Properties in Practice

Algebra 1 · Axiom Academy

The five fundamental rules that govern algebra — each with a precise statement and a transform you can watch. The order in which you add or multiply two numbers does not change the result. Think of the numbers as being able to "commute" — to travel past each other. This property is about grouping . When you add or multiply three or more numbers, the way you group them — which pair "associates" first — has no effect on the final answer. This property links multiplication and addition . Multiplying a number by a sum is the same as multiplying it by each term and adding the results — you "distribute" the multiplier across the parentheses. An identity is a number that leaves every other number unchanged under an operation. For addition that number is 0 ; for multiplication it is 1 . They preserve the "identity" of whatever they touch. An inverse is a number's partner that returns the identity. For addition, the partner of a number is its opposite (additive inverse); for multiplication, its reciprocal (multiplicative inverse). 6. The Five Properties at a Glance Five properties — the complete rulebook for rearranging expressions without changing their value. Watch them assemble, then keep the sheet below. Commutative : order doesn't matter for + and ×. Associative : grouping doesn't matter for + and ×. Distributive : multiplication spreads across a sum. Identity : 0 (for +) and 1 (for ×) change nothing. Inverse : opposites return 0; reciprocals return 1.

This is the written version of the interactive lesson above. See the full Algebra 1 course.