Count : To count means to find out the number of objects by adding one for every object.

Common denominator : The common denominator of two or more fractions is a number that is a multiple of all the denominators of the fractions. For example 12 and 24 are both common denominators of $\frac{3}{4}$ and $\frac{1}{6}.$

Denominator : The denominator of a fraction $\frac{a}{b}$ is the number $b$ below the fraction bar.

Equivalent fraction : Equivalent fractions are fractions that represent the same number. For example the fractions $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent. One can create equivalent fractions of a fraction by multiplying or dividing both the numerator and the denominator of the fraction by the same non-zero number.

Reduced fraction : A reduced fraction (or simplified fraction or fraction in simplified form or fraction in simplest form) is a fraction $\frac{a}{b}$ such that $a$ and $b$ do not have any common factors bigger than 1. For example the reduced fraction of the fraction $\frac{4}{6}$ is $\frac{2}{3}.$

Addition : Addition is the mathematical operation that describes increasing a number by an amount equal to a second number. The mathematical symbol for addition is the plus sign $+.$ The term addition is also used for a generalization of this basic operation on numbers to functions, vectors and matrices.

Equation : An equation is a mathematical statement in which two expressions are written with an equal sign in between. A solution of an equation is a set of variables that makes the statement a true statement.

Equivalence : Equivalent fractions are fractions that represent the same number. Equivalent equations or inequalities are equations or inequalities that have the same set of solutions.

Inequality : An inequality is a statement that contains an inequality sign between two expressions.

Multiplication : Multiplication is the mathematical operation that is a shorthand for adding the same amount several times. For example $3\cdot 4=4+4+4=12.$

Negative : A number is negative if it is $\lt 0.$

Number : A number $x$ is a mathematical symbol representing a quantity.

Positive : Positive means $\geq 0.$

Subtraction : Subtraction is the mathematical operation that describes decreasing a number by an amount equal to a second number. The mathematical symbol for subtraction is the minus sign $-.$ The term subtraction is also used for a generalization of this basic operation on numbers to functions, vectors and matrices.

Term : If an expression can be written as a sum of several parts we call these parts terms.