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

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

Partial products method : A method for calculating a product of two multi-digit numbers by writing both numbers as a sum of ones, tens, hundreds and so on, then multiplying each pair of terms and finally summing up all the terms. For example $12\cdot 34=(10+2)\cdot(30+4)$ $=10\cdot 30+10\cdot 4+2\cdot 30+2\cdot 4$ $=300+40+60+8=408.$

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 $x.$

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

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 $\frac{2}{3}.$

Two thirds : Two thirds refers to the number $\frac{2}{3}=0.\overline{6}.$