# knowledge_items

id: algebra_simplify_001
skill: algebra_simplification
prerequisite_skills: ["basic_arithmetic", "variables"]
created_at: 2025-11-02 05:59:20
content:
To simplify algebraic expressions, combine like terms by adding or subtracting coefficients of the same variable. For example, 3x + 2x = 5x.

facts:
["Like terms have the same variable raised to the same power", "Coefficients of like terms can be combined through addition", "The variable part remains unchanged when combining like terms"]


id: algebra_simplify_002
skill: algebra_simplification
prerequisite_skills: ["algebra_simplification", "division"]
created_at: 2025-11-02 05:59:20
content:
When simplifying expressions with division, first combine like terms in the numerator, then divide by the denominator. Example: (3x + 2x) / 5 = 5x / 5 = x.

facts:
["Division applies to the entire expression", "Simplify numerator before dividing", "A term divided by itself equals 1"]


id: linear_eq_001
skill: linear_equations
prerequisite_skills: ["algebra_simplification"]
created_at: 2025-11-02 05:59:20
content:
To solve linear equations, isolate the variable by performing inverse operations. Add/subtract to isolate the variable term, then multiply/divide to solve for the variable.

facts:
["Inverse operations undo each other (addition \u2194 subtraction, multiplication \u2194 division)", "Apply the same operation to both sides to maintain equality", "Goal is to isolate the variable on one side"]


id: fraction_div_001
skill: fraction_operations
prerequisite_skills: ["fraction_multiplication"]
created_at: 2025-11-02 05:59:20
content:
To divide fractions, multiply by the reciprocal of the second fraction. The reciprocal of a/b is b/a.

facts:
["Division is equivalent to multiplication by the reciprocal", "Reciprocal flips numerator and denominator", "Multiply numerators together and denominators together"]


id: ratio_001
skill: ratios
prerequisite_skills: ["proportions"]
created_at: 2025-11-02 05:59:20
content:
Ratios compare quantities. To solve ratio problems, set up proportions and cross-multiply. a:b = c:d means a×d = b×c.

facts:
["Ratios show relative sizes of quantities", "Equivalent ratios have the same value when simplified", "Cross-multiplication solves proportion equations"]


