Question

How do you solve `\frac { 8f + 11} { 8} = \frac { 1} { 6}`?

Answer 1

This can be easily be done using cross multiplication

`(8f + 11)/8 = 1/6`

Multiply the left numerator by the right denominator and set it equal to the right numerator times the left denominator.
top left * bottom right = top right * bottom left, like this:

`(8f + 11) * (6) = (1) * (8)`

Before we multiply out, we can see that both 6 and 8 are divisible by 2, so we can divide both sides by 2 to save us some time.

`(8f + 11) * (3) = (1) * (4)`

Multiply out:

`24f + 33 = 4`

Subtract both sides by 33 to get the `f` terms alone on the left side:

`24f + 33 - (33) = 4 - (33)`
`24f = - 29`

Divide both sides by 24 to get `f` alone on the left side:

`(24f)/24 = -29/(24)`
`f = -29/24`

That fraction can't be reduced, so you're done. If you want to check your answer, you can always plug it back in to the original equation.