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Transcript
M098
Carson Elementary and Intermediate Algebra 3e
Chapter 1 Review
Vocabulary
*
Variable
Constant
Expression
Equation
Inequality
Set
{}
Real numbers
Rational number
*
*
*
*
*
*
*
*
Irrational number
Natural numbers
Whole numbers
Integers
Absolute Value
Addends
Sum
Difference
Product
Quotient
Numerator
Denominator
Multiple
Least common
denominator (LCD)
Factors
Prime number
Prime factorization
Lowest terms
Additive inverses
Minuend
Subtrahend
Multiplicative
inverses
Dividend
Divisor
Undefined
Indeterminate
Exponent
Base
Terms
Coefficient
Like terms
A symbol that can vary in value
A symbol that does not vary in value (such as a number)
A constant, variable or any combination of constants, variables and arithmetic
operations that describes a calculation
A mathematical relationship that contains an equal sign
A mathematical relationship that contains an inequality symbol (≠, <, >, ≤, ≥)
A collection of objects.
The symbols used to write a set.
All of the numbers represented by the number line
Any real number that can be expressed in the form a/b, where a and be are
integers and b ≠ 0.
Any number that is not rational.
The counting numbers {1, 2, 3, 4…}
The natural numbers and 0 {0, 1, 2, 3…}
The positive and negative natural numbers and 0 {… -3,-2,-1,0,1,2...}
A given number’s distance from 0 on a number line.
Numbers that are added.
The result of an addition.
The result of a subtraction
The result of a multiplication
The result of a division
The top number of a fraction
The bottom number of a fraction
A number that is the product of a given number and an integer
The least common multiple of the denominators of a given set of fractions.
Numbers that are multiplied
A natural number that has exactly two different factors, a and the number itself
A factorization that contains only prime factors
Given a fraction a/b and b≠0, the only factor common to both a and b is 1.
Two numbers whose sum is 0.
First number in a subtraction
Second number in a subtraction
Two numbers whose product is 1.
The number being divided
The number being divided by
The result when a non-zero number is divided by 0.
The result when 0 is divided by 0.
A symbol written to the upper right of a base number that indicates how many
times to use the base as a factor
The number in an exponential expression that is repeatedly multiplied.
Expressions that are the addends in an expression that is a sum
The numerical factor in a term
Variable terms that have the same variable(s) raised to the same exponents, or
constant terms.
Prior Knowledge
Comparing Numbers: For any two real numbers a and b, a is greater than b if a is to the right of b on a
number line.
Which is larger: -12 or -20?
V. Zabrocki 2010
page 1
M098
Carson Elementary and Intermediate Algebra 3e
Chapter 1 Review
Simplify fractions
63
99
Add, Subtract, Multiply Divide real numbers (integers and fractions)
Review rules
!
2
2
- 5 vs. (- 5)
(Not much in the text on these but stress anyway)
2
2
- 5 : the additive inverse or the opposite of 5 = -25
2
(-5) : the base is -5 = (-5)(-5) = 25
Order of Operations
2.
16  5 2
24   9  33  4
3.
 3
4.
3 2
  
4 3
5.
 2 9  15  5  3
1.
6.
1. -4
2
2
2. -28
 18  6  3
2

6 2  3 4  25
4. -13/12
2
5. 4

5  20  2  3
6. undefined
2
7.
 3 2  16  57  2
8.
 15.54  3.7   2 
9.
3. 3
9
16 4


81 27 9
7. -50
4
49
100  64  18   3 2
8. 18.8
9. 18
Evaluating expressions
1. 10
1.
n2  8n  1
for n  1
2.
 2m2  4n
for m  3, n  2
2. -26
Determine numbers that will cause an
expression to be undefined
1. -3
1.
2.
8
x3
5a
a  4a  2
Distributive Property (watch for minus)
1.
 73  2m
V. Zabrocki 2010
2. 4, 2
1. -21 + 14m
page 2
M098
Carson Elementary and Intermediate Algebra 3e
Combining like terms
1.
2.
4a  9b  a  5  7c  2b  8  7c
5
1 3
2 1
y  x 
8
2 4
3 4
Chapter 1 Review
1. 3a + 11b – 3
2.

3
3
7
x y
4
8
6
New Concepts
V. Zabrocki 2010
page 3