Pre-Algebra Unit 5 study games — Variables and Expressions.
This unit covers evaluating expressions, combining like terms and distributive property — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers evaluating expressions, combining like terms and distributive property — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Evaluating Expressions
Students must be able to substitute given values for variables and simplify using the correct order of operations (PEMDAS). Exams will provide an expression and one or more variable values, expecting a single numerical answer. Errors in order of operations or sign handling are the most common mistakes.
Key Points
- Replace each variable with its given value using parentheses to avoid sign errors
- Always follow order of operations: Parentheses → Exponents → Multiply/Divide → Add/Subtract
- Negative values substituted into expressions must be wrapped in parentheses (e.g., substitute x = -3 as (-3))
- The final answer must be a single number, fully simplified
Evaluate 3x² - 2y + 5 when x = -2 and y = 4
Substitute to get 3(-2)² - 2(4) + 5. Handle the exponent first: (-2)² = 4, so the expression becomes 3(4) - 2(4) + 5 = 12 - 8 + 5. Finally, add and subtract left to right to get 9.
2 Combining Like Terms
Like terms have identical variable parts (same variable raised to the same power) and can be combined by adding or subtracting their coefficients. Students must be able to identify like terms across a multi-term expression and simplify completely. Unlike terms (e.g., 3x and 3x²) cannot be combined.
Key Points
- Like terms must match exactly in variable and exponent (e.g., 4x² and -x² are like terms; 4x² and 4x are not)
- Only the coefficients are added or subtracted — the variable part stays the same
- Constants (plain numbers) are like terms with each other
- Rearranging terms to group like terms first helps avoid errors on longer expressions
Simplify: 5x² - 3x + 7 + 2x² + 6x - 4
Group like terms: (5x² + 2x²) + (-3x + 6x) + (7 - 4). Combine each group by adding coefficients: 7x² + 3x + 3. The variable parts remain unchanged.
3 Distributive Property
The distributive property states that a(b + c) = ab + ac — the term outside the parentheses multiplies every term inside. Students must apply it correctly with negative multipliers and then combine any resulting like terms. Forgetting to distribute to all terms inside the parentheses is the most tested error.
Key Points
- Multiply the outside factor by EVERY term inside the parentheses, not just the first
- A negative outside factor flips the sign of every term inside: -3(2x - 5) = -6x + 15
- After distributing, always check whether like terms can be combined
- Distributing is often the first step before combining like terms in multi-step problems
Simplify: 4(2x - 3) + 5x
Distribute the 4: 4(2x) - 4(3) + 5x = 8x - 12 + 5x. Then combine like terms (8x + 5x): the simplified result is 13x - 12.
Questions, answered.
What is Variables and Expressions?
Variables and Expressions is Unit 5 of Pre-Algebra, covering evaluating expressions, combining like terms and distributive property.
How to study for Pre-Algebra Unit 5?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 25+ review questions across 5 different game modes.