[tex]\mathrm{Simplify} -\frac{3}2\div\frac{9}6.[/tex]
Dividing by a fraction is the same as multiplying by its reciprocal. (flipped version)
[tex]-\frac{3}2\div\frac{9}6=-\frac{3}2\times\frac{6}{9}[/tex]
6 and 9 are both divisible by 3, so we can simplify 6/9 = 2/3.
[tex]-\frac{3}2\times\frac{2}3[/tex]
We can multiply across right now, but we might as well cross cancel.
Look at the numbers diagonal from one another...-3 and 3 are both divisible by 3, so we can change them to -1 and 1...2 and 2 are both divisible by 2, so we can change them to 1 and 1...
[tex]-\frac{1}1\times\frac{1}1[/tex]
Any fraction over 1 can just be expressed as a whole number.
[tex]-1\times1[/tex]
Our final answer...[tex]-\frac{3}2\div\frac{9}6=\boxed{-1}[/tex]
If you were to multiply across, (maybe you don't like cross cancelling, idk?) you'd get the same answer, of course.
[tex]-\frac{3}2\times\frac{2}3=-\frac{6}6=\boxed{-1}[/tex]
