Master Algebraic Properties
Practice Commutative, Associative, and Distributive properties with negative integers. Build speed, accuracy, and deep algebraic intuition!
Property Identification
Examine an equation with negative numbers and identify which algebraic property is applied.
Fill in Missing Values
Use algebraic properties to find the missing integer or term that makes the statement true.
Simplify & Expand
Apply the distributive property with negative terms (e.g., expand -3(x - 4) or evaluate).
Mixed Master Challenge
Test all properties, integer operations, and problem types in a high-velocity challenge.
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Step-by-Step Explanation:
Algebraic Properties Reference
1. Commutative Property (Change Order)
Changing the order of terms does not change the result.
- Addition: a + b = b + a | e.g. -5 + 8 = 8 + (-5)
- Multiplication: a · b = b · a | e.g. -3 · (-4) = -4 · (-3)
2. Associative Property (Change Grouping)
Changing the grouping of terms (parentheses) does not change the result.
- Addition: (a + b) + c = a + (b + c)
- Multiplication: (a · b) · c = a · (b · c)
3. Distributive Property
Multiply the outside term by every term inside the parentheses.
- Formula: a(b + c) = ab + ac
- With Negatives: -2(x - 4) = -2x + 8