Math 1315-003 Week 1
Math 1315-003 Week 1 MATH 1315 - 003
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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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