To solve, we must turn the division problem into a multiplication problem by "flipping" the second fraction (dividing by a fraction is the same as multiplying by its reciprocal):

 \(\displaystyle \frac{5}{3}\div\frac{7}{6}=\frac{5}{3}\cdot\frac{6}{7}\).

Then, we multiply the numerators followed by the denomenators:

 \(\displaystyle \frac{5\cdot6}{3\cdot7}=\frac{30}{21}\).

Lastly, the fraction must be simplified by a factor of 3: 

\(\displaystyle \frac{30}{21}=\frac{10}{7}\), which gives us our final answer. 

Change all the fractions to improper fractions.

\(\displaystyle \frac{7}{6}\div 2\frac{3}{8}=\frac{7}{6}\div \frac{19}{8}\)

Convert the division sign to a multiplication sign, but flip the second term.  Simplify.

\(\displaystyle \frac{7}{6}\times \frac{8}{19}= \frac{7}{3}\times \frac{4}{19}= \frac{28}{57}\)

Multiplying fractions is a two-step process. First, you must flip the second fraction (make it its reciprocal) and then set up the equation as a multiplication problem:

\(\displaystyle \frac{2}{11}\cdot \frac{22}{}9\).

Then, cross-reduce: 11 goes into both 11 and 22, so you can take that out so it looks like:

\(\displaystyle \frac{2}{1}\cdot \frac{2}{9}\).

Then, multiply straight across so that you get \(\displaystyle \frac{4}{}9\).

You can't simplify any further, so that's your answer!

When dividing fractions, first we need to flip the second fraction. Then multiply the numerators together and multiply the denominators together:

\(\displaystyle \frac{15}{30}\div15=\frac{15}{30}*\frac{1}{15}=\frac{15*1}{30*15}\)

Simplify the fraction to get the final answer:

\(\displaystyle \frac{15*1}{30*15}=\frac{1}{30}\)

When dividing fractions, first we need to flip the second fraction. Then multiply the numerators together and multiply the denominators together:

\(\displaystyle \frac{8}{56}\div \frac{1}{8}=\frac{8}{56}*{8}=\frac{8*8}{56}=\frac{64}{56}\)

Simplify the fraction to get the final answer:

\(\displaystyle \frac{64}{56}\div \frac{8}{8}=\frac{8}{7}=1\frac{1}{7}\)

When dividing fractions, first we need to flip the second fraction. Then multiply the numerators together and multiply the denominators together:

\(\displaystyle \frac{36}{16}\div \frac{3}{2}=\frac{36}{16}* \frac{2}{3}=\frac{36*2}{16*3}=\frac{72}{48}\)

Simplify the fraction to get the final answer:

\(\displaystyle \frac{72}{48}\div \frac{12}{12}=\frac{6}{4}\div \frac{2}{2}=\frac{3}{2}=1\frac{1}{2}\)

When dividing fractions, first we need to flip the second fraction. Then multiply the numerators together and multiply the denominators together:

\(\displaystyle \frac{12}{54}\div6=\frac{12}{54}*\frac{1}{6}=\frac{12*1}{54*6}=\frac{12}{324}\)

Simplify the fraction to get the final answer:

\(\displaystyle \frac{12}{324}\div \frac{12}{12}=\frac{1}{27}\)

The correct answer is \(\displaystyle \frac{2}{3}\). 

In order to start solving this problem, we need to get each term to have a common denominator. 

The common denominator between 2 and 6 is 6. We can rewrite the expression and solve using the following method: 

\(\displaystyle \frac{1}{2}+\frac{1}{6} = \frac{3}{6}+\frac{1}{6} = \frac{4}{6} = \frac{2}{3}\)

1. Find the least common denominator:

The lowest number that both 4 and 6 can go into is 12 meaning that it is the least common denominator.

2. Use the new least common denominator to create two equivalent fractions with a denominator of 12.

\(\displaystyle (\frac{3}{4})(\frac{3}{3})=\frac{9}{12}\)

\(\displaystyle (\frac{5}{6})(\frac{2}{2})=\frac{10}{12}\)

3. Add the two fractions together.

\(\displaystyle \frac{9}{12}+\frac{10}{12}=\frac{19}{12}\)

4. Convert the fraction to a mixed number:

\(\displaystyle \frac{19}{12}=1 \frac{7}{12}\)

In fractions, to add or subtract the numerator, the denominators must be equal.

Find the least common denominator, multiply the top and bottom with what was multiplied on the denominator, and simplify.

\(\displaystyle -\frac{6}{5}+\frac{5}{6} = -\frac{6\cdot6}{5\cdot6}+\frac{5\cdot5}{6\cdot5}=-\frac{36}{30}+\frac{25}{30}\)

=\(\displaystyle -\frac{11}{30}\)