Question

How do you solve `40/56=k/7`?

Answer 1

`k=5`

Explanation:

To eliminate the fractions, multiply both sides of the equation by the `color(blue)"lowest common multiple "( LCM)` of 56 and 7

multiply both sides by 56

`cancel(56)^1xx40/cancel(56)^1=cancel(56)^8xxk/cancel(7)^1`

`rArr40=8k`

To solve for k, divide both sides by 8

`40/8=(cancel(8) k)/cancel(8)`

`rArrk=5" is the solution"`

`color(blue)"Note"` the fraction on the left side can be simplified by dividing the numerator/denominator by 8

`40/56=k/7`

`rArrcancel(40)^5/cancel(56)^7=k/7`

Since the fractions are equal then k = 5