# How do you translate "the product of 3 and x divided by the sum of x and y" into an algebraic expression?

Mar 22, 2018

$\frac{3 \cdot x}{x + y}$

#### Explanation:

The product of 3 and x divided by the sum of x and y is

$\frac{P r o \mathrm{du} c t o f 3 \mathmr{and} x}{S u m o f x \mathmr{and} y}$.

Okay break it into smaller parts. The product of $3 \mathmr{and} x$ is $3 \cdot x$ um of $x \mathmr{and} y$ is $x + y$

Now, we get

$\frac{3 \cdot x}{x + y}$

and that's it

Mar 22, 2018

$\frac{3 x}{x + y}$

#### Explanation:

$\textcolor{b l u e}{\text{Before we start have a think about this}}$

Although not normally done you can write whole number in fraction format.

Example:
Consider the numbers color(white)("ddd...")1,color(white)(".")2,color(white)("d")3,color(white)("d")4,color(white)("d")5" and so on"

You may if you chose write $\textcolor{w h i t e}{.} \frac{1}{1} , \frac{2}{1} , \frac{3}{1} , \frac{4}{1} , \frac{5}{1} \text{ and so on.}$

I will be using this.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Answering the question}}$
The product of 3 and x: $\textcolor{w h i t e}{\text{d")............color(white)("d") 3xx x ->color(white)("d}} 3 x$
divided by: color(white)("d")........................................->color(white)("d")3x-:?
The sum : color(white)("d").........................................->color(white)("d")3x-:(?+?)
of $x \mathmr{and} y : \textcolor{w h i t e}{\text{d")......................................->color(white)("d}} 3 x \div \left(x + y\right)$

This is the same as $\textcolor{w h i t e}{\text{d}} 3 x \div \frac{x + y}{1}$

Turn the $\frac{x + y}{1}$ upside down and change the sign from divide to multiply.

$3 x \times \frac{1}{x + y} \to \frac{3 x}{x + y}$