Chapter 1: Tools Of Algebra Flashcards
What is Absolute Value?
The absolute value of a real number is its distance from zero on a number line. Absolute value can NEVER be negative.
Ex:
The absolute value of 4.
|4|=4
The absolute value of negative 4.
|-4|=4
What are Natural Numbers?
- {1,2,3,4,5}
- Counting Numbers
What are Whole Numbers?
- {0,1,2,3,4,5}
- Begin with zero.
What are Integers?
- {….-3,-2,-1,0,1,2,3,4….}
- Negative and Positive numbers.
What are Rational Numbers?
- {1/2, 4/3, 0.25, -1.2, 9}
- Definition: rational numbers are all the numbers that can be written as quotients of integers. Each quotient must have a non-zero denominator.
- All rational numbers can be written (a) over (b), but (b) cannot equal zero.
- some are written as terminating decimals, all others are written as repeating decimals.
What are Irrational Numbers?
Ex: sqr. 7, 3.14(pie), 1.010110100110
- Numbers that cannot be written as a/b, where (b) does NOT equal (0).
- Decimals neither terminate nor repeat.
- If a Positive Rational Number is not a perfect square such as 25 or 4/9, then it’s square root is irrational.
Ex: The Square Root of 2 –> Irrational
What are the properties of real numbers?
- ) The opposite or additive inverse of any number (a) is (-a). The sum of the opposites is (0).
- ) The reciprocal or multiplicative inverse of any non-zero (a) is (1/a). The product of the reciprocal is (1).
What is the Closure Property of Addition?
A+B is a real number.
What is the Closure Property of Multiplication?
ab is a real number.
What is the Communitive Property of Addition?
a+b=b+a
What is the Communitive Property of Multiplication?
ab=ba
What is the Associative Property of Addition?
(a+b)+c=a+(b+c)
What is the Associative Property of Multiplication?
(ab)c=a(bc)
What is the Additive property of Identity?
a+0=a
What is the Multiplicative Property of Identity?
a*1=a
