[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-263912-105":59,"doc-detail-263912-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","ged-math-cram-sheet-math-number-systems-factors-ratios-and-more","GED Math Cram Sheet - Math Number Systems, Factors, Ratios, and More","","GED Math Cram Sheet provides a fast-reference review of core number concepts, including number classification (natural, whole, integers, rational, real, complex), relationships among number sets, and number lines. It summarizes absolute value, essential mathematical symbols, and lesser-known constants and set symbols. The guide also covers factors (GCF and factor trees), multiples (LCM and multiplication tables), ratios and simplified forms, scientific notation rules, exponent properties, and basic slope/linear equation ideas for GED practice.",{"@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/ged-math-cram-sheet-math-number-systems-factors-ratios-and-more/263912/",{"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/ged-math-cram-sheet-math-number-systems-factors-ratios-and-more/263912.png","ImageObject",300,407,{"name":92,"@type":93},"Margaret","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-27","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How are natural numbers, whole numbers, integers, and rational numbers related?","Question",{"text":113,"@type":114},"Each number system is a subset of another. Natural numbers are built from adding 1 repeatedly, whole numbers include 0, integers include opposites of whole numbers, and rational numbers can be written as a ratio or fraction.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What is the difference between GCF and LCM?",{"text":118,"@type":114},"The greatest common factor (GCF) is the largest number that divides all given whole numbers evenly. The least common multiple (LCM) is the smallest number that is a multiple of all given whole numbers.",{"name":120,"@type":111,"acceptedAnswer":121},"What are the key rules for simplifying scientific notation and exponents?",{"text":122,"@type":114},"Scientific notation uses a coefficient between 1 and 10 and moves the decimal to match the power of 10. Exponent rules include adding exponents when multiplying same bases, subtracting when dividing same bases, multiplying exponents for a power of a power, and using reciprocals for negative exponents.","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},263912,1789375417,{"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":44,"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":130,"read_time":144},137451207643,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","GED ® MATH CRAM SHEET  \nNUMBER CLASSIFICATION  \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 and 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\nNUMBER LINES  \n|2| |2|  \n-3 -2 -1 0 1 2 3  \nAbsolute Value  \nAbsolute value is the distance away from zero a number is on the number line. It is always positive and is written |x| .  \nFor example, the absolute value of 2 is written as |2|.  \nMATHEMATICAL SYMBOLS  \n\n| Phrase | Symbol |\n| --- | --- |\n| equal, is, was, will be, has, costs, gets to, is the same as, becomes | = |\n| times, of, multiplied by, product of, twice, doubles, halves, triples | × |\n| divided by, per, ratio of/to, out of | ÷ |\n| plus, added to, sum, combined, and, more than, totals of | + |\n| subtracted from, less than, decreased by, minus, difference between | − |\n| what, how much, original value, how many, a number, a variable | 􀀛, n, etc. |\n\nLesser Known Symbols  \nThe Golden Ratio: φ  \nInifinity: ∞  \nEuler’s Number: e Universal Quantifier: ∀  \nMembership Sign: ∈  \nGED ® MATH CRAM SHEET  \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\nRATIOS  \nRatios of Two Items  \n\n| Items | Ratio | Fraction | Written | Simplified Ratio |\n| --- | --- | --- | --- | --- |\n| 6 oranges, 8 apples | 6:8 | 6/8 | 6 oranges to 8 appl","cbCaio3oCwcNSkHJ","https://ap.wps.com/l/cbCaio3oCwcNSkHJ","pdf",3338826,"English","# Number Classification\n## Number Lines and Absolute Value\n## Mathematical Symbols and Constants\n# Factors and Multiples\n## Greatest Common Factor (GCF) and Factor Trees\n## Least Common Multiple (LCM) and Multiplication Tables\n# Ratios and Simplified Ratios\n# Scientific Notation\n# Rules of Exponents\n# Slope and Linear Equations","[{\"question\":\"How are natural numbers, whole numbers, integers, and rational numbers related?\",\"answer\":\"Each number system is a subset of another. Natural numbers are built from adding 1 repeatedly, whole numbers include 0, integers include opposites of whole numbers, and rational numbers can be written as a ratio or fraction.\"},{\"question\":\"What is the difference between GCF and LCM?\",\"answer\":\"The greatest common factor (GCF) is the largest number that divides all given whole numbers evenly. The least common multiple (LCM) is the smallest number that is a multiple of all given whole numbers.\"},{\"question\":\"What are the key rules for simplifying scientific notation and exponents?\",\"answer\":\"Scientific notation uses a coefficient between 1 and 10 and moves the decimal to match the power of 10. Exponent rules include adding exponents when multiplying same bases, subtracting when dividing same bases, multiplying exponents for a power of a power, and using reciprocals for negative exponents.\"}]","GED Math Cram Sheet - Math Number Systems, Factors, Ratios, and More | PDF",23]