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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: