To divide, we will follow these steps:

1. Write any whole number as a fraction.
2. Keep the first fraction as is.
3. Change the division sign to a multiplication sign.
4. Replace the second fraction with it's reciprocal.
5. Multiply.

Now, we will follow those steps for the problem

\(\displaystyle 6 \div \frac{1}{3}\)

1. We will write all whole numbers as fractions.  So the number 6 can be written as a fraction.  We know that any whole number can be written over 1.  So,
   
   \(\displaystyle \frac{6}{1} \div \frac{1}{3}\)
   
   
2. Now, we will keep the first fraction the way it is.  We get
   
   \(\displaystyle \frac{6}{1} \div \frac{1}{3}\)
   
   
3. Now, we will change the division sign to a multiplication sign. We get
   
   \(\displaystyle \frac{6}{1} \cdot \frac{1}{3}\)
   
   
4. Now, we will replace the second fraction with it's reciprocal.  To do that, the numerator will become the denominator, and the denominator will become the numerator.  In other words, we will flip the fraction.  We get
   
   \(\displaystyle \frac{6}{1} \cdot \frac{3}{1}\)
   
   
5. Now, we will multiply straight across. We get
   
   \(\displaystyle \frac{6 \cdot 3}{1 \cdot 1}\)
   
   \(\displaystyle \frac{18}{1}\)
   
   \(\displaystyle 18\)

Therefore, \(\displaystyle 6 \div \frac{1}{3} = 18\)

To divide fractions, use the following steps:

1. Leave the first fraction alone.
2. Change the division sign to a multiplication sign.
3. Replace the second fraction with it's reciprocal.
4. Multiply.

So, given the problem

\(\displaystyle \frac{4}{5} \div \frac{1}{5}\)

we will follow the steps.

1. Leave the first fraction alone.
   
   \(\displaystyle \frac{4}{5} \div \frac{1}{5}\)
   
   
2. Change the division sign to a multiplication sign.
   
   \(\displaystyle \frac{4}{5} \cdot \frac{1}{5}\)
   
   
3. Replace the second fraction with it's reciprocal.  To write the reciprocal of a fraction, the numerator will become the denominator, and the denominator will become the numerator.  In other words, we will flip the fraction.  
   
   \(\displaystyle \frac{4}{5} \cdot \frac{5}{1}\)
   
   
4. Multiply. To multiply, we will multiply straight across.  We get
   
   \(\displaystyle \frac{4 \cdot 5}{5 \cdot 1}\)
   
   \(\displaystyle \frac{20}{5}\)
   
   \(\displaystyle 4\)

To divide fractions, follow these steps:

1. Leave the first fraction alone.
2. Change the division sign to a multiplication sign.
3. Replace the second fraction with it's reciprocal.
4. Multiply.

So, given the problem

\(\displaystyle 10 \div \frac{1}{2}\)

we will follow the steps.

1. Leave the first fraction alone.  In this case, we need to write 10 as a fraction.  We know that whole numbers can be written as fractions over 1.  So, we get
   
   \(\displaystyle \frac{10}{1} \div \frac{1}{2}\)
   
   
2. Change the division sign to a multiplication sign.
   
   \(\displaystyle \frac{10}{1} \cdot \frac{1}{2}\)
   
   
3. Replace the second fraction with it's reciprocal.  To write the reciprocal, the numerator becomes the denominator, and the denominator becomes the numerator.  In other words, we will flip the second fraction.
   
   \(\displaystyle \frac{10}{1} \cdot \frac{2}{1}\)
   
   
4. Multiply.  We will multiply straight across.
   
   \(\displaystyle \frac{10 \cdot 2}{1 \cdot 1}\)
   
   \(\displaystyle \frac{20}{1}\)
   
   \(\displaystyle 20\)

To divide fractions, we will use the following steps:

1. Leave the first fraction alone.
2. Change the division sign to a multiplication sign.
3. Replace the second fraction with it's reciprocal.
4. Multiply.

So, given the problem

\(\displaystyle \frac{3}{4} \div \frac{1}{2}\)

we will follow the steps:

1. Leave the first fraction alone.
   
   \(\displaystyle \frac{3}{4} \div \frac{1}{2}\)
   
   
2. Change the division sign to a multiplication sign.
   
   \(\displaystyle \frac{3}{4} \cdot \frac{1}{2}\)
   
   
3. Replace the second fraction with it's reciprocal.  To find the reciprocal, the numerator becomes the denominator, and the denominator becomes the numerator.  In other words, we will flip the fraction.
   
   \(\displaystyle \frac{3}{4} \cdot \frac{2}{1}\)
   
   
4. Multiply.
   
   \(\displaystyle \frac{3 \cdot 2}{4 \cdot 1}\)
   
   \(\displaystyle \frac{6}{4}\)
   
   \(\displaystyle \frac{3}{2}\)

To divide fractions, we will use the following steps:

1. Keep the first fraction the same.
2. Change the multiplication sign to a division sign.
3. Replace the second fraction with it's reciprocal.
4. Multiply.

So, given the problem

\(\displaystyle \frac{2}{3} \div \frac{1}{4}\)

we will follow the steps.

1. Keep the first fraction the same.
   
   \(\displaystyle \frac{2}{3} \div \frac{1}{4}\)
   
   
2. Change the multiplication sign to a division sign.
   
   \(\displaystyle \frac{2}{3} \cdot \frac{1}{4}\)
   
   
3. Replace the second fraction with it's reciprocal.  To write the reciprocal, the numerator will become the denominator, and the denominator will become the numerator.  In other words, we will flip the fraction.
   
   \(\displaystyle \frac{2}{3} \cdot \frac{4}{1}\)
   
   
4. Multiply.
   
   \(\displaystyle \frac{2}{3} \cdot \frac{4}{1}\)
   
   \(\displaystyle \frac{2 \cdot 4}{3 \cdot 1}\)
   
   \(\displaystyle \frac{8}{3}\)

To divide fractions, we will use the following steps:

1. Leave the first fraction alone.
2. Change the division sign to a multiplication sign.
3. Replace the second fraction with it’s reciprocal.
4. Multiply.

So, given the problem

\(\displaystyle \frac{4}{8} \div \frac{1}{2}\)

We will follow the steps.

1.        Leave the first fraction alone.

\(\displaystyle \frac{4}{8} \div \frac{1}{2}\)

2.        Change the division sign to a multiplication sign.

\(\displaystyle \frac{4}{8} \cdot \frac{1}{2}\)

3.        Replace the second fraction with it’s reciprocal.  To find the reciprocal of a fraction, the numerator becomes the denominator, and the denominator becomes the numerator.  In other words, we will flip the fraction.

\(\displaystyle \frac{4}{8} \cdot \frac{2}{1}\)

4.        Multiply.

\(\displaystyle \frac{4 \cdot 2}{8 \cdot 1}\)

\(\displaystyle \frac{8}{8}\)

\(\displaystyle 1\)

To divide fractions, we will take the first fraction and multiply by the reciprocal of the second fraction.  So, we get

\(\displaystyle \frac{8}{9} \cdot \frac{1}{12}\)

We will simplify before we multiply to make things easier.  The 8 and the 12 can both be divided by 4.  We get

\(\displaystyle \frac{2}{9} \cdot \frac{1}{3}\)

\(\displaystyle \frac{2 \cdot 1}{9 \cdot 3}\)

\(\displaystyle \frac{2}{27}\)

To divide, we will multiply the first fraction by the reciprocal of the second fraction.  To find the reciprocal, the numerator becomes the denominator, and the denominator becomes the numerator (in other words, we will flip the fraction). 

We get

\(\displaystyle \frac{8}{9} \div \frac{1}{4}\)

\(\displaystyle \frac{8}{9} \cdot \frac{4}{1}\)

\(\displaystyle \frac{8 \cdot 4}{9 \cdot 1}\)

\(\displaystyle \frac{32}{9}\)

To divide fractions, we will take the first fraction and multiply it by the reciprocal of the second fraction. 

To find the reciprocal, the numerator will become the denominator, and the denominator will become the numerator.  In other words, we will flip the fraction.

So, we get

\(\displaystyle \frac{4}{5} \div \frac{1}{2}\)

\(\displaystyle \frac{4}{5} \cdot \frac{2}{1}\)

\(\displaystyle \frac{4 \cdot 2}{5 \cdot 1}\)

\(\displaystyle \frac{8}{5}\)

To divide fractions, we will take the first fraction and multiply it by the reciprocal of the second fraction.  To find the reciprocal, the numerator will become the denominator, and the denominator will become the numerator.  In other words, we will flip the fraction.  So, we get

\(\displaystyle \frac{8}{9} \div \frac{1}{2}\)

\(\displaystyle \frac{8}{9} \cdot \frac{2}{1}\)

\(\displaystyle \frac{8 \cdot 2}{9 \cdot 1}\)

\(\displaystyle \frac{16}{9}\)