By Mary Pletcher | Updated Aug 30, 2022
The basic properties of real numbers—including the associative, commutative, identity, inverse, and distributive properties—form the foundation of addition and multiplication. Mastering them also paves the way into algebra. By memorizing the name of each property and its meaning, you can confidently tackle a wide array of mathematical challenges.
Associate the associative property with the word "associate." It explains how you can group numbers or variables in different ways when adding or multiplying without affecting the outcome. For example, (2+3)+4 = 2+(3+4).
Connect the commutative property to the idea of commuting or traveling. This property states that the order of numbers or variables in addition or multiplication does not change the result. 3+4 = 4+3, and 5×6 = 6×5.
Remember that the identity property leaves a number unchanged when combined with another number. In addition, the identity is 0, because any number plus zero remains the same. In multiplication, the identity is 1, so any number times one stays the same.
Use the concept of reversal to recall the inverse property. For addition, every number x has an additive inverse –x such that x + (–x) = 0. For multiplication, each non‑zero number x has a multiplicative inverse 1/x because x × (1/x) = 1.
Think of distributing or handing out a factor across a group to remember the distributive property. For instance, 2(x + y) becomes 2x + 2y after distribution.
With these mnemonic anchors, you’ll find it easier to identify and apply each property whenever you encounter it in algebraic work.
