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

Aug 11, 2016

$x - \frac{1}{3} x$

#### Explanation:

We are working with an unknown number and we need to call it something.

$\text{Let the number be x}$

The word DIFFERENCE is an indication that we must subtract, to find out by how much one number is bigger than another number.

DIFFERENCE is always used with the word AND, telling us which two numbers we need to subtract.

The numbers we are working with are $x$ and $\text{one third of x}$

"One third of" , means the number, divided by 3.
It can be written as $\frac{1}{3} x , \mathmr{and} \frac{1 x}{3} , \mathmr{and} \frac{x}{3}$

The expression is: $x - \frac{1}{3} x$