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

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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 whichnumbers are represented by letterscalled literal numbers or simply literals.

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

For Example,

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Example 1 of Algebra 1 Help :

Example from Arithmetic 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 productremains 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.





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Example 2 of Algebra 1 Help :

Example from Geometry 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 thatthe perimeter of a rectangle is twicethe 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.

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