Final answer:
The algebraic expression for 'one-fourth of a number' is written as n/4, where n represents the number in question and the '/' denotes division.
Step-by-step explanation:
To write an algebraic expression for the English phrase 'one-fourth of a number', where the number is represented by the variable n, we use multiplication to signify the 'one-fourth' part.
In algebra, 'one-fourth of a number' can be represented as 1/4 * n or simply n/4. This means you take the number n and divide it by 4. In the realm of mathematical operations, multiplication by a fraction such as 1/4 is equivalent to dividing the number by the denominator of that fraction. Therefore, if you have a number n and you want one-fourth of it, you divide it by 4 to obtain your answer.
Remember that in algebra, when we talk about 'a number', we typically use variables to represent these unknown or general numbers. The variable n is commonly used to denote any number, and thus when we say one-fourth of n, we apply the operation of division because a fourth is the same as dividing by 4.