Algebraic expressions — Mathematics, 11–13 years
An algebraic expression uses letters and numbers to describe a calculation whose value may change. Learning to read and simplify one makes a changing situation easier to calculate and explain.
A calculation with a placeholder
In an expression such as 3x + 4, the letter x stands for a number we may not know yet or may want to change. The 3 tells us to multiply x by 3, and the + 4 tells us to add 4 afterwards. The letter is not a mysterious object; it is a useful name for a number.
Why use letters?
A list of separate calculations cannot show a rule for every possible number. A letter lets one short expression describe all those cases, such as the cost of x cinema tickets at 8 euros each: 8x. Algebra grew from the need to describe unknown amounts and repeated patterns clearly.
Simplifying 4x + 3x - 2
Look for terms that describe the same kind of thing. The terms 4x and 3x can join, because both contain x: 4x + 3x = 7x. The number -2 has no x, so it stays separate. The simplified expression is 7x - 2; if x = 5, its value is 35 - 2 = 33.
Joining unlike terms
It is tempting to say 3x + 2 = 5x because both parts contain numbers. But 3x means three groups of x, while 2 means two plain units; they are not the same kind of quantity. This mistake is reasonable when the letter feels like an ordinary digit, but keep unlike terms separate.
Rules that can change
Expressions describe costs, distances, scores and computer instructions when one amount changes. A taxi fare might be 4 euros plus 1.20 euros for each kilometre, written 4 + 1.2k. The expression lets you compare journeys quickly without writing a new rule for every distance.
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