# 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:

^{ 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
*
.