Question

How do you translate “the quotient of a number \[N\] and 4” into an algebraic expression?

Answer 1

Hint:Here we will use the concept of an algebraic expression and the quantities involved in an algebraic expression. Using these definitions, we will find the algebraic expression that can be used to express the quotient of \[N\] and 4.

Complete step by step solution:
An algebraic expression is a mathematical expression that is made up of quantities called “variables” and “constants” which are joined together using mathematical operations such as addition, subtraction, multiplication, and division.
The variables are those quantities whose values are not fixed. They take up values depending on the expression in which they appear. We use lowercase alphabets to denote variables.
Examples: \[x,y,z\]
On the other hand, constants are those quantities whose values are fixed. They do not change their values in any circumstance.
Examples: \[ - 3,0,15\]
Examples of algebraic expressions include \[x + 2y\], \[\dfrac{{ - 3}}{x} + 2\].
We can express \[x + 2y\] in words as “\[x\] is added to two times \[y\]”. Also, we can express \[\dfrac{{ - 3}}{x} + 2\] in words as “2 is added to the quotient of \[ - 3\] and \[x\]”.
We can also use algebraic expressions to form equations. Equations are mathematical expressions in which an algebraic expression is assigned a value.
Example: \[x + 2y = 5\]. In this equation, the sum of \[x\] and \[2y\] is equal to 5.
Now, we are required to find the algebraic expression which denotes the quotient of \[N\] and 4.
The quotient is the result obtained on division.
So, we have to find the expression of division of \[N\] and 4.
We can write this as
\[\dfrac{N}{4}\] or \[\dfrac{4}{N}\]
Since the value of \[N\] is not known, we cannot simplify the expression further.

Note:
When dealing with such problems, care should be taken to write the correct mathematical operations. The term “quotient” means the result of the division. Similarly, the terms “sum”, “difference”, and “product” are used to denote addition, subtraction, and multiplication respectively. Here \[N\] is the variable and 4 is the constant. If we equate an expression to 0 then it becomes an equation. The above expression has only 1 variable, so we can say that it is a linear expression.