Letters Meet Numbers: Variables & Expressions
Variables are letters or symbols that stand in for unknown or changing values, and algebraic expressions combine variables with numbers and operations. Learning to write, read, and evaluate expressions is the gateway from arithmetic to algebra, enabling students to describe patterns, translate word problems into math, and prepare for solving equations.
Components of Variables & Expressions
This section covers the building blocks of algebraic expressions:
- Variables: Symbols (usually letters like x, y, n) that represent unknown or variable quantities.
- Writing Expressions: Translating word phrases like "five more than a number" into algebraic form (n + 5).
- Evaluating Expressions: Substituting a given value for the variable and computing the result.
- Simplifying Expressions: Combining like terms and using the distributive property to write expressions in simpler form.
Examples of Variables & Expressions
Variable Examples
- If x represents the number of apples in a bag, then 3x means three times the number of apples.
- Let n = a student's test score. The expression n + 5 represents a 5-point bonus added to the score.
- If t stands for hours worked, then 12t represents total earnings at $12 per hour.
Writing Expressions Examples
- "Seven less than a number" translates to n - 7.
- "Twice a number increased by 3" translates to 2x + 3.
- "The product of 4 and the sum of a number and 6" translates to 4(n + 6).
Evaluating Expressions Examples
- Evaluate 3x + 2 when x = 5: Substitute to get 3(5) + 2 = 15 + 2 = 17.
- Evaluate 2aΒ² - 4 when a = 3: Substitute to get 2(3Β²) - 4 = 2(9) - 4 = 18 - 4 = 14.
- Evaluate 5(n - 1) + 3 when n = 4: Substitute to get 5(4 - 1) + 3 = 5(3) + 3 = 15 + 3 = 18.
Simplifying Expressions Examples
- Simplify 4x + 7 + 2x - 3: Combine like terms to get (4x + 2x) + (7 - 3) = 6x + 4.
- Simplify 3(2y + 5): Distribute to get 6y + 15.
- Simplify 2(x + 3) + 4x: Distribute first, 2x + 6 + 4x, then combine like terms to get 6x + 6.