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GG.1 Write variable expressions

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What are variable expressions?

Variable expressions are math phrases that include numbers, operations, and at least one variable (a letter that stands for an unknown number).

Examples:
  • n + 6 → a number plus 6
  • x − 12 → a number minus 12
  • 45 ÷ y → 45 divided by a number
Note

Variables are often represented by letters such as x, y, or n. Each letter can stand for a different number depending on the situation.

Understanding variables

A variable is a symbol, usually a letter, that stands for a number we do not yet know. Variables help us write math ideas in general form instead of using only specific numbers.

Examples:
  • If n = 8, then n + 6 = 14.
  • If x = 20, then x − 12 = 8.
  • If y = 9, then 45 ÷ y = 5.
Note

Always substitute the variable with its given value before solving. This helps you find the numerical answer to the expression.

How to write variable expressions

To write a variable expression, think about the relationship between numbers and the unknown quantity. Use words like “sum,” “difference,” or “quotient” to decide which operation to use.

Word Phrases and Expressions:
  • The sum of a number and 15 → n + 15
  • 1,254 minus a number → 1,254 − x
  • The quotient of a number and 3 → y ÷ 3
Note

Words like “sum,” “difference,” and “quotient” tell you which math operation to use.

Evaluating variable expressions

To evaluate a variable expression, replace the variable with a given number and perform the operation to find the result.

Examples:
  • n + 15 when n = 1010 + 15 = 25
  • 1,254 − x when x = 2001,254 − 200 = 1,054
  • y ÷ 3 when y = 2121 ÷ 3 = 7
Note

Be careful to follow the correct order of operations when evaluating expressions that include more than one operation.

Why variable expressions are useful

Variable expressions are important because they allow you to represent patterns, solve problems, and describe real-world situations mathematically.

Examples:
  • The total cost of n tickets at $8 each → 8n
  • The number of apples after giving away 6 → a − 6
  • Each person’s share when 45 candies are divided among y people → 45 ÷ y
Note

Variables help you describe changing quantities and make general rules that work for many situations, not just one example.