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Math I - 1 -
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BASIC ARITHMETIC AND ALGEBRA
POINTERS
Whole (natural) numbers
Natural numbers – numbers, which appear as a result of calculus of single subjects: peoples, animals, birds,
trees, different wares and so on. Series of natural numbers: 1, 2, 3, 4, 5, … is continued endlessly and is
called natural series .
Arithmetical 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:

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