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Introduce the concept of variables as a way of representing numbers using letters. (ACMNA175)


Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)

Using pronumerals

In algebra we are doing arithmetic with just one new feature − we use letters to represent numbers. Because the letters are simply stand-ins for numbers, arithmetic is carried out exactly as it is with numbers.
Pronumerals are used in many different ways, as shown below.
Substitution: 'Find the value of 2x + 3 if x = 4.' In this case the pronumeral is given the value 4.
Solving an equation: 'Find x if 2x + 3 = 8.' Here we are seeking the value of the pronumeral that makes the sentence true.
Identity: 'The statement of the commutative law: \(a + b = b + a\).' Here a and b can be any real numbers.
Formula: 'The area of a rectangle is \(A = lw\).' Here the values of the pronumerals are connected by the formula.
Equation of a line or curve: 'The general equation of the straight line is \(y = mx + c\).' 
Here \(m\) and \(c\) are parameters. That is, for a particular straight line, \(m\) and \(c\) are fixed.