# Arithmetical operations

Addition (addends, sum). Subtraction (minuend, subtrahend, difference).
Multiplication (multiplicand,  multiplier,  product,  factors). Division
(dividend, divisor, quotient, dividing integers, fraction, divisible numbers,
remainder, division without remainder, division with remainder). Raising
to a power
(power, base of a power, index or exponent of a power, value
of a power). Extraction of a root (root, radicand, index or degree of a
root, value of a root, square root, cube root). Mutually inverse operations.

Addition – an operation of finding a sum of some numbers: 11 + 6 = 17. Here 11 and 6 – addends ,  17 – the sum . If addends are changed by places, a sum is saved the same: 11 + 6 = 17 and 6 + 11 = 17.

Subtraction – an operation of finding an addend by a sum and another addend: 17 – 6 = 11.  Here 17 is a minuend ,  6 – a subtrahend ,  11 – the difference .

Multiplication. To multiply one number n ( a multiplicand ) by another m ( a multiplier ) means to repeat a multiplicand n as an addend m times. The result of  multiplying is called a product. The operation of multiplication is written as: n x m or n · m . For example, 12 x 4 = 12 + 12 + 12 + 12 = 48. In our case 12 x 4 = 48 or 12 · 4 = 48. Here 12 is a multiplicand, 4 – a multiplier, 48 – a product. If a multiplicand n and a multiplier m are changed by places, their product is saved the same:  12 · 4 = 12 + 12 + 12 + 12 = 48 and 4 ·12 = 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 48. Therefore, a multiplicand and a multiplier are called usually factors or multipliers.

Division – an operation of finding one of factors by a product and another factor: 48 : 4 = 12. Here  48  is a dividend ,  4 – a divisor ,  12 – the quotient . At dividing integers a quotient can be not a whole number. Then this quotient can be present as a fraction . If a quotient is a whole number, then it is called that numbers are divisible , i.e. one number is divided without remainder by another. Otherwise, we have a division with remainder . For example, 23 isn’t divided by 4 ; this case can be written as:  23 = 5 · 4 + 3.  Here 3 is a remainder .

Raising to a power. To raise a number to a whole (second, third, forth, fifth etc.) power means to repeat it as a factor two, three, four, five and so on. The number, repeated as a factor, is called a base of a power ; the quantity of factors is called an index or an exponent of a power ; the result is called a value of a power . A raising to a power is written as:

3 5 = 3 · 3 · 3 · 3 · 3 = 243 .

Here  3 – a base of the power,  5 – an exponent (an index) of the power,  243 – a value of the power.
The second power is called a square , the third one – a cube . The first power of any number is this number.

Extraction of a root – an operation of finding a base of a power by the power and its exponent:

Here 243 – a radicand , 5 – an index ( degree ) of the root , 3 – a value of the root . The second root is called a square root, the third root – a cube root .The second degree of square root isn’t written:

Addition and subtraction, multiplication and division, raising to a power and extraction of a root are two by two mutually inverse operations .