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.