Question

How do you find the product of `(10n^2)/4*2/n`?

Answer 1

`5n`

Explanation:

`(10n^2)/4xx2/n=(20n^2)/(4n)=(cancel((4n))5n)/cancel(4n)=5n`

Answer 2

`5n`

Explanation:

There are 2 approaches here. We could `color(blue)"simplify"` the fractions and then multiply what remains or we can multiply the fractions and then `color(blue)"simplify"`

`color(red)"Simplify and multiply"`

To simplify we `color(blue)"cancel"` common factors between the numerators/denominators.
Here we can cancel 10 and 4 by 2 or 4 and 2 by 2. `n^2` and n have a common factor of n.

`rArr(cancel(10)^5 xxnxxcancel(n)^1)/cancel(4)^2xx2/cancel(n)^1`

`=(5nxx2)/2=(5nxxcancel(2)^1)/cancel(2)^1=5n`

`color(red)"multiply and simplify"`

`(10n^2)/4xx2/n=(10n^2xx2)/(4n)=(20n^2)/(4n)`

now simplify by cancelling.

`=(cancel(20)^5xxnxxcancel(n)^1)/(cancel(4)^1cancel(n)^1)=5n`