This worksheet on the Divison of Fractional Numbers will provide different types of problems. Follow the complete concept and learn more about the Division of Fractional Numbers topic. We used different methods to solve a single problem in Dividing Fractions Worksheet. So, check out various problems along with answers and explanations provided in Fraction Division Worksheet and understand the concepts involved well.

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**Problem 1:**

Solve the equation by dividing a faction number \(\frac { 5 }{ 6 } \) with a whole number 8.

**Solution:**

Initially, we have to convert the given whole number 8 into a fractional number by adding 1 as its denominator. which gives \(\frac { 8 }{ 1 } \)

Now we have to find the multiplicative inverse of \(\frac { 8 }{ 1 } \) which gives \(\frac { 1 }{ 8 } \)

Now we can easily multiply both the fractional numbers \(\frac { 5 }{ 6 } * \frac { 1 }{ 8} \)

We can simplify this equation by multiplying numerators and denominators with each other \(\frac { 5 * 1 }{ 6 * 8 } \)

Which gives \(\frac { 5 }{ 48 } \).

The result of dividing a facrtion \(\frac { 5 }{ 6 } \) with a whole number 8 is \(\frac { 5 }{ 48 } \).

Since 5 and 48 do not have any common factorials so the fractional number can’t be simplified further, so the answer remains the same.

Answer: \(\frac { 5 }{ 48 } \).

**Problem 2:**

Solve the equation by dividing a faction number \(\frac { 6 }{ 4 } \) with a whole number 2.

**Solution:**

Initially, we have to convert the given whole number 2 into a fractional number by adding 1 as its denominator. which gives \(\frac { 2 }{ 1 } \)

Now we have to find the multiplicative inverse of \(\frac { 2 }{ 1 } \) which gives \(\frac { 1 }{ 2 } \)

Now we can easily multiply both the fractional numbers \(\frac { 6 }{ 4 } * \frac { 1 }{ 2 } \)

We can simplify this equation by multiplying numerators and denominators with each other \(\frac { 6 * 1 }{ 4 * 2 } \)

Which gives \(\frac { 6 }{ 8 } \).

The result of dividing a facrtion \(\frac { 6 }{ 4 } \) with a whole number 2 is \(\frac { 6 }{ 8 } \).

So Fractional number \(\frac { 6 }{ 8 } \) can be simplifed into lowest terms as \(\frac { 3 }{ 4 } \) since both these integers can be divided by 2.

Answer: \(\frac { 3 }{ 4 } \).

**Problem 3:**

Solve the equation by dividing a whole number 10 with a factional number \(\frac { 6 }{ 12 } \)

**Solution:**

Initially, we have to convert the given whole number 10 into a fractional number by adding 1 as its denominator. which gives \(\frac { 10 }{ 1 } \)

Now we have to find the multiplicative inverse of \(\frac { 10 }{ 1 } \) which gives \(\frac { 1 }{ 10 } \)

Now we can easily multiply both the fractional numbers \(\frac { 6 }{ 12 } * \frac { 1 }{ 10 } \)

We can simplify this equation by multiplying numerators and denominators with each other \(\frac { 6 * 1 }{ 12 * 10 } \)

Which gives \(\frac { 6 }{ 120 } \).

The result of dividing a whole number 10 with a facrtion \(\frac { 6 }{ 12 } \) is \(\frac { 6 }{ 120 } \).

So Fractional number \(\frac { 6 }{ 120 } \) can be simplifed into lowest terms as \(\frac { 1 }{ 20 } \) since both these integers can be divided by 6.

Answer: \(\frac { 1 }{ 20 } \).

**Problem 4:**

Solve the equation by dividing a whole number 3 with a factional number \(\frac { 6 }{ 5 } \)

**Solution:**

Initially, we have to convert the given whole number 3 into a fractional number by adding 1 as its denominator. which gives \(\frac { 3 }{ 1 } \)

Now we have to find the multiplicative inverse of \(\frac { 3 }{ 1 } \) which gives \(\frac { 1 }{ 3 } \)

Now we can easily multiply both the fractional numbers \(\frac { 6 }{ 5 } * \frac { 1 }{ 3 } \)

We can simplify this equation by multiplying numerators and denominators with each other \(\frac { 6 * 1 }{ 5 * 3 } \)

Which gives \(\frac { 6 }{ 15 } \).

The result of dividing a whole number 3 with a facrtion \(\frac { 6 }{ 5 } \) is \(\frac { 6 }{ 15 } \).

So Fractional number \(\frac { 6 }{ 120 } \) can be simplifed into lowest terms as \(\frac { 1 }{ 5 } \) since both these integers can be divided by 6.

Answer: \(\frac { 1 }{ 5 } \).

**Problem 5:**

Solve the equation by dividing two factional number \(\frac { 4 }{ 5 } \) and \(\frac { 3 }{ 2 } \).

**Solution:**

First, of all we have to find the multiplicative inverse of the given second fractional number \(\frac { 3 }{ 2 } \) which is \(\frac { 2 }{ 3 } \)

Now we need to multiply both these fractional numbers \(\frac { 4 }{ 5 } * \frac { 2 }{ 3 } \)

We can simplify this by multiplying numerators and denominators with each other \(\frac { 4 * 2 }{ 5 * 3 } \)

Which gives \(\frac { 8 }{ 15 } \)

The result of dividing a fractional number \(\frac { 4 }{ 5 } \)with another fractional number \(\frac { 3 }{ 2 } \) is \(\frac { 8 }{ 15 } \)

Since 15 and 8 do not have any common factorials so this fractional number can’t be simplified further, so the answer remains the same.

Answer: \(\frac { 8 }{ 12 } \).

**Problem 6:**

Solve the equation by dividing two factional number \(\frac { 6 }{ 4 } \) and \(\frac { 2 }{ 8 } \).

**Solution:**

First, of all we have to find the multiplicative inverse of the given second fractional number \(\frac { 2 }{ 8 } \) which is \(\frac { 8 }{ 2 } \)

Now we need to multiply both these fractional numbers \(\frac { 6 }{ 4 } * \frac { 8 }{ 2 } \)

We can simplify this by multiplying numerators and denominators with each other \(\frac { 6 * 4 }{ 8 * 2 } \)

Which gives \(\frac { 24 }{ 16 } \)

The result of dividing a fractional number \(\frac { 6 }{ 4 } \)with another fractional number \(\frac { 2 }{ 8 } \) is \(\frac { 24 }{ 16 } \)

So Fractional number \(\frac { 24 }{ 16 } \) can be simplifed into lowest terms as \(\frac { 3 }{ 2 } \) since both these integers can be divided by 2.

Answer: \(\frac { 3 }{ 2 } \).

**Problem 7:**

Solve the equation by dividing a whole number 12 with a mixed factional number 2\(\frac { 9 }{ 13 } \).

**Solution:**

First, of all, we have to convert the given whole number 12 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 12 }{ 1 } \)

Now we have to find the multiplicative inverse of \(\frac { 12 }{ 1 } \) which gives \(\frac { 1 }{12} \)

Now we need to convert the given mixed fractional number into the simple fractional number 2\(\frac { 9 }{ 13 } \) becomes \(\frac { 35 }{ 13 } \)

We have to multiply both fractional numbers \(\frac { 1 }{ 12 } * \frac { 35 }{ 13 } \)

We can simplify this by multiplying numerators and denominators with each other \(\frac { 1 * 35 }{ 12 * 13 } \)

Which gives \(\frac { 35 }{ 156 } \)

The result of dividing a whole number 12 with a fractional number 2\(\frac { 9 }{ 13 } \) is \(\frac { 35 }{ 156 } \)

Since 35 and 156 do not have any common factorials this fractional number can’t be simplified further. so the answer remains the same.

Answer: \(\frac { 35 }{ 156 } \).

**Problem 8:**

Solve the equation by dividing a whole number 2 with a mixed factional number 2\(\frac { 2 }{ 3 } \).

**Solution:**

First, of all, we have to convert the given whole number 2 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 2 }{ 1 } \)

Now we have to find the multiplicative inverse of \(\frac { 2 }{ 1 } \) which gives \(\frac { 1 }{ 2 } \)

Now we need to convert the given mixed fractional number into the simple fractional number 2\(\frac { 2 }{ 3 } \) becomes \(\frac { 8 }{ 3 } \)

We have to multiply both fractional numbers \(\frac { 1 }{ 2 } * \frac { 8 }{ 3 } \)

We can simplify this by multiplying numerators and denominators with each other \(\frac { 1 * 8 }{ 2 * 3 } \)

Which gives \(\frac { 8 }{ 6 } \)

The result of dividing a whole number 2 with a fractional number 2\(\frac { 2 }{ 3 } \) is \(\frac { 8 }{ 6 } \)

So Fractional number \(\frac { 8 }{ 6 } \) can be simplifed into lowest terms as \(\frac { 4 }{ 3 } \) since both these integers can be divided by 2.

Answer: \(\frac { 4 }{ 3 } \).

**Problem 9:**

Solve the equation by dividing mixed factional number 3\(\frac { 1 }{ 4 } \) with a whole number 10.

**Solution:**

First, We need to convert the given mixed fractional number into the simple fractional number 3\(\frac { 1 }{ 4 } \) which gives \(\frac { 13 }{ 4 } \)

Now we need to convert the given whole number 10 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 10 }{ 1 } \)

Let us find the Multiplicative inverse of \(\frac { 10 }{ 1 } \) which gives \(\frac { 1 }{ 10 } \)

Next, we need to multiply the both fractional numbers \(\frac { 13 }{ 4 } * \frac { 1 }{ 10 } \)

We can simplify this by multiplying numerators and denominators with each other \(\frac { 13 * 1 }{ 4 * 10 } \)

Which gives \(\frac { 13 }{ 40 } \)

The result of dividing a mixed fractional number 3\(\frac { 1 }{ 4 } \) with a whole number 10 is \(\frac { 13 }{ 40 } \)

Since 13 and 40 do not have common any this factional number can not be simplified further, so the answer remains the same.

Answer: \(\frac { 13 }{ 40 } \).

**Problem 10:**

Solve the equation dividing mixed factional number 2\(\frac { 2 }{ 3 } \) with a whole number 12

**Solution:**

First, We need to convert the given mixed fractional number into the simple fractional number 2\(\frac { 2 }{ 3 } \) which gives \(\frac { 8 }{ 3 } \)

Now we need to convert the given whole number 12 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 12 }{ 1 } \)

Let us find the Multiplicative inverse of \(\frac { 12 }{ 1 } \) which gives \(\frac { 1 }{ 12 } \)

Next, we need to multiply the both fractional numbers \(\frac { 8 }{ 3 } * \frac { 1 }{ 12 } \)

We can simplify this by multiplying numerators and denominators with each other \(\frac { 8 * 1 }{ 3 * 12 } \)

Which gives \(\frac { 8 }{ 36 } \)

The result of dividing a mixed fractional number 2\(\frac { 2 }{ 3 } \) with a whole number 12 is \(\frac { 8 }{ 36 } \).

So Fractional number \(\frac { 8 }{ 36 } \) can be simplifed into lowest terms as \(\frac { 2 }{ 9 } \) since both these integers can be divided by 2.

Answer: \(\frac { 2 }{ 9 } \)