Page 12 - Calculating Agriculture Cover 20191124 STUDENT - A

1-2 Numbers and Fundamental Arithmetic CH 1]

Review of signs, symbols, operations, relations and orders of
operations.

You have already been introduced to these arithmetic concepts since you began taking
mathematics courses, so this will be a review, a reminder, and for you to rejuvenate your
memory banks.

1. An Equation or Formula is the expression of a general rule or principle; that is, by
symbols.

2. A Unit is one thing, or one. One thing is a concrete unit; one is an abstract unit.
Concrete numbers:
A concrete number or 3. Number is the expression of a definite quantity. Numbers are either abstract or concrete.
numerous. An abstract number is one in which the kind of unit is not named; a concrete number is
Numeratus is a one in which the kind of unit is named. Concrete numbers are also called Denominate
number associated
with the things being Numbers.
counted, in contrast
to an abstract 4. Numbers are also divided into Integral, Fractional, and Mixed.
number or numerous. An Integral number, or Integer, is a whole number; a Fractional number is an
Numerans which is a expression for one or more of the equal parts of a divided whole; a Mixed number is an
number as a single Integer and Fraction united.
entity. For example,
"five apples" and "half 5. A Sign is a character used to show a relation among numbers, or that an operation is to
of a pie" are concrete be performed.
numbers, while "five"
and "one half" are 6. The signs most used in Arithmetic are
abstract numbers.
+ −  √ ÷ /
= : :: ( ) . . . . 

7. The sign of Addition is [ + ], and is called plus. The numbers between which it is placed,
are to be added. Thus, 3 + 5 equals 8.
Plus is described as a perpendicular cross, in which the bisecting lines are equal.

8. The sign of Subtraction is [ − ], and is called minus. When placed between two numbers,
the one that follows it is to be taken from the one that precedes it. Thus, 7 – 4 equals 3.
Minus is described as a short horizontal line.
Plus and Minus are Latin words. Plus means more; minus means less.
Michael Steifel, a German mathematician, first introduced + and - in a work published in 1544.

9. The sign of Multiplication is [  ], and is read multiplied by, or times. Thus, 4  5 is to be
read, 4 multiplied by 5, or 4 times 5.
The multiplication sign is described as an oblique cross.
William Oughtred, an Englishman, born in 1573, first introduced the sign of multiplication.

10. The sign of Division is [ ÷ ], and is read divided by. When placed between two numbers,
the one on the left is to be divided by the one on the right. Thus, 20 ÷ 4 equals 5.
The sign is described as a short horizontal line and two dots = one dot directly above the middle
of the line, and the other beneath the middle of it.
Dr. John Pell, an English analyst, born in 1610, introduced the sign of division.

11. The Radical sign, [ √ ], indicates that some root is to be found. Thus, √25 indicates
3
that the square root of 25 is required; √ 125, that the cube root of 125 is to be found;
4
and √ 625 indicates that the fourth root of 625 is to be extracted.
The root to be found is shown by the small figure placed between the branches of the Radical
sign. The figure is called the index.

12. The signs, +, −, , ÷, √, are symbols of operation.

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