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Quantum Arithmetic
8
8
Domain
8
8
8
8
Taxonomy
Super Set
Zero and One
Dimensional
Arithmetic Operations
Applied
Mathematics
The Logos (
λ
ό
γος
) Imperium
Imperial Corp of Civil Engineers
Liberal Arts Training
Academy
Arithmetic
1. The branch of mathematics
concerned with the activity of
numerical calculations, such as
addition, subtraction,
multiplication, and division. [12]
from Greek arithmētikē, from
arithmein to count, from arithmos
number
Quantum
2. A quantity or amount. 4.
Something that can be counted or
measured. [2]
Latin, how great;
see quantity.
Semantics
2. (Logic) the study of the
relationships between signs and
symbols and what they represent [1]
Syntax
1.c. The pattern of formation of
sentences or phrases in a
language. 3. A systematic, orderly
arrangement.
from Late Latin
syntaxis, from Greek suntaxis, to
put in order,
[2]
Parse
The process of analyzing a
string of symbols, either in natural
language, computer languages or
data structures, conforming to the
rules of a formal grammar. from
Latin pars (orationis), meaning
part (of speech)[5]
Measure
4.a. A definite quantity that has been
measured out: [2] 8. a quantity,
degree, or proportion.
Horizontal
2. Flat or level from left to right:
[12]
Latin horizont-, s. of horizōn
Dimension
1. A measurement of the size of
something in a particular direction,
such as the length, width, height,
diameter or depth. [1]
from Latin
dīmētīrī, to measure out
0
Distance
From
Center
Right
Left
0
1
1
2
3
4
5
6
2
3
4
5
6
-
+
Distance
From
Center
Intergers
0
1
1
2
3
4
5
6
2
3
4
5
6
-
+
Coordinate
One of a set of numbers that
determines the position of a point.
Only one coordinate is needed if
the point is on a line. [18]
Axis
2. Mathematics b. A reference line
from which distances or angles
are measured in a coordinate
system. [2] 1. (Mathematics) a real
or imaginary line about which a
body, such as an aircraft, can rotate
or about which an object, form,
composition, or geometrical
construction is symmetrical. [1]
from Latin: axletree, earth's axis;
related to Greek axōn axis].
Register
6. A state of proper alignment. 3.a. To
indicate (data). Used of an instrument
or scale. b. To be indicated as. 7. To
adjust so as to be properly aligned. [2]
from Latin, to record.
Segment
1. The portion of a line between any
two of its points. [2] 1. one of the
parts into which something is divided;
a division, portion, or section.
from
Latin segmentum, from secāre to cut
Pointer
2. (Mechanical Engineering) an
indicator on a measuring instrument.
[1] In computer science, a pointer is
an object in many programming
languages that stores a memory
address.[5]
X
Axis
Right
Segment
Left
Segment
0
Dimension
Pointer
0
1
1
2
3
4
5
6
2
3
4
5
6
-
+
The x-axis is a horizontal line (left
to right).
Left Units
Right Units
=
Absolute value
The value of a number without regard to
its sign. [2
X
Right
Left
0
1
1
2
3
4
5
6
2
3
4
5
6
-
+
0
1
1
2
3
4
5
6
2
3
4
5
6
-
+
+
+
-
-
-
+
-
+
Parse from
Left
to
Right
Parse from
Right
to
Left
Segment Register
1
+
0
D
1
2
3
4
5
6
2
3
-
4
5
6
Set
Addition
2. The process of adding or joining
something to something else,
typically to make it larger. [2] 3.
(Mathematics) a mathematical
operation in which the sum of two
numbers or quantities is
calculated. Usually indicated by
the symbol +
[from Latin additiō,]
Increment
1. The process of increasing in
number, size, quantity, or extent. [2]
from Latin incrēmentum, from
incrēscere, to increase
Absolute value
The value of a number without regard
to its sign.
The absolute value of +3 is
│3│. The absolute value of -3 is│3│
. [12]
Pointer Arithmetic
Addition
To add Integers of the same signs.
Add the absolute values.
Attach the common sign to the result.
Subtraction
2.To remove (a part of a thing,
quantity, etc) from the whole. [1] The
act, process, or operation of
subtracting one number or quantity
from another to compute their
difference. [2]
from Latin subtractus
withdrawn
The inverse of addition.
Inverse
1.Something that is opposite, as in
sequence or character; the reverse.
[2 ] Latin inversus, to invert
Decrement
1. The act or process of decreasing
or becoming gradually less. [2]
Latin
dēcrēmentum, from dēcrēscere,
dēcrē-, to decrease
Pointer Arithmetic
Subtraction
Set
-
+
1
7
8
9
+
0
D
1
2
3
4
5
6
2
3
-
+
-
1
1
2
3
4
5
6
2
3
4
5
6
0
-1
-2
(-1)+(-2)
|1|+|2|=|3|
(
-3
)=(
-2
)+(
-1
)
+
-
1
1
2
3
4
5
6
2
3
4
0
1
5
6
+
+
2
1
+
1
2
3
2
3
-
4
0
D
5
6
7
8
9
(1)+(2)
|1|+|2|=|3|
(
1
)+(
2
)=(
3
)
To add Integers of different signs.
Subtract the absolute values.
Attach the sign of the greater number.
(
ADD
)
absolute values.
|1|+|2|=3
(-1)-(2)
NEGATIVE Minus POSITIVE.
1
7
8
+
1
2
3
4
5
6
2
3
-
4
1
+
-
1
2
3
4
5
6
2
3
4
0
1
5
6
0
D
(-3)+(1)
|3|-|1|=|2|
(
-3
)+(1)=(
-2
)
+
+
+
-
2
1
2
3
4
5
6
2
3
4
0
1
5
6
(2)+(-1)
|2|-|1|=|1|
(
2
)+(-1)=(
1
)
+
+
1
+
2
3
-
4
0
D
2
3
4
5
1
5
6
7
NEGATIVE Minus NEGATIVE
(–3)–(–1)
(
SBUTRACT
)
absolute values.
|3|–|1|=2
Then
(
Additive Inverse
)
Reverse in order.
(–3)
+(1)
Attach sign of greater (Addend).
(–3)–(–1)=
(-2)
(5)-(8)
(
SUBTRACT
)
absolute values.
|8|-|5|=3
Then
(
Additive Inverse
)
Reverse in order.
(5)+
(-8)
Attach sign of greater (Addend)
.
(5)-(8)=
(-3)
POSITIVE Minus POSITIVE
(-1)+(-2)
Negative + Negative = Negative
After Inverse
(-3)
=(-1)-(2)
Then
(
Additive Inverse
)
Reverse in Order.
(POSITIVE) Minus NEGATIVE)
Then
(
Additive Inverse
)
Reverse in order.
(1)+(1)
Positive + Positive = Positive
After Inverse
(1)-(-1)=
(2)
(1)-(-1)
(
ADD
)
absolute values.
|1|+|1|=2
+
0
D
1
2
3
4
7
8
-
1
2
3
4
5
6
+
-
1
1
2
3
4
5
6
2
3
4
5
6
0
-1
+
+
+
-
1
1
2
3
4
5
6
2
3
4
5
6
0
-2
-
+
7
8
9
+
0
D
1
2
3
4
5
6
-
1
2
3
0
D
1
+
-
1
1
2
3
4
5
6
2
3
4
5
6
0
+
+
+
1
2
3
4
-
1
2
3
5
6
7
8
9
4
-
-
+
-
1
1
2
3
4
5
6
2
3
4
5
6
0
-8
+
0
D
1
2
3
4
-
1
2
3
5
6
7
8
9
-
+
Set
Multiplication
1. (Mathematics) an arithmetical
operation, defined initially in terms
of repeated addition. [1]
from Latin
multiplicare, "to increase
Rational Numbers
A number that can be expressed as an
integer or a quotient of integers.
For
example, 2, -5, and 1/2 are
rational numbers. [2]
+
0
0
0
0
0
0
0
0
0
0
0
001
2
(
1
)
0
0
0
1
00
2
1
0
1
10
1
1
0
10
2
.
01
1
01
2
0
0
01
1
(
1
)
0
1
3
1
00
2
1
0
1
10
1
1
0
10
2
.
1
01
2
7
5
01
1
001
2
1
2
3
4
5
6
7
9
0
8
+
+
+
+
+
+
+
+
+
1
2
3
4
5
6
7
9
0
8
+
+
+
+
+
+
+
+
+
1
2
3
4
5
6
7
9
0
8
+
+
+
+
+
+
+
+
+
1
2
3
4
5
6
7
9
0
8
+
+
+
+
+
+
+
+
+
1
2
3
4
5
6
7
9
0
8
+
+
+
+
+
+
+
+
+
-
1
-
2
-
3
-
4
-
5
-
6
-
7
-
9
0
-
8
-
1
-
2
-
3
-
4
-
5
-
6
-
7
-
9
0
-
8
-
1
-
2
-
3
-
4
-
5
-
6
-
7
-
9
0
-
8
-
1
-
2
-
3
-
4
-
5
-
6
-
7
-
9
0
-
8
-
1
-
2
-
3
-
4
-
5
-
6
-
7
-
9
0
-
8
01
-
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Scale
1.a. A system of ordered marks at fixed
intervals used as a reference standard
in measurement: a ruler whose scale
is in inches. [2]
Vertical
2. extending in a perpendicular
direction [1]
from Latin vertex.
the highest point.
Perpendicular
1. vertical; straight up and down;
upright. [3]
Latin perpendiculāris
vertical =perpendicul(um) plumb line
Perpend
To consider carefully; ponder.
Latin
perpendere : per-, per- + pendere,
to weigh [2]
Plumb Line
1. (Navigation) a string with a metal
weight at one end that, when
suspended, points directly towards
the earth's centre of gravity. 2.
(Building) another name for plumb
rule.
The y-axis is a vertical line
(up and down).
Form(s)
1. a. The shape and structure of an
object: 4.a. Method of arrangement
or manner of coordinating
elements in verbal or musical
composition: 1. c. To develop in the
mind; conceive: 4. To constitute or
compose, especially out of separate
elements: [2]
from Latin fōrma,
possibly from Greek morphē.
Vertical Dimensions
Objective
1. Composed of or relating to things
that occupy space and can be
perceived by the senses: [17]
Multiplier
2. Mathematics
The number which
multiplies another
number.
Multiplicand
The number
to be multiplied.
Latin to multiply
multiplicandum,
Product
3. Mathematics a. The number or
quantity obtained by multiplying two
or more numbers together. [2]
Latin
prōductum from prōdūcere to bring
forth
Multiplication
1. (Mathematics) an arithmetical
operation, defined initially in terms
of repeated addition. [1]
from Latin
multiplicare, "to increase"
4 = 5 x .8
.8
.6
.4
.2
.9
.7
.5
.3
.1
1
0
2
3
4
1
0
2
3
4
.2
.4
.6
.8
.1
.3
.5
.7
.9
.8
.6
.4
.2
.9
.7
.5
.3
.1
0
1
2
3
4
1
0
2
3
4
.2
.4
.6
.8
.1
.3
.5
.7
.9
0
3.2 = 4 x .8
2.4 = 3 x .8
1.6 = 2 x .8
.8 = 1 x .8
5
4
3
2
1
5
4
3
2
1
-3
= 5 x
-.6
-2.4
= 4 x
-.6
-1.8
= 3 x
-.6
-1.2
= 2 x
-.6
-6
= 1 x
-.6
3 Times 15
X
45
15
3
=
+
15
1
+
15
3
X
2
15
+
45
15
1
3
2
15
15
Set
Division
Mathematics The operation of
determining how many times one
quantity is contained in another; the
inverse of multiplication 3. The
proportional distribution of a
quantity or entity: [2]
from Latin
dīvīsus, to divide
Numerator/Dividend
1. Mathematics
a. The expression written above the
line in a common fraction to
indicate the number of parts of the
whole. b. An expression to be
divided by another; a dividend. 2.
One that numbers; an enumerator.
[2]
Late Latin numerātor a counter
The number written above the line
to indicate the quantity to be
divided into equal propotions .[12]
0
1
2
3
4
5
6
7
8
9
10
5
10
1
2
3
4
5
0
Division
The inverse
of multiplication, which is,
repeat subtraction.
Denomination
2. (Units) a grade or unit in a series
of designations of value, weight,
measure, etc: [1]
from Latin
dēnōminātiō a calling by name;
see denominate
Denominator/Divisor
1. the term of a fraction, usu.
written under or after the line,
that indicates the number of
equal parts into which the unit
is divided; divisor. 2. something
held in common; standard. [3]
[
1535–45; < Medieval Latin
] 2.
archaic a person or thing that
denominates or designates [1]
Below the line, the number of
equal proportions the numerator
is to be divided. [12]
Quotient
The number obtained by dividing
one quantity by another. In 10 ÷ 5
= 2, 2 is the quotient.
0
1
2
3
4
5
6
7
8
9
10
5
10
1
2
3
4
5
0
5x2=10
-
45
15
Enumerator:Enumerate:
Enumeration
2. To determine the number of; count.
Latin ēnumerāre, ēnumerāt-, to count
out : numerus, number;
[8]
30
=
-
15
15
=
-
15
00
=
1
2
3
45 Dollars Divided By 15
Quotient
Percentage
2. A proportion or part of a whole
when the whole is designated to be
of 100 parts; a part of 100 [12]
from
Latin per centum 'by a hundred'
45 Dollars
Divided By 15
= 3 Dollars
3
6
Scale
To increase or reduce proportionately
in size, etc [1]
Scale (3) Up
10 x
=
-
24
=
18
12
6
00
1
2
3
30
6
6
6
-
=
-
-
=
=
6
-
=
6
4
5
Enumerate
Proportion
1. the relationship between
different things or parts with
respect to comparative size, number,
or degree; relative magnitude or
extent; ratio [1]
Latin prōportiōn-,
from prō portiōne, according to
(each) part
3 of 6 = 3/6 = .5 x 100 = 50%
6
3
1
2
3
4
5
0
6
Part
Whole
Scale (5)
Down
.10 x
.5
.5 x 100 = 50%
Ratio
1. the relation between two
similar magnitudes with respect to
the number of times the first
contains the second: the ratio of 5
to 2, written 5:2 or 5/2.
2. proportional relation; rate [3] 2.
(Mathematics) a quotient of two
numbers or quantities. [1]
Latin
ratiō reckoning, proportion
Rate
1. A quantity measured with respect
to another measured quantity: a rate
of speed of 60 miles an hour. [2]
Medieval Latin rata, proportion,
short for Latin (prō) ratā (parte),
(according to a) fixed (part) to
consider, reckon
Magnitude
1 b. Greatness in size or extent: 3.
Mathematics a. A number assigned to
a quantity so that it may be
compared with other quantities. [2]
from Latin magnitūdō, greatness, size
,
6
12
18
24
30
0
1
2
3
4
5
0
Dollars
Hours
6 Dollars for 1Hour
6
12
18
24
30
0
1
2
3
4
5
0
Cabinet Drawers
Spoons
6 spoons per drawer. 30 spoons
per cabinet
3 of 6
Divide 3 by 6
2 of 10 = 2/10 = .2 x 100 = 20%
Length
0
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
0
Truck
Car
Percentage Equations
The percentage of a length
compared to a greater length.
Car and Truck
1 of 5 = 1/5 = .2 x 100 = 20%
Formula
2. (Mathematics) maths physics a
general relationship, principle,
or rule stated, often as an
equation, in the form of symbols.
[2]
Latin fōrmula, fōrma, form.
Equation
3. Mathematics A statement
asserting the equality of two
expressions, usually written as a
linear array of symbols that are
separated into left and right sides
and joined by an equal sign. [2]
Latin
Percentage = (Part / Whole) × 100
Expression
Left
Right
Equal
Car length is what percent of
Truck length?
Percentage
= (
Part
/
Whole
) × 100
Percentage Equations
Variable
1.a. Likely to change or vary;
3. Mathematics Having no fixed
quantitative value. b. A symbol
representing such a quantity. [2]
from Latin variābilis changeable.
Variables
Q
P
%
Quotient
Percentage
W
DD
Whole
Denominator
Divisor
Calculating Percentages
0
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
0
Truck
1
5
2
10
Car
4
20
Use Known Quantities to Resolve
Unknown Quantities.
Q
P
% = (
P
N
D
/
W
D
D
) x 100
What percentage is twelve spoons
out of thirty.
Q
P
% = P
N
D
/
W
D
D
x 100
Q
P
% = 12/30 x 100 = 40%
6
12
18
24
30
0
1
2
3
4
5
0
P
N
D
W
D
D
P
N
D
Part
Numerator
Dividend
What number of spoons equals 60%.
P
N
D
= Q
P
%/100 x
W
D
D
50% of what quantity is 15
W
D
D
=
P
N
D
/(Q
P
%/100)
6
12
18
24
30
0
1
2
3
4
5
0
P
N
D
W
D
D
P
N
D
= 60%/100 x 30 = 18
6
12
18
24
30
0
15
1
2
3
4
5
0
P
N
D
W
D
D
W
D
D
= 15/(50%/100) = 30
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