[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-460600-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-460600-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","numerical-reasoning-cheat-sheet-12minprep","Numerical Reasoning Cheat Sheet - 12minprep","","Numerical Reasoning Cheat Sheet by 12minprep consolidates essential quick methods for fractions, decimals, percentages, number series, and word problems. It includes cross-multiplication for comparing fractions, inverse-based fraction division, rapid mental techniques for finding 1% and 10%, and methods to reverse percentage price changes for discounts and markups. Conversions between decimals and percentages, along with letter-series mapping, are summarized. It also provides number-series patterns, core formula reminders like work rate, distance, average, ratio interpretation, profit, and multiplication/division shortcuts with estimating and skipping strategies.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/numerical-reasoning-cheat-sheet-12minprep/460600/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/numerical-reasoning-cheat-sheet-12minprep/460600.png","ImageObject",300,407,{"name":42,"@type":43},"Logic","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-30","2026-09-30",true,{"@type":52,"interactionType":53,"userInteractionCount":22},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"How do you compare two fractions quickly?","Question",{"text":62,"@type":63},"Use cross-multiplication: multiply the numerator of the first fraction by the denominator of the second, and vice versa, then compare the products.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What is the quickest way to calculate 1% and 10%?",{"text":67,"@type":63},"For 1%, move the decimal point left twice; for 10%, move the decimal point left once. The sheet gives examples using values like 350 and 180.",{"name":69,"@type":60,"acceptedAnswer":70},"How do you solve word problems involving ratios?",{"text":71,"@type":63},"Treat the ratio as units and order matters. Count total ratio units to find one unit’s value, then multiply by the required number of units to get the target amount.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},460600,1790758869,{"code":4,"msg":81,"data":82},"success",[83,87,91,94,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":92,"slug":93},70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},5,"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":95,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":22,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":26,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":79,"read_time":95,"preview_page_count":4},1099513958762,"https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253","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)  \nFor Letter Series:  \n\n| A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |\n\n[12minprep.com](12minprep.com)  \nNumber series  \n• Descending: 223 ,199, 175,   (-24)  \n• Two series, in odd and even places: 1, 5, 3, 10, 5, 20,  \n• 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• 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)","cbCaieDqwS3qGis7","https://ap.wps.com/l/cbCaieDqwS3qGis7","pdf",212750,"English","# Fractions and Percentages\n## Fractions comparisons and operations\n## Finding and reversing percentages\n## Decimal-percent conversions\n## Letter series mapping\n# Number Series\n## Descending and place-based patterns\n## Incremental increases and operation pairs\n## Operation changes and term relationships\n# Word Problems\n## Work rate, average, and distance\n## Ratios and profit\n# Multiplication/Division Shortcuts\n## Component multiplication and rounding\n## Ignoring zeros\n# Time Management Strategy\n## When to skip time-consuming questions","[{\"question\":\"How do you compare two fractions quickly?\",\"answer\":\"Use cross-multiplication: multiply the numerator of the first fraction by the denominator of the second, and vice versa, then compare the products.\"},{\"question\":\"What is the quickest way to calculate 1% and 10%?\",\"answer\":\"For 1%, move the decimal point left twice; for 10%, move the decimal point left once. The sheet gives examples using values like 350 and 180.\"},{\"question\":\"How do you solve word problems involving ratios?\",\"answer\":\"Treat the ratio as units and order matters. Count total ratio units to find one unit’s value, then multiply by the required number of units to get the target amount.\"}]","Numerical Reasoning Cheat Sheet - 12minprep | PDF"]