BASIC ALGEBRA -- INTRODUCTION TO ALGEBRA

Please study
Algebra 1 Help before Basic Algebra,
if you have not already done so.

There you have seen that
Since literals stand for numbers,
operations can be performed on them
as on numbers.

i.e. we do arithmetic with literals.
And that is what we deal with here.

BASIC ALGEBRA deals with methods
of doing arithmetic calculations like
addition, subtraction, multiplication etc
with literal numbers.

Basic operations with literal numbers :

The symbols +, -, x, '>', '<' etc carry the
same meaning in algebra as they do in arithmetic.

Similarly the commutative, associative,
distributive laws etc, which are true with
numbers also hold good with literal symbols.

Addition in Basic Algebra :

(i) 5 added to x is written as x + 5;

(ii) y added to x is written as x + y ;

Subtraction in Basic Algebra :

(i) x decreased by 7 is written as x - 7;

(ii) x subtracted from 8 is written as 8 - x ;

(iii) y subtracted from x is written as x - y ;

Multiplication in Basic Algebra :

(i) 6 times x is written as 6 x x , denoted by 6. x or 6x.
x x 6 is written as 6x (not x6).

(ii)The product of x and y is x x y , written as x.y or xy.
a x b x c is written as a bc.
x x y x 9 is written as 9xy (not as xy9).

(iii) 1 x x is simply written as x and not 1x.
Similarly (-1) x x is written as -x.

This symbolism can not be adopted in Arithmetic, as product of 5 and 6 can not be written as 56, as 56 gives a different meaning (Fifty six). Hence the product of 5 and 6 has to be written as 5 x 6 only.

In the product ab , both 'a' and 'b'' are called factors of 'ab'.
In the product abc , 'a', 'b', 'c' are called factors of 'abc' .

Division in Basic Algebra :

(i) x divided by 2 is written as x⁄2.

(ii) 9 divided by x is written as 9⁄x.

(iii) x divided by y is written as x⁄y.

It may be observed from above that the symbolism between arithmetic and algebra is same except in the case of multiplication.

Literal Multiplied more than once :

When a (literal) number is multiplied more than once,
we use a special notation to represent it.

The number of times the literal or number is multiplied is called exponent.

For study about this notation and Exponents go to

EXPONENTS AND POWERS

Various other Links pertaining to Exponents are

Laws of Exponents.

Math Exponents.

Rational Exponents.

Fractional Exponents.

Logarithms.

Logarithm Tables.

Variables and Constants :

The Letter Symbols used in algebra
have no particular value and may
have any value (of a certain set)
assigned to them. We explain the
concept of Variables and Constants
in Algebra at

Algebra Symbols as Constants and Variables