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.

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

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 $x.$

Remainder : In the division of a whole number $x$ by a natural number $y$ the remainder is the unique whole number $r$ with $0\leq r\lt y$ with $x=m\cdot y+r$ for some whole number $m.$ The remainder is the number of leftover wholes in the division. For example the remainder of the division of 14 by 3 is 2 as $14=4\cdot 3+2.$ Remainders are fundamental for the concept of congruence modulo $y$ in number theory.

Standard algorithm : By standard algorithm we refer to any one of the algorithms that are commonly taught at school to add, subtract, multiply or divide multi-digit numbers such as long division and partial products multiplication.

Decimal : A decimal is a number represented by digits in front and after a decimal point. In front of the decimal point the digits are the ones digit, tens digit, hundreds digit and so on. After the decimal point there are the tenths digit, hundredths digit, thousandths digit and so on. For example the decimal 1.3 can be written as $1\frac{3}{10}.$

Digit : A digit is a symbol used in the representation of a number.

One sixth : One sixth is the number $\frac{1}{6}=0.1\overline{6}.$

Period : A decimal is called periodic with period $a_1a_2,\ldots,a_n$ if the sequence $a_1a_2,\ldots,a_n$ keeps on repeating forever in the decimal. For example $\frac{1}{3}=0.3333\ldots=0.\overline{3}$ has a period equal to 3. A function $f$ is called periodic with period $a$ if $f(x+a)=f(x)$ for all $x.$

Remainder : In the division of a whole number $x$ by a natural number $y$ the remainder is the unique whole number $r$ with $0\leq r\lt y$ with $x=m\cdot y+r$ for some whole number $m.$ The remainder is the number of leftover wholes in the division. For example the remainder of the division of 14 by 3 is 2 as $14=4\cdot 3+2.$ Remainders are fundamental for the concept of congruence modulo $y$ in number theory.

Tenth : Tenth refers to the number $\frac{1}{10}=0.1=10^{-1}.$

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