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

Feb 8, 2016

$\frac{1}{2} n + \frac{3}{4} n$

#### Explanation:

Definition
Let $n$ be a variable representing "a number"

Writing the Expression
"one-half of a number" means we need to multiply the number by $\frac{1}{2}$
$\textcolor{w h i t e}{\text{XXX}} \frac{1}{2} \times n$

"three fourths of a number" means we have to multiply the number by $\frac{3}{4}$
$\textcolor{w h i t e}{\text{XXX}} \frac{3}{4} \times n$

"the sum of " something "and" something-else means that we have to add the two thing together
$\textcolor{w h i t e}{\text{XXX}} = \left(\frac{1}{2} \times n\right) + \left(\frac{3}{4} \times n\right)$

Note that the multiplication symbol ($\times$) is typically omitted and simply assumed by default.