15 terms

simplified expression

A less complicated expression that has no parentheses and no like terms.

term

A single number, variable, or the product of numbers and variables, such as -45, 1.2x, and 3xy2.

expression

A combination of individual terms separated by plus or minus signs.

order of operations

The specific order in which certain operations are to be carried out to evaluate or simplify expressions: parentheses (or other grouping symbols), exponents (powers or roots), multiplication and division (from left to right), and addition and subtraction (from left to right).

integers

The set of numbers {..., -3, -2, -1, 0, 1, 2, 3, ...}.

evaluate an expression

To find the numerical value of. Substitute the value(s) given for the variable(s) and perform the operations according to the order of operations.

substitution

Replacing one symbol with a number, a variable, or another algebraic expression of the same value.

additive inverse

The number you need to add to a given number to get a sum of 0. For example, the additive inverse of −3 is 3. It is also called the opposite.

multiplicative inverse

The number we can multiply by to get the multiplicative identity, For example, for the number 5, the multiplicative inverse is the fraction 1/5 ; for the number 2/3 the multiplicative inverse is 3/2.

rational numbers

Numbers that may be expressed in the form a/b , where a and b are integers and b ≠ 0. For example, 0.75 is a rational number because 0.75 may be expressed in the form 3/4 .

quotient

The result of a division problem.

commutative property of addition

States that if two terms are added, then the order may be reversed with no effect on the total. That is, a + b = b + a . For example, 7 + 12 = 12 + 7.

associative property of addition

States that if a sum contains terms that are grouped, then the sum may be grouped differently with no effect on the total, that is, a + (b +c) = (a + b) + c. For example, 3 + (4 + 5) = (3 + 4) + 5.

commutative property of multiplication

States that if two expressions are multiplied, then the order may be reversed with no effect on the result. That is, ab = ba . For example, 5 · 8 = 8 · 5.

associative property of multiplication

States that if a product contains terms that are grouped, then the product may be grouped differently with no effect on the result, that is, a(bc) = (ab)c. For example, 2·(3·4) = (2·3)·4.