Question

How do you define a variable and write an expression for the phrase: the difference between a number and one-third of a number?

Answer 1

Hint: The given question has two parts: firstly, define variables. Secondly, write an expression from the given words. Assume a number and then, find its one third. Subtract both of them and finally we get the required answer.

Complete step-by-step solution:
In the first part of the question, we have to define a variable.
Let us see what a variable is.
In mathematics, a variable is a symbol which does not have any particular value, but it can have any value.
Basically, it functions as a placeholder for varying quantities.
Now, let us move towards the second part of the question.
In this part, we are given a phrase and we have to convert it into an equation.
The phrase goes like: the difference between a number and one-third of a number.
Since we are not given any number, let us assume our number as $n$.
One third of our number, $n = \dfrac{1}{3}n$
Now, we have to find the difference between the two and we can write it as,
$ \Rightarrow n - \dfrac{1}{3}n$
Hence, the required answer is $n - \dfrac{1}{3}n$.

Note: A constant is a symbol whose value cannot change ever. As the name implies, its value remains constant. On the other hand, a variable is a symbol whose value keeps on changing as per the given conditions.
Constants and variables, together with mathematical symbols, make up an equation or expression.
If the mixture of constants and variables has a sign of ‘equal to’, then it is an equation. If it does not have, then it is an expression.