THE NATURE OF ALGEBRA
Algebra is a generalization of arithmetic. Each statement of arithmetic deals with particular numbers: the statement (20 + 4)2 = 202 + 2x20x4+42 = 576 explains how the square of the sum of the two numbers, 20 and 4, may be computed. The same procedure applies if the numbers 20 and 4 are replaced by any two other numbers. In order to state the general rule, we write symbols, ordinarily letters instead of particular numbers. In this case the square of the sum of any two numbers A and В can be computed4 by the rule (A4-B)2 = A2+2AB+B2.
This is general rule which remains true no matter what particular numbers may replace the symbols A and B. A rule of this kind is often called a formula.
Algebra is the system of rules concerning the operations with numbers. Those rules can be stated as formulas in terms of letters.
The characteristic of algebra is the use of letters to represent numbers. Since the letters used represent numbers, all the laws of arithmetic hold for operations with letters.
For convenience the operation of multiplication is generally denoted by dot as by placing the letters adjacent to each other. For example, axb is written simply as ab.
The operations of addition, subtraction, multiplication, division, raising to a power and extracting roots are called algebraic expressions.
NOTES:
to deal with - иметь дело с, рассматривать
may be computed - может быть вычислена
instead of - вместо
to hold for - годиться
to raise to a power - возвести в степень
to extract root - извлекать корень
EXERCISES:
1. Read the following words paying attention to the pronunciation:
concern, length, generally, width, division, addition, total, power, call.
2. Form nouns and translate them into Russian:
add, divide, multiply, subtract, operate, state, express, represent, introduce.
Достарыңызбен бөлісу: |
