Corner : A corner of a shape is a point in the shape such that this point does not lie on the line segment between any two other points in the shape. Every triangle has 3 corners and every quadrilateral has 4 corners.

Face : In mathematics a face of a 3-dimensional shape is any of the two-dimensional shapes that form the boundary of the three-dimensional shape. For example the 6 faces of a cube are 6 squares.

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

Square : A square is a quadrilateral with four right angles and four equal length sides. A square is a special case of a rectangle and a special case of a rhombus.

Triangle : A triangle is a polygon with three corners and three sides. You can calculate the area of a triangle by multiplying half the length of the base by the height on that base. The sum of the interior angles in a triangle is always $180^{\circ}.$

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

Fraction : A fraction is a number that can be written as $\frac{a}{b}$ with an integer $a$ and a natural numbers $b.$ A fraction $\frac{a}{b}$ is the result of the division $a\div b.$ Examples of fractions are $\frac{1}{2}, -\frac{2}{3}$ and $\frac{3}{2}.$

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

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

Numerator : The numerator of a fraction $\frac{a}{b}$ is the number $a$ above the fraction bar.

Whole number : A whole number is any of the numbers $0,1,2,\ldots.$

Factor : If a natural number is divisible by a second natural number, that second natural number is called a factor of the first natural number. For example the factors of 12 are 1,2,3,4,6 and 12.

Greatest common factor : The greatest common factor of two natural numbers $m$ and $n$ is a natural number $k$ that is a factor of $m$ and $n$ such that there is no bigger number that is also a factor of $m$ and $n.$ For example the greatest common factor of 12 and 15 is 3. To simplify a fraction one can divide both the numerator as well as the denominator by the greatest common factor of the numerator and the denominator. The exponents in the prime factorization of the greatest common factor of two numbers are the minima of the exponents in the prime factorization of the two numbers.