# How do you define a variable and write an expression for each phrase: a number decreased by three-fourths of the number?

Apr 16, 2016

$n - \frac{3 n}{4}$ (which can be simplified to $\frac{n}{4}$)

#### Explanation:

A variable is just anything in the question that we don't know, and in most questions we try to find out its value.

For this question, the variable is the 'number', which we'll call $n$.

Now we can convert the word question into an equation bit by bit:

A number decreased by three-fourths of the number =
$n - \left(n \cdot \frac{3}{4}\right)$
=$n - \frac{3 n}{4}$ , and this is the expression for the question.

However, we can simplify this:
$= \frac{4 n}{4} - \frac{3 n}{4}$
$= \frac{n}{4}$