• Home
  • Download PDF
  • Order CD-ROM
  • Order in Print
Chapter 1 Mathematics and Units of Measurement
Decimal equivalents

Engineering Aid 3 - Beginning Structural engineering guide book
Page Navigation
  1  2  3    4    5    6    7  
books   are   the   result   of   the   mathematicians’ efforts  to  solve  mathematical  problems  with  ease. Methods of arriving at solutions may differ, but the end results or answers are always the same. These  different  approaches  to  mathematical problems  make  the  study  of  mathematics  more interesting,  either  by  individual  study  or  as  a group. You  can  supplement  your  study  of  mathe- matics  with  the  following  training  manuals: 1.  Mathematics,   Vol.   1,   N A V E D T R A 10069-D1 2.  Mathematics,  Vol.  2-A,   N A V E D T RA 10062 3.   Mathematics, Vol.  2-B,  N A V E D T RA 10063 4.  Mathematics,   Vol.   3,   N A V E D T R A 10073-A1 TYPES OF NUMBERS Positive and negative numbers belong to the class  called  REAL  NUMBERS.  Real  numbers  and imaginary numbers make up the number system in algebra. However, in this training manual, we will  deal  only  with  real  numbers  unless  otherwise indicated. A real number may be rational or irrational. The word rational  comes from the word  ratio. A number is rational if it can be expressed as the quotient,   or   ratio,    of  two  whole  numbers. Rational  numbers  include  fractions  like  2/7, whole  numbers  (integers),  and  radicals  if  the radical  is  removable.  Any  whole  number  is rational  because  it  could  be  expressed  as  a quotient with 1 as its denominator. For instance, 8 equals 8/1, which is the quotient of two integers. A  number  like  v’TZ  is  rational  since  it  can  be expressed as the quotient of the two integers in the  form  4/1.  An  irrational  number  is  a  real number that cannot be expressed as the ratio of two  integers.  The  numbers and 3.1416 (n) are examples of irrational numbers. An  integer  may  be  prime  or  composite.  A number  that  has  factors  other  than  itself  and 1  is  a  composite  number.  For  example,  the number  15  is  composite.  It  has  the  factors  5 and 3. A number that has no factors except itself and 1 is a prime number. Since it is advantageous to  separate  a  composite  number  into  prime factors, it is helpful to be able to recognize a few prime  numbers.  The  following  are  examples  of prime numbers: 1, 2, 3, 5, 7, 11, 13, 17, 19, and 23. A composite number may be a multiple of two or more numbers other than itself and 1, and it may contain two or more factors other than itself and  1.  Multiples  and  factors  of  numbers  are  as follows: Any number that is exactly divisible by a given number is a multiple of the given number. For example, 24 is a multiple of 2, 3, 4, 6, 8, and 12 since it is divisible by each of these numbers. Saying  that  24  is  a  multiple  of  3,  for  instance, is   equivalent   to   saying   that   3   multiplied   by some whole number will give 24. Any number is a  multiple  of  itself  and  also  of  1. FRACTIONS,   DECIMALS, AND  PERCENTAGES The most general definition of a fraction states that  “a  fraction  is  an  indicated  division.  ”  Any division  may  be  indicated  by  placing  the  dividend over the divisor with a line between them. By the above  definition,  any  number,  even  a  so-called “whole”  number,  may  be  written  as  a  common fraction.  The  number  20,  for  example,  may  be written  as  20/1.  This  or  any  other  fraction that amounts to more than 1 is an IMPROPER fraction.  For  example,  8/3  is  an  improper fraction,  The  accepted  practice  is  to  reduce  an improper  fraction  to  a  mixed  fraction  (a  whole number   plus   a   proper   fraction).   Perform   the indicated division and write the fractional part of the  quotient  in  its  lowest  term.  In  this  case, 8/3  would  be  2  2/3.  A  fraction  that  amounts  to less  than  1  is  a  PROPER  fraction,  such  as  the fraction   1/4. To refresh your memory, we are including the following  rules  in  the  solution  of  fractions: 1.   If   you   multiply   or   divide   both   the numerator and denominator of a fraction by the same  number,  the  value  does  not  change.  The resulting  fraction  is  called  an  EQUIVALENT fraction. 2.  You  can  add  or  subtract  fractions  only  if the denominators are alike. 3. To multiply fractions, simply find the prod- ucts  of  the  numerators  and  the  products  of  the denominators.  The  resulting  fractional  product must  be  reduced  to  the  lowest  term  possible. 1-2







Western Governors University

Privacy Statement
Press Release
Contact

© Copyright Integrated Publishing, Inc.. All Rights Reserved. Design by Strategico.