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## Math 1315-003 Week 1

by: Alexis Williams

34

6

2

# Math 1315-003 Week 1 MATH 1315 - 003

Alexis Williams
UTA

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1.1 Real Numbers
COURSE
COLLEGE ALGEBRA FOR ECONOMICS & BUSINESS ANALYSIS
PROF.
Shelley D Hamilton
TYPE
Class Notes
PAGES
2
WORDS
KARMA
Free

## Popular in Math

This 2 page Class Notes was uploaded by Alexis Williams on Sunday September 11, 2016. The Class Notes belongs to MATH 1315 - 003 at University of Texas at Arlington taught by Shelley D Hamilton in Fall 2016. Since its upload, it has received 34 views. For similar materials see COLLEGE ALGEBRA FOR ECONOMICS & BUSINESS ANALYSIS in Math at University of Texas at Arlington.

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Date Created: 09/11/16
Math 1315-003 1.1Real Numbers Shelley Hamilton 1.1     Real Numbers:  Real numbers are: 1,2,3,4   Whole Numbers are: 0,1,2,3,4  Rational Numbers are: where numbers can be written in the form p/q. But q cannot be equal to  zero. So if q is a zero then it is not a rational number.  Irrational numbers: all numbers that is not rational. Ex. Pie­ is irrational. Properties of real numbers:  Commutative Prop.: a+b=b+a and ab=ba  ­it doesn’t matter how you switch it, you will still get the same answers. Ex. 1+2=3 same  as 2+1=3 and 5*6=30 same as 6*5=30.  Associate Prop.: (a+b) +c = a+(b+c) and (ab)c = a(bc) ­Remember that the order of the numbers stays the same. Just the parentheses move.  Ex. 4+(9+8) = (4+9) +8 and 3(9x^2) = (3*9) x^2.  Identity Prop.: a+0=a and 0+a=a.  ­Identity Prop only has to do with either 0 or 1. There are two different types of identity  prop. There is a multiply and addition. And you will usually get the same answer from  with what you started with.  Ex. ­8+0= ­8 and (­9) *1= ­9  Inverse Prop.: a+(­a) =0 and (­a) +a=0 ­there are two different types of inverse prop. There is an addition and multiply.  Ex. 9+(­9) =0.   ­8*(1/­8) =1.   ­15+15=0. It is also like cancelling it out.   Multiplicative Inverse: a*1/a=1 and 1/a*a=1 ­just like inverse prop. You are basically just cancelling it out.  Distributive Prop.: a(b+c) = ab+bc and (b+c) a=ba+ca. ­whatever number is left out of the parentheses you distribute it in the parentheses with  each number. Ex. 9(6+4) =9*6+9*4.    3(x+y) = 3x+3y. Square Root:  Square Root of 40 is 6^2 and 7^2 because the answer is between those two numbers.  Ex. 5square root of 7. Well square root of 7 is between 2 and 3 because 2^2=4 and 3^2=9. So 5  square root of 7 must be between 10 and 15 because 5*2=10 and 5*3=15. Absolute Value:  Absolute value of a real number is the distance from a to 0. |a|  Ex. |9|=9 and |­9|=9 because the distance from 0 to ­9 is 9.  Ex. |­6|=6.   ­|7|=­7.   ­|­2|=­2.   |­3­4|=7.   |2­7|=5. Always answer what is in the Absolute Value  first then distribute the negative in with the answer. So when there is a neg. outside of the  absolute value ignore it, answer the question like it is not there and then put it in the answer. Math 1315-003 1.1Real Numbers Shelley Hamilton Work comes from lecture and part from the textbook: Applications in Mathematics: Custom  edition for the University of Texas at Arlington.

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