# Properties of One

Pronunciation: /ˈpɹɑp.ər.tiz ʌv wʌn/ Explain

The number 1 has several important properties that are useful in algebra. Table 1 gives these properties.

PropertyDescriptionEquationMore Information
Multiplication by 1 Anything times one equals itself. a · 1 = 1 · a = a Property of Multiplication by 1
Division by 1 Anything divided by one remains unchanged. a / 1 = a Property of Division by 1
Exponent of 1 Any number raised to the power of 1 equals itself. a1 = anone
Idempotence1 is idempotent under multiplication and exponentiation. 1 · 1 = 1, 11 = 1 Idempotence
Table 1: Properties of one.

### Cite this article as:

McAdams, David E. Properties of One. 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/p/propertiesofone.html.

### Revision History

1/5/2019: Corrected copy error. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/1/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
3/5/2010: Initial version. (McAdams, David E.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2018 Life is a Story Problem LLC. All rights reserved.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License