# How do you define a variable and write an expression for each phrase: 5 increased by the quotient of 4 and 5?

Jun 17, 2017

See a solution process below:

#### Explanation:

First, let's call the result we are looking for as $n$:

Quotient means to divide. Therefore:

"the quotient of 4 and 5" can be written as:

$4 \div 5$ or $\frac{4}{5}$

We can now add this to "5 increased by" which means to add:

$n = 5 + \frac{4}{5}$

We can solve this as follows:

$n = 5 + \frac{4}{5}$

$n = \left(\frac{5}{5} \times 5\right) + \frac{4}{5}$

$n = \frac{25}{5} + \frac{4}{5}$

$n = \frac{25 + 4}{5}$

$n = \frac{29}{5}$