","pdf",289390,"English","# Quick Review and Helpful Hints\n## Proportional Ratios\n## Example and Word Problems\n## Answer Keys\n## Step-by-Step Explanations","[{\"question\":\"When are two ratios proportional?\",\"answer\":\"Two ratios are proportional when they are equal, like ab = cd in the proportion setup.\"},{\"question\":\"What is the fastest method to solve a proportion?\",\"answer\":\"Use cross-multiplication: multiply each numerator by the other denominator. Then divide to isolate the variable and get the missing value.\"},{\"question\":\"How do you solve a missing value in a proportion when you have a variable?\",\"answer\":\"Cross-multiply to form an equation, then divide both sides to isolate the variable. The worksheet emphasizes isolating the variable after simplifying the cross-products.\"}]","Proportional Ratios - Quick Review and Helpful Hints | PDF"]