Answer:
[tex]\frac{\frac{8}{9} - \frac{5}{6} }{\frac{1}{6} }[/tex] = [tex]\frac{1}{3}[/tex]
Explanation:
There is two ways of doing this problem. I will show both ways.
Solving Problem (First way):
First, let's find a common denominator between [tex]\frac{8}{9}[/tex] and -[tex]\frac{5}{6}[/tex].
They both can multiply to 36, so that is their (least) common denominator.
Multiply each fraction by the amount it would take to get to 36.
[tex]\frac{8}{9}[/tex] [tex]* \frac{4}{4}[/tex] = [tex]\frac{32}{36}[/tex] and - [tex]\frac{5}{6}[/tex] * [tex]\frac{6}{6}[/tex] = -[tex]\frac{30}{36}[/tex]
Now, add these two together:
[tex]\frac{32}{36}[/tex] - [tex]\frac{30}{36}[/tex] = [tex]\frac{2}{36}[/tex]
This reduces down to [tex]\frac{1}{18}[/tex].
[tex]\frac{1}{18}[/tex] divided by [tex]\frac{1}{6}[/tex] is the same as
This is equal to [tex]\frac{6}{18}[/tex], which reduces down to [tex]\frac{1}{3}[/tex].
Solving Problem (Second way):
[tex]\frac{\frac{8}{9} - \frac{5}{6} }{\frac{1}{6} }[/tex] is the same as saying [tex]\frac{\frac{8}{9} }{\frac{1}{6} }[/tex] and [tex]\frac{-\frac{5}{6} }{\frac{1}{6} }[/tex].
These are being divided by [tex]\frac{1}{6}[/tex], which is the same as multiplying b 6.
The values should now look like this:
[tex]\frac{16}{3}[/tex] - [tex]5[/tex].
(If you want the same denominator, convert 5 into parts of 3, so [tex]\frac{15}{3}[/tex])
When you add these together, you get [tex]\frac{1}{3}[/tex].
I hope this helps!!
