Algebra Final Exam Study Guide: Section 8.1 - 8.7
If a is a real number then...
-(-a) = a
Identify the numerical coefficient of -x
-1
Find the opposite of 1/2
-1/2
Find the reciprocal of: -9/13
-13/9
Multiply. -7(6)
-42
Divide: -18 divided by 3
-6
Multiply. -2/3 x 3/6
-8/21
The number ____ does not have a reciprocal.
0
Whole numbers
0,1,2,3,4,5,6
if a is a nonzero real number, then....
0/a = 0
Natural numbers
1,2,3,4,5,6
Find the reciprocal of: 22
1/22
A number SUBTRACTED from 10
10 - x
10 DECREASED by a number
10-x
3 SUBTRACTED from 12 is a number
12 - 3 = x
The QUOTIENT of 15 and a number is 4
15/x = 4
Bad example of exponential notation.
2 x 2 x 2 = 2(3)
Good example of exponential notation.
2 x 2 x 2 = 2^3
TWICE a number, PLUS 6
2x + 6
Find the opposite of -3
3
The PRODUCT of 3 and a number
3x or 3(x)
Four TIMES the SUM of a number and 3
4x + 12
17 ADDED four TIMES a number is 21
4x + 17 = 21
Five PLUS the SUM of a number and 1
5 + (x + 1)
5 TIMES a number, INCREASED by 7
5x + 7
Example of Quotient of Two Real Numbers
6 divided by 2 = 6/2 = 6 x 1/2
Divide: -14/-2
7
The QUOTIENT of 7.3 and a number
7.3/x
Equation
A mathematical sentence that contains an equals sign.
Solution
A value that makes an equation a true statement when substituted.
Quotient of Two Real Numbers
If a and b are real numbers and b is not 0, then a divided b = a/b = a x 1/b
Element
Part of a set
Dividing Real Numbers
The quotient of two numbers with the same sign is positive, while a quotient of two numbers with different signs is negative.
reciprocals
Two numbers whose product is 1. Also called multiplicative inverses.
Integers
Whole numbers and their opposites (-3, -2, -1, 0, 1, 2, 3)
Set
a collection of objects
term
a number or the product of a number and variable(s) raised to powers.
Distributive Property
a(b + c) = ab + ac
Adding real numbers with the same sign
add the values and keep the sign
real numbers
all numbers that corresponds to a point on the number line.
combining like terms
combine the numerical coefficients by finding the sum or difference of like terms
If you multiply an _____ number of negative numbers, the answer is positive.
even
Associative Properties
have to do with the grouping of the numbers
Commutative Properties
have to do with the order of the numbers
Subtracting Real Numbers
if a and b are real numbers then, a - b = a + (-b)
negative integers
integers to the left of 0
positive integers
integers to the right of 0
Variable
letters used to represent quantities
Variables
letters used to represent unknown quantities
Rational numbers
numbers that can be represented by a fraction; in a decimal form they are either terminating or are repeating.
Irrational integers
numbers that do not terminate or repeat in a pattern.
If you multiply an ____ number of negative numbers, the answer is negative.
odd
A ____ number will either terminate or repeat in a pattern.
rational
Both _______ and _______ can be written as decimal numbers .
rational and irrational
The ____ numbers are (all numbers that correspond to points on a number line).
real
Example of a irrational numbers
square root of 3
Adding real numbers with different signs
subtract the values and keep the sign of the larger number
like terms
terms with the same variables raised to the same powers
absolute value
the distance between a number and 0 on the number line; denoted.
exponent
the number of times a base is used as a factor.
numerical coefficient
the numerical factor of a term
Multiplying Real Numbers
the product is two numbers with the same sign is positive or a product is two numbers with different songs is negative
Base
the repeated factor
Adding Real Numbers
to add two real numbers
additive inverses
two numbers that are the same distance from 0 but lie on opposite sides of 0
a/0 is...
undefined
exponential notation
used to write products
The SUM of a number and 3
x + 3
A number DECREASED by 10
x - 10
The DIFFERENCE of a number and 4, DIVIDED by 7
x - 4/7
