# How do you define a variable and write an expression for each phrase: nine times the quotient of a number and three?

Jul 28, 2016

$9 \times \left(x \div 3\right) = 9 \times \frac{x}{3} = \frac{9 \times x}{3}$

#### Explanation:

In algebra we can work with numbers even if we do not know their exact value.

WE can always just call a number $x , \mathmr{and} y , \mathmr{and} a , \mathmr{and} b$

This is called defining the variable.

In this question where a number is being referred to, let's call the number "x".

Let the number be $x$

The word "quotient" means the answer to a division and is always used with the word "AND".

The QUOTIENT of $15 \mathmr{and} \text{3 is 5 because } \frac{15}{3} = 5$.

"nine times the quotient of a number and three" means

Muliply 9 by the answer to our number (x), divided by 3.

$9 \times \left(x \div 3\right)$

OR $9 \times \frac{x}{3}$