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

Division : Division is the mathematical operation that divides objects equally into groups. More generally $x\div y$ is defined as the number that if multiplied by $y$ equals $x.$

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 $\frac{3}{2}.$

Half : A Half is the number equal to $\frac{1}{2}=0.5.$

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

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

Reciprocal fraction : The reciprocal fraction of a fraction $\frac{a}{b}$ is defined as $\frac{b}{a}.$ The reciprocal fraction is used in the division by a fraction because instead of dividing by a fraction one can equivalently multiply by the reciprocal fraction.