[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-497828-105":59,"doc-detail-497828-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","numerical-reasoning-cheat-sheet-quick-reference","Numerical Reasoning Cheat Sheet - Quick Reference","","Numerical reasoning cheat sheet providing practical shortcuts for fractions, decimals, and percentages. Includes rules for comparing fractions via cross-multiplication, dividing by a fraction using the inverse, and calculating common percentage values by shifting decimals. Covers reversing percentage changes for price reductions and increases, conversion between decimals and percents, number series patterns, and word problem essentials such as work rate, averages, distance, ratios, and profit. Also provides multiplication/division tactics, rounding estimates, and guidance to skip overly time-consuming questions.",{"@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/numerical-reasoning-cheat-sheet-quick-reference/497828/",{"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/numerical-reasoning-cheat-sheet-quick-reference/497828.png","ImageObject",300,407,{"name":92,"@type":93},"Theodore","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-25","2026-10-02",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you compare two fractions quickly?","Question",{"text":112,"@type":113},"Compare by cross-multiplying: multiply the numerator of each fraction by the opposite denominator and compare the resulting products.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the shortcut to find 1% or 10%?",{"text":117,"@type":113},"Find 1% by moving the decimal point left twice; find 10% by moving the decimal point left once (e.g., 10% of 180 is 18).",{"name":119,"@type":110,"acceptedAnswer":120},"How are ratio questions handled in this cheat sheet?",{"text":121,"@type":113},"Treat 3:2 as 3/2 and count total ratio units, then compute one unit value from the given total (e.g., if 24 boys equals 3 units, one unit is 8, so girls are 8×2=16).","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},497828,1791635560,{"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":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"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":24,"preview_page_count":4},7971461740886,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","12minprep’s Numerical Reasoning Cheat Sheet  \n\n| Fraction | 1/2 | 1/3 | 2/3 | 1/4 | 1/5 | 1/6 | 1/7 | 1/8 | 1/9 | 1/10 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| Decimal | 0.5 | 0.333 | 0.666 | 0.25 | 0.2 | 0.166 | 0.142 | 0.125 | 0.111 | 0.1 |\n| Percent | 50% | 33.33% | 66.66% | 25% | 20% | 16.66% | 14.2% | 12.5% | 11.1% | 10% |\n\nFractions  \n• Compare two fractions by cross-multiplying: 􀮺􀮻 􀝒􀝏 􀮼􀮽 is 􀜣 ∗ 􀜦 􀝒􀝏 􀜤 ∗ 􀜥  \n• Divide by fraction = multiply by inverse (1/(1/3) = 1x3) Percentages (Percent = value/100)  \n• Find 1%: move decimal point left twice (1% of 350 is 3 .5)  \n• Find 10%: move decimal point left once (10% of 180 is 18)  \nExample: 11% of 840: 10% is 84. 1% is 8.4. 84+8 .4=92 .4  \n• Reverse % for price reduction:  \nOriginal price = newwhat’psrilceeft (shoes cost $120 after 20% off, the original price is 120/0.8=$150)  \n• Reverse % for price increase:  \nOriginal price = whnatewwapsraicdeded ( shoes cost $120 after 20% up, original price is 120/1.2=$100)  \n• Quick tricks: 20% of 30 is 2x3; 25% of 40 is 2.5x4; 35% of 20 = 20% of 35; and so on…  \nConversions  \nDecimal to percent: multiply by 100 (0 .12 = 12%); Percent to decimal: divide by 100 (3 .7% = 0 .037)  \nNumber series  \n• Descending: 223 ,199, 175,   (-24)  \n• Two series, in odd and even places: 1, 5, 3, 10, 5, 20,• Incremental increase 1, 3, 6, 10, 15, 21,(+2, +3, +4,…)  \n• Pairs of operations 6, 12, 7, 14, 9, 18, (*2, -5)  \n• Changing operations 8, 10, 8, 4, 8, (+2,-2,/2,*2)  \n[12minprep.com](12minprep.com)  \n• Two first terms add/multiply up to give the third 12, 3, 15, 4, 19, (12+3=15, 15+4=19)  \n• Powers of two/three/four 9, 16, 25, 36,(3², 4², 5²,…)  \nWord problems  \n• Work rate = (job to be done)/(time unit): 1 house/12 hours = 1/12  \n• Average = (Sum of values)/(\\# of values)  \n• Distance = Speed *Time  \n• Ratios. 3:2 is like 3/2 . Order matters! count total ratio units to find the value of one unit. Example: 3:2 is ratio of boys to girls in class, there are 24 boys. How many girls? 24 boys = 3 ratio units. 1 ratio unit 24/3= 8. Therefore, girls are 8*2=16 .  \n• Profit = Revenue-Cost  \nMultiplication/division shortcuts  \n• Multiplying two-digit numbers: break down one number into components as follows: 24*12 = 24* (10+2) = 240+48 = 288  \n• Rounding/Estimating: round a number to the closest 0 and/or 5:  \n35x48 ~ 35x50; 27x42 ~ 25x40; 1460/30~1500/30  \n• Ignoring 0s when multiplying/dividing:  \n35x40=35x4 and add the 0 when done.  \n840/7=84/7 and add the 0 when done.  \nTime-consuming questions are (usually) not worth your time  \nIs it too lengthy? Are there too many details and operations involved?  \nSKIP IT!  \n(best to try this out and see if it works for you)  \n[12minprep.com](12minprep.com)","cbCais077nGLq4lV","https://ap.wps.com/l/cbCais077nGLq4lV","pdf",208409,"English","# Fractions\n## Percentages\n# Conversions\n# Number Series\n# Word Problems\n# Multiplication/Division Shortcuts\n## Estimation and Rounding\n## Time Management Tips","[{\"question\":\"How do you compare two fractions quickly?\",\"answer\":\"Compare by cross-multiplying: multiply the numerator of each fraction by the opposite denominator and compare the resulting products.\"},{\"question\":\"What is the shortcut to find 1% or 10%?\",\"answer\":\"Find 1% by moving the decimal point left twice; find 10% by moving the decimal point left once (e.g., 10% of 180 is 18).\"},{\"question\":\"How are ratio questions handled in this cheat sheet?\",\"answer\":\"Treat 3:2 as 3/2 and count total ratio units, then compute one unit value from the given total (e.g., if 24 boys equals 3 units, one unit is 8, so girls are 8×2=16).\"}]","Numerical Reasoning Cheat Sheet - Quick Reference | PDF",1790967649]