Arithmatical operations (All Mathematical Formulae) --By: Vinod Kumar Dhundhara

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.