Introduction to Algebra — Summary

Algebra is a branch of mathematics that uses letters, numbers and symbols to solve problems. Letters are used when a number is unknown or can change.

1. Variables and Constants

A variable is a symbol, usually a letter such as x, y, a or b, that can take different values. A constant has a fixed numerical value.

For example, in 5x, x is the variable and 5 is the constant. The number multiplying a variable is called its numerical coefficient, while the variable itself is called the literal coefficient.

A relationship can be expressed using a variable. For example, if every row of an auditorium has 5 more seats than the previous row, the number of seats in row x can be written as:

5x

2. Variables in Rules

Algebra can be used to create general rules for shapes.

For a rectangle with length l and breadth b:

Perimeter = 2(l + b)

For a square with side s:

Perimeter = 4s

For an equilateral triangle with side a:

Perimeter = 3a

The perimeter of any closed figure is the sum of all its sides.

3. Rules from Arithmetic

Algebra can express familiar arithmetic properties using variables.

* Commutative property of addition:
    a + b = b + a
* Commutative property of multiplication:
    a × b = b × a
* Associative property of multiplication:
    (a × b) × c = a × (b × c)
* Distributive property:
    a × (b + c) = (a × b) + (a × c)

These rules allow arithmetic relationships to be written generally r
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