MATHEMATICAL SYMBOLS

Formulas, which are in effect statements of equality (equations), require the use of symbols to state the relationship between constants in any given set of conditions. To illustrate:

Consider triangle ABC.

Distance (D) around triangle ABC is equal to the sum of a, b, and c.

Expressed as a formula,

This formula would express the distance around a triangle regardless of conditions.

ADDITION AND SUBTRACTION OF MATHEMATICAL SYMBOLS

1. The sum of any two symbols, a and b, is written a+b.

2. The difference of any two symbols, a being the greater and b being the smaller, is written a -b.

MULTIPLICATION OF MATHEMATICAL SYMBOLS

1. The product of any two symbols, a and b, is written as a x b or ab.

2. The sum of any number of like symbols, such as a+ a + a + a, may be combined and written once, preceded by a numeral designating the number of times the symbol occurs, as 4a.

DIVISION OF MATHEMATICAL SYMBOLS

The quotient of any two symbols a and b where a is the dividend and b is the divisor maybe written a/b.

Summary

GROUPING-USE OF PARENTHESES

Occasionally a combination of symbols must be treated as a single symbol. When this occurs, the group is set apart by use of parentheses.

In order to symbolize 5 times the sum of a + b, you should write 5(a + b).

The quotient of a + b divided by 2 is written

REMOVAL OF COMMON FACTORS FROM AN EXPRESSION BY USE OF PARENTHESES

In the expression 2a + 2b + 2c: the common factor may be removed and the remainder combined in parentheses: 2(a + b + c) or in the following: 4ab + 2ac + 6ax.

All the terms contain the factor 2a. The expression may be changed to read 2a(2b + c + 3x).

Since the parentheses indicate that each term within is to be multiplied by the factor outside the parentheses, the parentheses may be removed by multiplying each term by the common factor.

SUBSTITUTION OF NUMERICAL VALUES FOR GROUPED SYMBOLS

Consider the expression:

Assign numerical values to a and b.

Let a=4 and b=2.

Substitute:

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