ALGEBRA 1 HELP WITH EXAMPLES
FROM ARITHMETIC AND GEOMETRY
TO SHOW THE USE OF LITERALS :
LINKS TO ALGEBRA TOPICS

Please study
What is Algebra before Algebra 1 Help
if you have not already done so.

There we have defined Algebra as

ALGEBRA is generalized arithmetic in which numbers are represented by letters called literal numbers or simply literals.

By using literals, we can talk about any number and not just a particular number. This allows us to write rules and formulas in a general way.

For Example,

Example 1 of Algebra 1 Help :

From Arithmetic We know that

3 x 2 = 2 x 3;

-4 x 5 = 5 x -4;

-0.8 x 9.5 = 9.5 x -0.8;

3⁄7 x 5⁄8 = 5⁄8 x 3⁄7.

From the above, we note that whatever may be the order
in which two numbers are multiplied, the product remains the same.

We may write this as a rule
a x b = b x a ,

where a and b are any two numbers.

Let us see one more Example, this time from geometry.

Example 2 of Algebra 1 Help :

From Geometry, we know

The perimeter of a rectangle of length 5 units and width 3 units
= 2x5 + 2x3 = 2x(5+3) = 16 units.

The perimeter of a rectangle of length 10 units and width 2 units
= 2x10 + 2x2 = 2x(10+2) = 24 units.

The perimeter of a rectangle of length 7 units and width 4 units
= 2x7 + 2x4 = 2x(7+4) = 22 units.

We observe from the above results that the perimeter of a rectangle is twice the sum of its length and breadth.

So we can generalise the fact as
perimeter of a rectangle = 2(length + breadth).

We may write this as a formula
p = 2(l+b),

where p = perimeter of a rectangle
l = length of the rectangle
b = width of the rectangle.

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

BASIC ALGEBRA is all about?

The Basic Algebra page provides links to
various other topics of Algebra.