Problems on Divison of Fractional Numbers are provided with the various types of problems. Follow this complete concept and learn more about the division of the Fractional Numbers topic. Here on this page, we will explain different methods which are given to solve a single problem. So, let us check out different problems with explanations for the division of Fractional Number Problems.

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## Fraction – Definition

A fractional number is nothing but a section, portion, or part of any given quantity. Fractions are usually represented in the form of \(\frac { m }{ n } \), where m is called a numerator, and n is known as a denominator.

### How to Divide Fractional Numbers?

We have to convert the given second fraction into its reciprocal and then multiply it with the given first fraction. Next, we just need to simplify the fraction to its lowest terms.

## Problems on Division of Fractional Numbers

All the below-mentioned solved problems on dividing fractions numbers will help you to get every piece of detailed information and also helps you to score better marks in the exam. So let’s see few problems.

### Division of a Fraction with a Whole Number

**Problem 1:**

Solve the equation dividing a faction number \(\frac { 6 }{ 5 } \) with a whole number 10

**Solution:**

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

Now we need to find the reciprocal of \(\frac { 10 }{ 1 } \) which gives \(\frac { 1 }{ 10 } \)

Now we have to multiply both fractions \(\frac { 6 }{ 5 } * \frac { 1 }{ 10 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 6 * 1 }{ 5 * 10 } \)

Which gives \(\frac { 30 }{ 10 } \).

The result of dividing a facrtion \(\frac { 6 }{ 5 } \) with a whole number 10 is \(\frac { 30 }{ 10 } \).

Fractional number \(\frac { 30 }{ 10 } \) can be simplifed into lowest terms as \(\frac { 3 }{ 1 } \) since both these integers can be divided by 2.

Answer: 3

**Problem 2:**

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

**Solution:**

First, we need to convert our given whole number 6 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 6 }{ 1 } \)

Now we need to find the reciprocal of \(\frac { 6 }{ 1 } \) which gives \(\frac { 1 }{ 6 } \)

Now we have to multiply both fractions \(\frac { 2 }{ 4 } * \frac { 1 }{ 6 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 2 * 1 }{ 4 * 6 } \)

Which gives \(\frac { 2 }{ 24 } \).

The result of dividing a facrtion \(\frac { 2 }{ 4 } \) with a whole number 6 is \(\frac { 2 }{ 24 } \).

Fractional number \(\frac { 2 }{ 24 } \) can be simplifed into lowest terms as \(\frac { 1 }{ 12 } \) since both these integers can be divided by 2.

Answer: \(\frac { 1 }{ 12 } \)

### Division of a Whole Number with a Fractional Number.

**Problem 3:**

Solve the equation dividing a whole number 5 with a factional number \(\frac { 3 }{ 15 } \)

**Solution:**

First, we need to convert our given whole number 5 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 5 }{ 1 } \)

Now we need to find the reciprocal of \(\frac { 5 }{ 1 } \) which gives \(\frac { 1 }{ 5 } \)

Now we have to multiply both fractions \(\frac { 1 }{ 5 } * \frac { 3 }{ 15 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 1 * 3 }{ 5 * 15 } \)

Which gives \(\frac { 3 }{ 75 } \)

The result of dividing a whole number 5 with a fractional number \(\frac { 3 }{ 15 } \) is \(\frac { 3 }{ 75 } \).

Fractional number \(\frac { 3 }{ 75 } \) can be simplifed into lowest terms as \(\frac { 1 }{ 25 } \) since both these integers can be divided by 3.

Answer: \(\frac { 1 }{ 25 } \)

**Problem 4:**

Solve the equation dividing a whole number 2 with a factional number \(\frac { 5 }{ 4 } \)

**Solution:**

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

Now we need to find the reciprocal of \(\frac { 2 }{ 1 } \) which gives \(\frac { 1 }{ 2 } \)

Now we have to multiply both fractions \(\frac { 1 }{ 2 } * \frac { 5 }{ 4 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 1 * 5 }{ 2 * 4 } \)

Which gives \(\frac { 5 }{ 6 } \)

The result of dividing a whole number 2 with a fractional number \(\frac { 5 }{ 4 } \) is \(\frac { 5 }{ 6 } \)

The answer remains the same since 5 and 6 do not have common factorials so it can be simplified further.

Answer: \(\frac { 5 }{ 6 } \).

### Dividing a Fractional Number with another Fractional Number

**Problem 5:**

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

Solution:

First, we need to find the reciprocal of the second fractional number \(\frac { 2 }{ 3 } \) which gives \(\frac { 3 }{ 2 } \)

Now we have to multiply both fractions \(\frac { 5 }{ 4 } * \frac { 3 }{ 2 } \)

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

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

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

The answer remains the same since 15 and 8 do not have common factorials so it can be simplified further.

Answer: \(\frac { 15 }{ 8 } \).

**Problem 6:**

Solve the equation dividing these factional number \(\frac { 9 }{ 4 } \) and \(\frac { 2 }{ 3 } \).

Solution:

First, we need to find the reciprocal of the second fractional number \(\frac { 2 }{ 3 } \) which gives \(\frac { 3 }{ 2 } \)

Now we have to multiply both fractions \(\frac { 9 }{ 4 } * \frac { 3 }{ 2 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 9 * 3 }{ 4 * 2 } \)

Which gives \(\frac { 27 }{ 8 } \)

The result of dividing a fractional number \(\frac { 9 }{ 4 } \)with another fractional number \(\frac { 2 }{ 3 } \) is \(\frac { 27 }{ 8 } \)

The answer remains the same since 27 and 8 do not have common factorials so it can be simplified further.

Answer: \(\frac { 27 }{ 8 } \)

### Division of a Whole Number with a Mixed Fractional Number

**Problem 7:**

Solve the equation dividing a whole number 4 with a mixed factional number 2\(\frac { 9 }{ 13 } \)

**Solution:**

First, we need to convert our given whole number 4 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 4 }{ 1 } \)

Now we need to find the reciprocal of \(\frac { 4 }{ 1 } \) which gives \(\frac { 1 }{ 4 } \)

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

Now we have to multiply both fractions \(\frac { 1 }{ 4 } * \frac { 35 }{ 13 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 1 * 35 }{ 4 * 13 } \)

Which gives \(\frac { 35 }{ 52 } \)

The result of dividing a whole number 2 with a fractional number 2\(\frac { 9 }{ 13 } \) is \(\frac { 35 }{ 52 } \)

The answer remains the same since 35 and 52 do not have common factorials so it can be simplified further.

Answer: \(\frac { 35 }{ 52 } \).

**Problem 8:**

Solve the equation dividing a whole number 6 with a mixed factional number 2\(\frac { 2 }{ 3 } \)

**Solution:**

First, we need to convert our given whole number 6 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 6 }{ 1 } \)

Now we need to find the reciprocal of \(\frac { 6 }{ 1 } \) which gives \(\frac { 1 }{ 6 } \)

We have to convert the given mixed fractional number into the simple fractional number 2\(\frac { 2 }{ 3 } \) becomes \(\frac { 8 }{ 3 } \)

Now we have to multiply both fractions \(\frac { 1 }{ 6 } * \frac { 8 }{ 3 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 1 * 8 }{ 6 * 3 } \)

Which gives \(\frac { 8 }{ 18 } \)

The result of dividing a whole number 6 with a fractional number 2\(\frac { 2 }{ 3 } \) is \(\frac { 8 }{ 18 } \)

Fractional number \(\frac { 8 }{ 18 } \) can be simplifed into lowest terms as \(\frac { 4 }{ 9 } \) since both these integers can be divided by 2.

Answer: \(\frac { 4 }{ 9 } \).

### Division of a Mixed Fractional Number with a Whole Number

**Problem 9:**

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

**Solution:**

We have to convert the given mixed fractional number into the simple fractional number 3\(\frac { 1 }{ 4 } \) becomes \(\frac { 13 }{ 4 } \)

Now to convert our given whole number 3 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 3 }{ 1 } \)

Let us find the reciprocal of \(\frac { 3 }{ 1 } \) which gives \(\frac { 1 }{ 3 } \)

Now we have to multiply both fractions \(\frac { 13 }{ 4 } * \frac { 1 }{ 3 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 13 * 1 }{ 4 * 3 } \)

Which gives \(\frac { 13 }{ 3 } \)

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

The answer remains the same since 13 and 3 do not have common factorials so it can be simplified further.

Answer: \(\frac { 13 }{ 3 } \).

**Problem 10:**

Solve the equation dividing mixed factional number 2\(\frac { 2 }{ 3 } \) with a whole number 8.

**Solution:**

We have to convert the given mixed fractional number into the simple fractional number 2\(\frac { 2 }{ 3 } \) becomes \(\frac { 8 }{ 3 } \)

Now to convert our given whole number 8 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 8 }{ 1 } \)

Let us find the reciprocal of \(\frac { 8 }{ 1 } \) which gives \(\frac { 1 }{ 8 } \)

Now we have to multiply both fractions \(\frac { 8 }{ 3 } * \frac { 1 }{ 8 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 8 * 1 }{ 3 * 8 } \)

Which gives \(\frac { 8 }{ 24 } \)

The result of dividing a mixed fractional number 2\(\frac { 2 }{ 3 } \) with a whole number 8 is \(\frac { 8 }{ 24 } \)

Fractional number \(\frac { 8 }{ 24 } \) can be simplifed into lowest terms as \(\frac { 1 }{ 3 } \) since both these integers can be divided by 2.

Answer: \(\frac { 1 }{ 3 } \).