By Amy Harris | Updated August 30, 2022
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Mastering algebraic expressions starts with a solid grasp of basic operations and terminology. A variable—denoted by a letter—serves as a placeholder for an unknown value. A constant is a fixed number that doesn’t involve a variable. In an expression, variables, constants, and arithmetic symbols (such as + or –) appear together, but an equals sign never does; adding one would transform the expression into an equation.
Choose any lowercase letter as your variable. For example, when asked to “write an expression for the sum of twice a number and six,” we’ll use n.
Look for keywords: “twice,” “thrice,” “multiplied,” “times,” or “product” signal multiplication; “halved,” “divided,” or “quotient” signal division.
If multiplication is indicated, write the variable immediately after the multiplier—e.g., “2n” (the “x” is implied). If division is indicated, form a fraction: “n/2.”
Keywords such as “sum,” “plus,” “added,” “more,” “increased,” or “total” mean addition; “difference,” “minus,” “subtracted,” “less,” or “decreased” mean subtraction.
Place a “+” between terms for addition: “2n + 6.” For subtraction, place a “–”: “2n – 6.” If the phrase uses “less,” reverse the order: “five less than a number” becomes “n – 5.”
You may swap the order of terms in addition (e.g., 2n + 6 = 6 + 2n), but maintain the exact order for subtraction and division unless the word “less” dictates otherwise.
Always write variables and constants in the sequence they appear in the wording when performing subtraction or division. Misplacing them changes the meaning.
