[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-359274-105":59,"doc-detail-359274-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","identifying-proportional-relationships-in-tables-a-proportional-relationships-worksheet","Identifying Proportional Relationships in Tables (A) - Proportional Relationships Worksheet","","Worksheet focused on identifying proportional relationships in tables by checking whether the ratio y ÷ x stays constant across every given pair of values. Directions emphasize computing y ÷ x for each table entry and marking whether the relationship is proportional. A first set of problems requires determining proportionality, while a second set asks students to confirm proportionality and find the constant of proportionality k when applicable, with a provided answer key.",{"@graph":69,"@context":123},[70,84,106],{"@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/identifying-proportional-relationships-in-tables-a-proportional-relationships-worksheet/359274/",{"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/identifying-proportional-relationships-in-tables-a-proportional-relationships-worksheet/359274.png","ImageObject",300,407,{"name":92,"@type":93},"Jacob","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-09-23",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you determine if a relationship is proportional in these tables?","Question",{"text":113,"@type":114},"Compute y ÷ x for every pair. If the ratio is the same constant for all pairs, the relationship is proportional; if any ratio differs, it is not proportional.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What is the constant of proportionality k in this worksheet?",{"text":118,"@type":114},"k is the constant value of the ratio y ÷ x when the relationship is proportional. In Part 2, k is explicitly requested for proportional cases.",{"name":120,"@type":111,"acceptedAnswer":121},"What steps are required for each problem?",{"text":122,"@type":114},"For each table, show work by dividing y by x for each pair, then answer whether it is proportional. In Part 2, also find k when the relationship is proportional.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},359274,1790639119,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":24,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},962084931830,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Name:  \n______________________________________  \nIdentifying Proportional Relationships in Tables (A)  \nRemember: A relationship is proportional if y/x is the same constant for every pair. Check every pair: divide y by x. If all answers match, it IS proportional. If any answer is different, it is NOT proportional. The constant ratio is k, the constant of proportionality.  \nDirections: For each table, determine whether the relationship is proportional. Show your work by  \ncomputing y ÷ x for each pair.  \nPart 1—Is it Proportional?  \n1.) Hours and miles biked  \n\n| Hours | 1 | 2 | 3 | 4 |\n| --- | --- | --- | --- | --- |\n| Miles Biked | 3 | 6 | 9 | 12 |\n\nShow work (y ÷ x):   Proportional?    \n2.) Gallons and cost ($)  \n\n| Gallons | 2 | 4 | 6 | 8 |\n| --- | --- | --- | --- | --- |\n| Cost | 6 | 12 | 18 | 24 |\n\nShow work (y ÷ x):   Proportional?    \n3.) Items and total cost  \n\n| Items | 1 | 2 | 3 | 4 |\n| --- | --- | --- | --- | --- |\n| Total Cost | $2 | $5 | $8 | $11 |\n\nShow work (y ÷ x):    \nProportional?    \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \n4.) Minutes and distance (km)  \n\n| Minutes | 3 | 6 | 9 | 12 |\n| --- | --- | --- | --- | --- |\n| Distance\u003Cbr>(km) | 5 | 10 | 15 | 20 |\n\nShow work (y ÷ x):   Proportional?    \n5.) Days and pages read  \n\n| Days | 1 | 2 | 3 | 4 |\n| --- | --- | --- | --- | --- |\n| Pages Read | 4 | 7 | 10 | 13 |\n\nShow work (y ÷ x):   Proportional?    \n6.) Cups sugar and cups flour  \n\n| Cups of\u003Cbr>Sugar | 2 | 4 | 6 | 8 |\n| --- | --- | --- | --- | --- |\n| Cups of\u003Cbr>Flour | 1 | 2 | 3 | 4 |\n\nShow work (y ÷ x):   Proportional?    \n7.) Seconds and heartbeats  \n\n| Seconds | 5 | 10 | 15 | 20 |\n| --- | --- | --- | --- | --- |\n| Number of\u003Cbr>Heartbeats | 2 | 4 | 6 | 8 |\n\nShow work (y ÷ x):    \nProportional?    \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \n8.) Meters and seconds  \n\n| Meters\u003Cbr>Traveled | 1 | 3 | 5 | 7 |\n| --- | --- | --- | --- | --- |\n| Seconds | 2 | 5 | 8 | 11 |\n\nShow work (y ÷ x):   Proportional?    \nPart 2—Proportional? If Yes, Find k  \n9.) Hours and earnings ($)  \n| Hours\u003Cbr>Worked | 1 | 2 | 3 | 4 |\n| --- | --- | --- | --- | --- |\n| Earnings | $6 | $12 | $18 | $24 |\n\nShow work (y ÷ x):   Proportional?    \n10.) Pounds and cost ($)  \n\n| Pounds | 2 | 4 | 6 | 8 |\n| --- | --- | --- | --- | --- |\n| Cost | $5 | 10 | 15 | 20 |\n\nShow work (y ÷ x):   Proportional?   If yes, k =    \n11.) Days and miles run  \n\n| Days | 1 | 2 | 3 | 4 |\n| --- | --- | --- | --- | --- |\n| Miles Run | 3 | 7 | 11 | 15 |\n\nShow work (y ÷ x):    \nProportional?   If yes, k =    \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \n12.) Feet and meters  \n\n| Feet | 4 | 8 | 12 | 16 |\n| --- | --- | --- | --- | --- |\n| Meters | 3 | 6 | 9 | 12 |\n\nShow work (y ÷ x):   Proportional?   If yes, k =    \n13.) Items and total price  \n\n| Items | 1 | 2 | 3 | 4 |\n| --- | --- | --- | --- | --- |\n| Total Price | $5 | $9 | $13 | $17 |\n\nShow work (y ÷ x):   Proportional?   If yes, k =    \n14.) Cups and batches  \n\n| Cups | 3 | 6 | 9 | 12 |\n| --- | --- | --- | --- | --- |\n| Batches | 4 | 8 | 12 | 16 |\n\nShow work (y ÷ x):   Proportional?   If yes, k =    \n15.) Miles and gallons  \n\n| Miles | 10 | 20 | 30 | 40 |\n| --- | --- | --- | --- | --- |\n| Gallons | 6 | 12 | 18 | 24 |\n\nShow work (y ÷ x):    \nProportional?   If yes, k =    \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \nANSWER KEY  \nPart 1:  \n1.) y÷x: 3 3 3 3 → Yes—y/x = 3 for all pairs  \n2.) y÷x: 3 3 3 3 → Yes—y/x = 3 for all pairs  \n3.) y÷x: 2 5/2 8/3 11/4 → No—y/x varies: 2, 5/2, 8/3, 11/4  \n4.) y÷x: 5/3 5/3 5/3 5/3 → Yes—y/","cbCaihzUqEkRONlA","https://ap.wps.com/l/cbCaihzUqEkRONlA","pdf",2115718,"English","# Part 1—Is it Proportional?\n## 1.) Hours and miles biked\n## 2.) Gallons and cost ($)\n## 3.) Items and total cost\n## 4.) Minutes and distance (km)\n## 5.) Days and pages read\n## 6.) Cups sugar and cups flour\n## 7.) Seconds and heartbeats\n## 8.) Meters and seconds\n# Part 2—Proportional? If Yes, Find k\n## 9.) Hours and earnings ($)\n## 10.) Pounds and cost ($)\n## 11.) Days and miles run\n## 12.) Feet and meters\n## 13.) Items and total price\n## 14.) Cups and batches\n## 15.) Miles and gallons","[{\"question\":\"How do you determine if a relationship is proportional in these tables?\",\"answer\":\"Compute y ÷ x for every pair. If the ratio is the same constant for all pairs, the relationship is proportional; if any ratio differs, it is not proportional.\"},{\"question\":\"What is the constant of proportionality k in this worksheet?\",\"answer\":\"k is the constant value of the ratio y ÷ x when the relationship is proportional. In Part 2, k is explicitly requested for proportional cases.\"},{\"question\":\"What steps are required for each problem?\",\"answer\":\"For each table, show work by dividing y by x for each pair, then answer whether it is proportional. In Part 2, also find k when the relationship is proportional.\"}]","Identifying Proportional Relationships in Tables (A) - Proportional Relationships Worksheet | PDF",1790136567,13]