Question

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

Answer 1

`(3*x)/(x+y)`

Explanation:

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

`(Product of 3 and x)/(Sum of x and y)`.

Okay break it into smaller parts. The product of `3 and x` is `3*x` um of `x and y` is `x+y`

Now, we get

`(3*x)/(x+y)`

and that's it

Answer 2

`(3x)/(x+y)`

Explanation:

`color(blue)("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 `color(white)(.) 1/1,2/1,3/1,4/1,5/1" and so on."`

I will be using this.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`
The product of 3 and x: `color(white)("d")............color(white)("d") 3xx x ->color(white)("d")3x`
divided by: `color(white)("d")........................................->color(white)("d")3x-:?`
The sum : `color(white)("d").........................................->color(white)("d")3x-:(?+?)`
of `x and y: color(white)("d")......................................->color(white)("d")3x-:(x+y)`

This is the same as `color(white)("d")3x -:(x+y)/1`

Turn the `(x+y)/1` upside down and change the sign from divide to multiply.

`3x xx1/(x+y ) -> (3x)/(x+y)`