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Algebraic manipulations are governed by the properties of operations and exponents, and the conventions of algebraic notation. At times, an expression is the result of applying operations to simpler expressions. For example, 𝑝 + 0.05𝑝 is the sum of the simpler expressions 𝑝 and 0.05𝑝. Viewing an expression as the result of operation on simpler expressions can sometimes clarify its underlying structure.
Reading an expression with comprehension involves analysis of its underlying structure. This may suggest a different but equivalent way of writing the expression that exhibits some different aspect of its meaning. For example, 𝑝 + 0.05𝑝 can be interpreted as the addition of a 5% tax to a price 𝑝. Rewriting 𝑝 + 0.05𝑝 as 1.05𝑝 shows that adding a tax is the same as multiplying the price by a constant factor.
An expression is a record of a computation with numbers, symbols that represent numbers, arithmetic operations, exponentiation, and, at more advanced levels, the operation of evaluating a function. Conventions about the use of parentheses and the order of operations assure that each expression is unambiguous. Creating an expression that describes a computation involving a general quantity requires the ability to express the computation in general terms, abstracting from specific instances.