Grade 7 - Chapter 5 - Expressions

Like terms

"Like terms" are terms whose variables (and their exponents such as the 2 in x2) are the same. In other words, terms that are "like" each other. Note: the coefficients (the numbers you multiply by, such as "5" in 5x) can be different.

Monomial

(1): A monomial, also called power product, is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions. The constant 1 is a monomial, being equal to the empty product and x0 for any variable x.

Variable

...A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x , y , and z are common generic symbols used for variables.

Algebraic Expression

...An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add,subtract,multiply, and divide). ... In the above expression the "/" means divide. The "3x" means multiply the variable x by 3.

Counterexample

A counterexample is a special kind of example that disproves a statement or proposition. Counterexamples are often used in math to prove the boundaries of possible theorems. In algebra, geometry, and other branches of mathematics, a theorem is a rule expressed by symbols or a formula.

Constant

A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants. If it is not a constant it is called a variable.

Simplest Form

A fraction is in simplest form when the top and bottom cannot be any smaller (while still being whole numbers). Example: 2/4 can be simplified to 1/2. To simplify a fraction, divide the top and bottom by the highest number that can divide into both numbers exactly.

Equivalent Epressions

Algebraic Expressions. An algebraic expression is a string of numbers, variables, mathematical operations, and possibly exponents. For example, 4x + 3 is a basic algebraic expression. Or, we could get a little more complex with 3x(2x^2 + 2x - 5) + 6y.

Define a variable (action)

Choosing a variable and a quantity for the variable to represent in an expression or equation.

Commutative Property

In Algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs. See: Variable. Algebra - Definitions.

Term

In Algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs. See: Variable. Algebra - Definitions.

term

In Algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs. See: Variable. Algebra - Definitions.

Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence.

arithmetic sequence

In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15 ... is an arithmetic progression with common difference of 2.

Linear expression

It is made up of two expressions set equal to each other. A linear equation is special because: It has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction.

Multiplicative Property of Zero

One of zero's unique rules is called the multiplication property. The multiplication property states that the product of any number and zero is zero. It doesn't matter what the number is, when you multiply it to zero, you get zero as the answer. ... 2 x 0 = 0.

Distributive Property

The Distributive Property is easy to remember, if you recall that "multiplication distributes over addition". Formally, they write this property as "a(b + c) = ab + ac". In numbers, this means, for example, that 2(3 + 4) = 2×3 + 2×4.

Multiplicative Identity

The Multiplicative Identity Property. For a property with such a long name, it's really a simple math law. The multiplicative identity property states that any time you multiply a number by 1, the result, or product, is that original number.

Additive Identity

The additive identity property says that if you add a real number to zero or add zero to a real number, then you get the same real number back. The number zero is known as the identity element, or the additive identity.

Associative Property

The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis. Add some parenthesis any where you like!.

Property

There are four mathematical properties which involve addition. The properties are the commutative, associative, additive identity and distributive properties. Additive Identity Property: The sum of any number and zero is the original number. For example 5 + 0 = 5.

Factor

a number or quantity that when multiplied with another produces a given number or expression.

Coefficient

a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g., 4 in 4x y).

Algebra

algebra. (āl'jə-brə) A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or quantities and express general relationships that hold for all members of a specified set. The American Heritage® Science Dictionary.