Chapter 2
Additive identity
The nuber 0 is the additive identity, because the sum of any number and 0 is the number: a+0=0+a=a.
Integers
..., -3, -2, -1, 0, 1, 2, 3, ...
Whole numbers
0, 1 , 2, 3, ...
If-then statement
A conditional statement with an if part and a then part. The if part contains the hypothesis and the then part contains the conclusion.
Rational number
A number a/b where a and b are integers and b≠0
Irrational number
A number that cannot be written as the quotient of two integers. The decimal form of an irrational number neither terminates nor repeats.
Perfect square
A number that is the square of an integer.
Distributive property
A property that can be used to find the product of a number and a sum or difference: a(b+c)=ab+ac (b+c)a=ba+ca a(b-c)=ab-ac (b-c)a=ba-bc
Conditional statement
A statement with a hypothesis and a conclusion.
Constant term
A term with a number part but no variable part.
Counterexample
An example used to show that an if-then statement is false.
Square root
If b²=a, then b is a square root of a. The radical symbol √ represents a nonnegative square root.
Positive integer
Integers greater than 0.
Negative integer
Integers less than 0.
Like terms
Terms that have the same variable parts. Constant terms are also like terms.
Absolute value
The absolute value of a number a is the distance between a and 0 on a number line. The symbol |a| represents the absolute value of a.
Additive inverse
The additive inverse of a number a is its opposite, -a. The sum of a number and its additive inverse is 0: a+(-a)=-a+a=0
Multiplicative inverse
The multiplicative inverse of a nonzero number a is its reciprocal, 1/a. The product of a nonzero number and its multiplicative inverse is 1: a*(1/a)=(1/a)*a=1, a≠0.
Multiplicative identity
The number 1 is the multiplicative identity, because the product of any number and 1 is the number: a*1=1*a=a
Radicand
The number or expression inside a radical symbol.
Coefficient
The number part of a term with a variable part.
Term
The parts of an expression that are added together.
Real numbers
The set of all rational and irrational numbers.
Equivalent expressions
Two expressions that have the same value for all values of the variable.
Opposites
Two numbers that are the same distance from 0 on the number line but are on opposite sides of 0 are called opposites.