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# Class Note for MATH 1300 with Professor Flagg at UH 2

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This 9 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 21 views.

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Date Created: 02/06/15
Math 1300 Chapter 1 The Real Number Field Part 2 Rational and Irrational Numbers Using only integers we do not have a number to describe dividing one whole pie into four equal pieces The rational numbers were created to solve this problem A RATIONAL NUMBER is a number that can be represented as a ratio of two integers a E for any integer a and any nonzero integer b Note that a over b and a divided by b mean the same thing solving the division problem is built into the de nition of a rational number Note also that every integer is also a rational number since aninteger z can also be Z expressed as I z dividedby 1 Now that we know what a rational number is how do we add subtract multiply and divide them ADDITION and SUBTRACTION Adding and Subtracting Fractions 0 Find a least common denominator using method for LCM 0 Change the numerators of each fraction 0 Add or subtract the numerators keep denominator unchanged O Reduce fxagnpleszi a h 239 L 2 r 39FE 5 54 54 54 2 1123 LL 1 2x2 i s E 9X3 4 2397 17x2 59 LcM swim waxcw 26x3 53 2 7 3gtlt37lt3gtlt3fJ LCM 0239 x 3 airmail 1 4 0 Al39gIQSVPOUJE l 2111 9391 5 105 Alma ET TB t 73 wrath LCM gngx g QLCM 5X33 SS 32 3gtlt3gtlt33 L u3933 1 3935 15 153 3 13 2 7 27x5 35 MULTIPLICATION and DIVISION Multiplying Fractions 0 Simplify the fractions if not in lowest terms 0 Multiply the numerators of the fractions to get the new numerator 0 Multiply the denominators of the fractions to get the new denominator Examples LLXZ h 2 53 h F 5X2 0 SgtltZ 5 8 U qg 39i Uf mcquotm a VQ Dividing Fractions 0 Multiply the rst fraction by the reciprocal of the second f 3 X 7 3x7 Z7 392777 3 a 2ng gxax Ll 4x2 2k hi L Qty X ll i T 7 9 7x IN I x J 9x2 9x2 9 S POWERS 7 SHORTHAND for multiplication and division De ne 1 r O a01 W W 45 Pouv 21930 2 2 7 7 231x2x2 anaaaa ggmm quot 3X3x3x3x3x323 aim i 1 sLcw no all 92 E 3 1 TheSe powc pubis WonQ LOM or W M la oi cs like 3 allac39 35 at 3 5 2 gtlt22 2 33 3331 3 CK Q539amp4 ampZ 53123P27 Camp Nodjrl m 313J U5 Medas 3 Egem Acs are C C pmgmm ISSUES 68 2 522c z b 39b 3CciC L 7 395 391 5 3 E735 JZZGZ39E a 0 iffy 1 a gg 36 7 5 P t T Z l 7 of J g 744 0amp6 1 N S 2 j j w 52 I lt 336225 5 NH Mon W y o 0 O39HLVJ S 390 39 op gradw 01449 44x31 was Me 049 erm on 90 or as Hom Itave Ck Y LA 1 s place 1e 3 Q BXW 1223 3y 2 2 Ig 2 1 39125 b3y1551 3 Byz g Different Ways of Expressing a Rational Number Proper and Improper Fractions PROPER FRACTION IMPROPER FRACTION To WWW Top W 5 57 3 3 7 5 23 3 quotZZ MiZdNurnbers21 61101 3l f 2 3 2 4 A L CL 1 2 3 2 I 1 Q3 23 TJ 3 r 1L3 31 jr3 I 032 g 0 1 7 Z t 9 Qquot 7 91 7 397 r 7 I l i A Q39i39f 3 Li T KAHOMAL Norway KNCLUDE InfED NUMBEK Decimals 7 Fractions meet the base ten number system 0 w l 03910110 0 efmmakmj O t 5939ng 034532 ac lamb 100000 E ATM0PM 0 A UMBEQS How do you turn a fraction into a decimal Divide Witl long division I 7 E o 9 25 3WD 25 t a 98 539 0 1 a g g 0 3 3 3 033333 L5 3 o o To iiiii g iTa bMBERsu b Notation Jj Or 2 Q 3 Q up 4LFLF4LF a 5 225555 975 a 5 s5 An example of a decimal number that goes on forever but does not repeat L WW2444444 Nat Kama a7 Noun VGme Order and Rational Numbers Z The expression x lt y is equivalent to saying y 7 x gt 0 How to compare two rational numbers 1 In Decimal Form 04443252 p 04433324 3440 lt 3442 10l3 lt 10390 0332 lt 10004 BIGGEL if gt 2 C 011394 2 In Fraction Form a Express both numbers as fractions 7 proper or improper b Find the common denominator c Express both fractions as equivalent fractions over the common denominator a d Compare the nurnerators lt if and only if a lt b C C Practice 13 lt 1 N 7 13 I 8 3 M5q X7 41 LCM 5 3X3 w gQ Lc g3 3 7 7x13 3 a 3 33 j L ii 3 1 5 33 g f 3 33 1739 411 lt 3 v 30 4 2 2 5 I 16 LCM OLQMQS O T395 46 32914quot 05 35 33 1 0 W v fr 0 Summary We now have the rational num ers and we can perform all four operations with them and get a rational number answer So we have all the numbers we need OR DO WE Problem 1 Given a square with sides of length one inch how long is the diagonal 1 7 1 1 I I gtlt fgt gtlt a Problem 2 Find the ratio of the circumference of a circle to its diameter Q C 7ramp Neither of there two problems have answers that are rational numbers We need more numbers to describe REAL PHYSICAL LENGTHS Irrational Numbers are real numbers real points on the number line that CANNOT be expressed as a ratio of two integers fraction Examples pi the square root of2 We Will work With square roots in this class Other classes Will introduce you to other irrational numbers N Simplifying Radicals F M M N I4 iC LUE 5 W M w r u ois unvul N l R A fr a nca m Note Whenthereisn tanumber fornitmeans there sreallya2there I g I m Examples a 1 8100 2 39 L g0 IO 9 f O 3 L 4 x4 K 5 zxfo g 3 WW gt Alec J TrW q o 0 3J5 44m QKGLf 5amp1 igg ang X X 6Zlt9 1l if 9 9 65 6 a9 91 glx lx 39939 Kirk posiHVe W m s erHOMJL

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