Page 13 - CalcBus_Flipbook

CH 1] Calculating Business 1-3

13. The sign of Equality is [ = ], two short horizontal parallel lines, and is read equals or is
equal to, and signifies that the quantities between which it is placed are equal. Thus, 3 +
5 = 9 − 1. This is called an equation, because the quantity 3 + 5 is equal to 9 − 1.

14. Ratio is the relation which one number bears to another of the same kind. The sign of
Ratio is [ : ]. Ratio is expressed thus, 6 : 3 = 6/3 = 2, and is read, the ratio of 6 to 3 = 2,
or is 2. 1
The sign of ratio may be described as the sign of division with the line omitted, It has the same
force as the sign of division, and is used in place of it by the French.

15. Proportion is an equality of ratios. The sign of Proportion is [ :: ], and is used thus, Aggregation: In
3 : 6 : : 4 : 8; this may be read, 3 is to 6 as 4 is to 8; another reading, the ratio of 3 Mathematics a
to 6 is equal to the ratio of 4 to 8. horizontal line drawn
over a group of terms in
16. The sign [ ( ), ], are signs of Aggregation – the first is the Parenthesis, the second a mathematical
expression to indicate
the Vinculum. They are used for the same purpose; thus, 24 − (8 + 7), or 24 − 8+7 , that they are to be
means that the sum of 8 + 7 is to be subtracted from 24. The numbers within the operated on as a single
parenthesis, or under the vinculum, are considered one quantity. entity by the preceding
or following operator.
17. The dots [ . . . . ], used to guide the eye from words at the left to the right, are called
Leaders, or the sign of Continuation, and are read, 'and so on. Vinculum: A vinculum
is a horizontal line used
in mathematical
18. The sign of Deduction. is [  ], and is read therefore, hence, or consequently. notation for a specific
purpose. It may be
19. The signs, =, : , :: , ( ), , . . . . ,  are symbols of relation. placed as an overline
(or underline) over (or
20. Arithmetic depends upon this primary proposition: that any number may be increased under) a mathematical
or diminished. "Increased" comprehends Addition, Multiplication, and Involution; expression to indicate
that the expression is to
"decreased," Subtraction, Division, and Evolution. be considered grouped
together. Source: Latin
21. The fundamental operations of Arithmetic in the order of their arrangement, are: — bind or bound.
Numeration and Notation, Addition, Subtraction, Multiplication, and Division.

22. Order of operations: When you have a mathematical problem as in an equation or a
statement that involves more than one operation—for example, addition and Involution: In
subtraction, or subtraction and multiplication—There is a defined order in which the Mathematics a function,
operations of arithmetic are to be completed. transformation, or
operator that is equal to
Example A: 8 – 4 x 2 = ? its inverse, i.e. which
 Do you do the subtraction first (8 – 4 = 4) and then the multiplication (4 x 2 = 8)? gives the identity when
 Or do you start with the multiplication (4 x 2 = 8) and then subtract (8 – 8 = 0)? applied to itself.

PEMDAS defines the Order of Operations
With problems and equations order of operations rules. As with all things learn the rules to
the game and play the game by the rules better than anyone else. The order in which Order of
operations are to be applied and the steps are abbreviated as PEMDAS: Operations:
PEMDAS
1. Parentheses 1. Parentheses.
2. Exponents and Roots
3. Multiplication and Division (from left to right) 2. Exponents and
4. Addition and Subtraction (from left to right) Roots √
(Best way to learn this is by doing and practice. Another way for poets is to memorize and 3. Multiplication and
think upon this phrase Please Excuse My Dear Aunt Sally.) Division (from left
to right)
 In the above example, 8 – 4 x 2 = ?, reading the Order of Operations (PEMDAS) you
deal with Multiplication first and then the Subtraction. 4. Addition and
Subtraction (from
left to right)
Consequently ( the solution is 4 x 2 = 8; then 8 − 8 = 0.

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