Question

what is the quotient of 5/18 divided by 5/12

Answer 1

Having this:
\[\frac{ \frac{ 5 }{ 18 } }{ \frac{ 5 }{ 12 } }\]
or for more gentle looking:
\[\frac{ 5 }{ 18 }\div \frac{ 5 }{ 12 }\]
Now there's a little trick in algebra, for fractionary divisions, let's take a look at it:
\[\frac{ a }{ b } \div \frac{ c }{ d } = \frac{ a }{ b }\times \frac{ d }{ c }\]
Now, what does it mean?
Well, it means I cant transform the division sign to a multiplication sign, if I switch places on the second fractions... Let's try that:
\[\frac{ 5 }{ 18 }\div \frac{ 5 }{ 12 }=\frac{ 5 }{ 18 }\times \frac{ 12 }{ 5 }\]
Now, let's take a look at the fractionary multiplication:
\[\frac{ a }{ b }\times \frac{ c }{ d }=\frac{ ac }{ bd }\]
It only means that you multiply the numbers above, and the numbers below all together.
Let's apply that:
\[\frac{ 5 }{ 18 }\times \frac{ 12 }{ 5 }=\frac{ (5)(12) }{ (18)(5) }\]
All we have to do now is multiply :)
\[\frac{ (5)(12) }{ (18)(5) }=\frac{ 60 }{ 90 }\]
And there we got it :)
That fractions can be simplified yes, but I'll leave that to you.