Introductory Algebra Glossary

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Slide 43

Commutative property of addition

The order of numbers in an addition problem can be changed without changing the sum:

6 + 4 + 3 = 3 + 6 + 4

Slide 44

Commutative property of multiplication

The product in a multiplication problem remains the same regardless of the order of the factors:

6 • 4 = 4 • 6

Slide 45

Associative property of addition

The way in which numbers being added are grouped does not change the sum:

6 + (3 + 2) = (6 + 3) + 2

Slide 46

Associative property of multiplication

The way in which numbers being multiplied are grouped does not change the product:

6 • (2 • 3) = (6 • 2) • 3

Slide 47

Identity property

The sum of zero and any number equals the number, and the product of one and any number equals the number:

X + 0 = x x • 1 = x

Slide 48

Inverse property

A number added to its opposite is zero and a number multiplied by its reciprocal is one:

1 + (-1) = 0 1 • (1/2) = 1

Slide 49

Distributive property

For any real numbers a, b, and c, the distributive property states that:

a (b + c) = ab + ac.

Slide 50

Term

A number, a variable, or the product or quotient of a number and one or more variables raised to powers.

Slide 51

Numerical coefficient

The numerical factor in a term. In the term 6x2 the numerical coefficient is 6.

Slide 52

Like terms

The same variables raised to exactly the same powers. The terms 2x2 and 7x2 are like terms.

Slide 53

Unlike terms

Terms that do not have the same variable or the variables are not raised to the same powers. The terms 2x2 and 7x3 are unlike terms.

Slide 54

Combining like terms

A method of adding or subtracting like terms by using the properties of real numbers:

2x2 + 7x2 = 9x2.

Slide 55