[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-400039-105":3,"detail-sidebar-cat-0-en-105":85,"doc-detail-400039-en":134},{"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":78,"head_meta":80,"extra_data":82,"updated_unix":84},105,"en","tachs-math-cram-sheet-math-number-basics","TACHS MATH CRAM SHEET - math number basics","","TACHS MATH CRAM SHEET for rapid review of core middle-school math topics. Covers number systems and relationships among natural, whole, integer, rational, real, and complex numbers, including definitions, examples, and subset reasoning. Includes place value and metric conversion rules, distance, capacity, weight, and temperature conversions. Summarizes factors and greatest common factor, least common multiple, and multiple patterns. Provides fraction types, fraction operations and simplification steps, and ratio and proportion setups for solving missing values.",{"@graph":14,"@context":77},[15,34,56],{"@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/tachs-math-cram-sheet-math-number-basics/400039/",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/tachs-math-cram-sheet-math-number-basics/400039.png","ImageObject",300,407,{"name":42,"@type":43},"pop out","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-11","2026-09-27",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",9,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69,73],{"name":60,"@type":61,"acceptedAnswer":62},"What are the major number systems covered, and how are they related?","Question",{"text":63,"@type":64},"The sheet defines natural, whole, integers, rational, real, and complex numbers and notes that each system is a subset of another (e.g., rational numbers are real numbers).","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you convert units using the metric system on this sheet?",{"text":68,"@type":64},"Metric conversions are based on powers of 10: to convert to a larger unit divide by the appropriate 10-based base, and to convert to a smaller unit multiply by that base. It also provides key examples and equivalences.",{"name":70,"@type":61,"acceptedAnswer":71},"How are fractions added or subtracted when denominators differ?",{"text":72,"@type":64},"Change to equivalent fractions with common denominators using a scale factor, then add or subtract using the same-denominator rules (add/subtract numerators, keep the denominator, and simplify).",{"name":74,"@type":61,"acceptedAnswer":75},"How do ratios and proportions are used to find an unknown value?",{"text":76,"@type":64},"The sheet shows ratio relationships and proportion setup, such as part-to-part and part-to-whole comparisons, then uses proportional equivalence to solve for the missing quantity.","https://schema.org",{"og:url":32,"og:type":79,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":81,"canonical":32},"index,follow",{"doc_id":83,"site_id":7},400039,1790716469,{"code":4,"msg":86,"data":87},"success",[88,92,96,99,104,109,114,119,123,126,130],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":97,"slug":98},70,"exam",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},5,"Comic",60,"comic",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},6,"Technology",50,"technology",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},7,"Healthcare",40,"healthcare",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},8,"Research & Report",30,"research-report",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":121,"slug":122},"Religion & Spirituality",20,"religion-spirituality",{"id":121,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":121,"slug":125},"World Cup","world-cup",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":127,"slug":129},10,"Lifestyle","lifestyle",{"id":131,"doc_module":4,"doc_module_name":25,"category_name":132,"show_sort_weight":100,"slug":133},19,"General","general",{"code":4,"msg":86,"data":135},{"doc_id":83,"user_id":136,"nickname":42,"user_avatar":137,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":138,"file_id":139,"file_url":140,"file_type":141,"file_size":142,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":143,"language":144,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":145,"faqs":146,"seo_title":147,"seo_description":12,"update_tm":148,"read_time":149,"preview_page_count":4},962090760408,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","TACHS MATH CRAM SHEET  \nNUMBER BASICS  \nRational Numbers  \nIntegers  \nWhole Numbers  \nNatural Numbers  \nEach number system is a subset another.  \nA rational number is also a real number, areal number is also a complex number, etc.  \n\n| Number Class | Definition | Examples |\n| --- | --- | --- |\n| Natural Numbers | The number 1 or any number obtained by adding 1 to it one or more times. | 1, 2, 3, 4, 5,   |\n| Whole Numbers | Whole numbers do not include fractions or decimal parts an`d is a positive integer or zero. | 0, 1, 2, 3, 4, 5,   |\n| Integers | Any whole number or its opposite. |   , −5, −4, −3, −2,−1, 0, 1, 2, 3, 4, 5,   |\n| Rational Numbers | A number can that be expressed as a ratio or fraction. | • 2/10 .6\u003Cbr>• 3/10\u003Cbr>• 2.957 |\n| Real Numbers | A number that has no imaginary part. All real numbers can be located on a number line. | • −92\u003Cbr>• 5/9\u003Cbr>• √2 |\n| Complex Numbers | a + bi where a and b are real numbers and i (imaginary number) is a formal square root of −1 (i= √-1, i2 = -1) | • -1 + 2i\u003Cbr>• 7-9i\u003Cbr>• -6i |\n\nPlace Value  \n\n| Place | thousands | hundreds | tens | ones | tenths | hundredths | thousandths |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| Value | 1,000 | 100 | 10 | 1 | 0.1 | 0.01 | 0.001 |\n\nMETRIC CONVERSIONS  \nMetric units are multiples of 10s. To convert to a larger unit, divide numbers by base of 10s. To convert to a smaller unit, multiply numbers by base of 10s.  \nKing  \nkilo  \n1,000.0  \n(103)  \nHenry  \nhecto  \nDied  \ndeca  \n100.0 10.0  \n(102) (101)  \n1.0 0.1 0.01 0.001  \n(100) (10-1) (10-2) (10-3)  \nlarger units smaller units  \nTACHS MATH CRAM SHEET  \nDISTANCE  \n1 ft = 12 in  \n1 in = 2.54 cm  \n1 yd = 3 ft  \n1 m ≈ 3.28 ft ≈ 1.09 yd  \n1 mi = 5,280 ft ≈ 1.61 km  \n\n| \u003Cbr>CAPACITY\u003Cbr>1 oz ≈ 28.35 g\u003Cbr>1 cup = 8 oz\u003Cbr>2 cups = 1 pint\u003Cbr>2 pints = 1 quart\u003Cbr>4 quarts= 1 gallon\u003Cbr>1 gallon ≈ 3.8 L | \u003Cbr>WEIGHT\u003Cbr>1 lb = 16 oz\u003Cbr>1 kg ≈ 2.2 lb ≈ 35.27 oz\u003Cbr>1 t = 2,000 lb ≈ 907.19 kg |\n| --- | --- |\n\nTEMPERATURE  \n°F = ~~ ~~95~~ ~~ (°C) + 32  \n°C = ~~ ~~95~~ ~~ (°F)– 32  \nFACTORS  \nWhat is a factor?  \nA whole number is a factor of another whole number if it divides it evenly.  \n\n| Greatest common factor (GCF)\u003Cbr>The greatest common factor of two or more whole numbers is the largest number that is a factor of them all. | 7: 1, 7 \u003Cbr>28: 1, 2, 7, 14 \u003Cbr>GCF: 7 | Factor Tree\u003Cbr>28\u003Cbr>2 14\u003Cbr>2 7\u003Cbr>|\n| --- | --- | --- |\n\nMULTIPLES  \nWhat is a multiple?  \nA whole number is a multiple if it is the result of multiplying another whole number by an integer.  \n\n| Least Common Multiple (LCM)\u003Cbr>The least common multiple of two or more whole numbers is the smallest number that is a multiple of them all. | 3: 3, 6, 9, 12, 15, 18, 21, 24\u003Cbr>7: 7, 14, 21, 28, 35, 42, 49, 56\u003Cbr>LCM: 21 |\n| --- | --- |\n\nMultiples of 3  \n\n| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | multiplication |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 3 × 1 = 3 |\n| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 3 × 2 = 6 |\n| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 3 × 3 = 9 |\n| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 3 × 4 = 12 |\n| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 3 × 5 = 15 |\n| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 3 × 6 = 18 |\n| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 3 × 7 = 21 |\n| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 3 × 8 = 24 |\n\nMultiples of 7  \n\n| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | multiplication |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 7 × 1 = 7 |\n| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 7 × 2 = 14 |\n| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 7 × 3 = 21 |\n| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 7 × 4 = 28 |\n| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 7 × 5 = 35 |\n| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 7 × 6 = 42 |\n| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 7 × 7 = 49 |\n| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 7 × 8 = 56 |\n\nTACHS MATH CRAM SHEET  \nFRACTIONS  \n\n| Proper Fraction\u003Cbr> 1","cbCaik4DvadP2Nan","https://ap.wps.com/l/cbCaik4DvadP2Nan","pdf",4274010,15,"English","# Number Basics\n## Place Value\n## Metric Conversions\n## Distance, Capacity, Weight, Temperature\n# Factors, GCF, and Factor Trees\n# Multiples, LCM, and Multiplication Tables\n# Fractions\n## Adding/Subtracting\n## Multiplying/Dividing\n## Mixed Numbers\n# Ratios and Proportions","[{\"question\":\"What are the major number systems covered, and how are they related?\",\"answer\":\"The sheet defines natural, whole, integers, rational, real, and complex numbers and notes that each system is a subset of another (e.g., rational numbers are real numbers).\"},{\"question\":\"How do you convert units using the metric system on this sheet?\",\"answer\":\"Metric conversions are based on powers of 10: to convert to a larger unit divide by the appropriate 10-based base, and to convert to a smaller unit multiply by that base. It also provides key examples and equivalences.\"},{\"question\":\"How are fractions added or subtracted when denominators differ?\",\"answer\":\"Change to equivalent fractions with common denominators using a scale factor, then add or subtract using the same-denominator rules (add/subtract numerators, keep the denominator, and simplify).\"},{\"question\":\"How do ratios and proportions are used to find an unknown value?\",\"answer\":\"The sheet shows ratio relationships and proportion setup, such as part-to-part and part-to-whole comparisons, then uses proportional equivalence to solve for the missing quantity.\"}]","TACHS MATH CRAM SHEET - math number basics | PDF",1790506816,38]