Algebra 1 Unit 1 study games — Foundations of Algebra.
This unit covers real number properties, order of operations and variables and expressions — essential concepts for Algebra 1. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers real number properties, order of operations and variables and expressions — essential concepts for Algebra 1. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Real Number Properties
Students must know the commutative, associative, distributive, identity, and inverse properties by name and be able to identify which property justifies a given step. Exams frequently ask students to name the property used in an equation or to apply a property to simplify an expression. The distributive property is the most tested and appears in nearly every unit.
Key Points
- Commutative: a + b = b + a and a × b = b × a (order changes, result does not)
- Associative: (a + b) + c = a + (b + c) (grouping changes, result does not)
- Distributive: a(b + c) = ab + ac (multiply the outside term by each inside term)
- Identity: a + 0 = a and a × 1 = a; Inverse: a + (−a) = 0 and a × (1/a) = 1
Which property justifies the step: 3(x + 4) = 3x + 12?
The term outside the parentheses, 3, is being multiplied by each term inside: 3 · x = 3x and 3 · 4 = 12. This is the Distributive Property. No other property involves multiplying a single term across a sum or difference.
2 Order Of Operations
Students must evaluate expressions by following PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right). Exams test whether students incorrectly add before multiplying or mishandle division and subtraction when they appear together. Absolute value bars and fraction bars act as grouping symbols and must be simplified before applying other operations.
Key Points
- Grouping symbols (parentheses, brackets, fraction bars, absolute value) are always simplified first
- Multiplication and division have equal priority — work left to right, do not always multiply first
- Addition and subtraction have equal priority — work left to right
- Exponents are applied before any multiplication, division, addition, or subtraction outside a grouping symbol
Evaluate: 3 + 2² × (8 − 5) ÷ 6
First, simplify the parentheses: 8 − 5 = 3, giving 3 + 2² × 3 ÷ 6. Next, apply the exponent: 2² = 4, giving 3 + 4 × 3 ÷ 6. Then multiply and divide left to right: 4 × 3 = 12, then 12 ÷ 6 = 2, giving 3 + 2. Finally, add: the answer is 5.
3 Variables And Expressions
Students must be able to translate between written English phrases and algebraic expressions, identify terms, coefficients, and constants, and simplify expressions by combining like terms. Exams test translation (e.g., 'five less than twice a number') and simplification of multi-term expressions. Like terms must share the same variable raised to the same exponent — only the coefficients are added or subtracted.
Key Points
- A term is a number, variable, or product of both; terms are separated by + or − signs
- The coefficient is the numerical factor of a term (in −7x, the coefficient is −7)
- Like terms have identical variable parts; combine them by adding/subtracting coefficients only
- Key phrase translations: 'less than' reverses order (5 less than x = x − 5), 'quotient of' means division, 'product of' means multiplication
Simplify: 4x² + 3x − x² + 7 − 2x
Group like terms: x² terms are 4x² and −x², combining to 3x². The x terms are 3x and −2x, combining to x. The constant 7 has no like term. Writing the simplified expression in standard form gives 3x² + x + 7.
Questions, answered.
What is Foundations of Algebra?
Foundations of Algebra is Unit 1 of Algebra 1, covering real number properties, order of operations and variables and expressions.
How to study for Algebra 1 Unit 1?
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.