Step-by-step explanation:
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.
In some languages other than English, one distinguishes between ‘variables’ in functions and ‘unknown quantities’ in equations (‘incógnita’ in Portuguese/Spanish, ‘inconnue’ in French) but this does not completely clarify the situation. The terms such as variable and parameter cannot be precisely defined at this stage and are best left to be introduced later in the development of algebra.
An algebraic expression is an expression involving numbers, parentheses, operation signs and pronumerals that becomes a number when numbers are substituted for the pronumerals. For example 2x + 5 is an expression but +) × is not.
Examples of algebraic expressions are:
3x + 1 and 5(x2 + 3x)
As discussed later in this module the multiplication sign is omitted between letters and between a number and a letter. Thus substituting x = 2 gives
3x + 1 = 3 × 2 + 1 = 7 and 5(x2 + 3x) = 5(22 + 3 × 2) = 30.
In this module, the emphasis is on expressions, and on the connection to the arithmetic that students have already met with whole numbers and fractions. The values of the pronumerals will therefore be restricted to the whole numbers and non-negative fractions.
