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