Question

How do you solve `10/k=8/4`?

Answer 1

`k=5`

Explanation:

We have one fraction equal to another. In this situation we can `color(blue)"cross-multiply"` to solve.

`rArrcolor(blue)(10)/color(red)(k)=color(red)(8)/color(blue)(4)`

Now cross-multiply(X) the values on either end of an 'imaginary' cross and equate them. That is multiply the `color(blue)"blue"` values together and the `color(red)"red"` values together and equate them.

`rArrcolor(red)(8k)=(color(blue)(10)xxcolor(blue)(4))rArr8k=40`

now divide both sides by 8 to solve for k.

`rArr(cancel(8)^1 k)/cancel(8)^1=(cancel(40)^5)/cancel(8)^1rArrk=5`