This chapter introduces algebra by using letters to stand for numbers. A letter such as \(a\) or \(s\) used to represent a number is called a letter-number (a variable). For example, if Aftab's age is \(a\) and Shabnam is 3 years older, then Shabnam's age is \(s = a + 3\); substituting \(a = 23\) gives \(s = 26\). Expressions containing letter-numbers, like \(a + 3\) or \(2n - 1\), are called algebraic expressions, and replacing the letter by a number to compute a value is called substitution. You learn to translate word relationships into expressions, to read patterns in sequences (the \(n\)th multiple of 4 is \(4n\); the \(n\)th even number is \(2n\); the \(n\)th odd number is \(2n-1\)), and to use these generalisations to explain why a pattern holds. The power of letter-numbers is that one short expression captures infinitely many cases at once, making it possible both to predict values and to justify mathematical claims — a major step beyond arithmetic.
Letter-numbers (variables)Writing algebraic expressionsSubstitution and evaluating expressionsPatterns and the nth termGeneralisation using algebra
Key terms
Letter-number (variable)
A letter used to represent a number, e.g. \(a\) for Aftab's age.
Algebraic expression
A mathematical expression containing one or more letter-numbers, e.g. \(a + 3\).
Substitution
Replacing a letter-number by a particular number to find the value of an expression.
Generalisation
A statement that captures a pattern for all cases, written using letter-numbers.
\(n\)th term
An expression in \(n\) giving the value at position \(n\) of a sequence, e.g. \(4n\).
Constant
A fixed number in an expression whose value does not change.
Extra questions & answers
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What is a letter-number?
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Practice quiz · Expressions Using Letter-Numbers
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