Learn completely about the concept of multiplying fractions with whole numbers by going through the entire article. Know what is meant by a fraction and whole numbers, the procedure to multiply improper and mixed fractions with whole numbers, solved examples on the same explained clearly.

Read More:

- Multiplication of a Whole Number by a Fraction
- Multiplication of Fractional Number by a Whole Number

## Fractional Number and Whole Numbers – Definition

A number is said to be a fractional number if it is of the form b/d such that d should be greater than 0. Whole numbers are natural numbers including zero. The whole numbers are 0, 1, 2, 3, 4, 5, ………….

As discussed, fractional numbers are of the form b/d. We use natural numbers to represent these fractional numbers.

### Multiplication of Fractional Number by a Whole Number

Multiplication of Fractional Number and Whole number looks a little interesting. When we observe the whole numbers they are simple numbers. This is not the same case for Fractional Numbers. Fractional numbers are of form b/d. So, multiplying these numbers looks a little difficult. Here, we provide you with a simple explanation that helps you to easily understand the multiplication of whole numbers and Fractional numbers.

When we observe the Fractional numbers, they have a numerator and a denominator. The whole numbers have a numerator but not a denominator. Do you have any idea of how to proceed further?

### How to Multiply Fractional Numbers with Whole Numbers?

We follow simple few steps to multiply fractional numbers with whole numbers

Step 1: Here, we observe that the whole number does not have a denominator. So, we need to put the denominator as 1.

Step 2: When you multiply the whole number and the fractional number, you should multiply the numerator with a numerator and a denominator with a denominator.

Step 3: The solution will be either a fraction of a whole number and this gives us the final result.

### Multiplying Fractions with Whole Numbers Examples

**Example 1: **

Multiply a fraction, \(\frac { 2}{ 7 } \) with some whole number 3?

**Solution:**

Here we combine simple logic with mathematics which helps us to do the following Multiplication.

For a whole number, we only have a numerator and no denominator. So, here we take the denominator for a whole number as 1. This does not change the actual value of the whole number and so we can multiply the whole number with a fractional number.

The multiplication of fractional numbers is done by multiplying the numerators and denominators.

Here, the fraction is \(\frac { 2 }{ 7 } \) and the whole number is 3.

We do not have a denominator for 3. So, put the denominator as 1.

Now, the whole number becomes 3/1.

Multiply these numbers \(\frac { 2 * 3 }{ 7 * 1 } \)

The result will be \(\frac { 6 }{ 7 } \).

Hence, the result obtained by multiplying the whole number 3 and factional number \(\frac { 2}{ 7 } \) is \(\frac { 6 }{ 7 } \).

**Example 2: **

Multiply a fraction \(\frac { 22 }{ 7 } \) with some whole number 14?

**Solution:**

For a whole number, we only have a numerator and no denominator. So, here we take the denominator as 1.

The multiplication of fractional numbers is done by multiplying the numerators and denominators.

Here, the fraction is \(\frac { 22 }{ 7 } \) and the whole number is 14.

We do not have a denominator for 14. So, put the denominator as 1.

Now, the whole number becomes \(\frac { 14 }{ 1 } \).

Multiply these numbers \(\frac { 22 * 14 }{ 7 * 1 } \)

The result will be 44.

Hence, the result obtained by multiplying the whole number 14 and factional number \(\frac { 22 }{ 7 } \)is 44.

**Example 3: **

Multiply a fraction \(\frac { 234 }{ 26 } \) with some whole number 171?

**Solution:**

For a whole number, we only have a numerator and no denominator. So, here we take the denominator as 1.

The multiplication of fractional numbers is done by multiplying the numerators and denominators.

Here, the fraction is \(\frac { 234 }{ 26 } \) and the whole number is 171.

We do not have a denominator for 171. So, put the denominator as 1.

Now, the whole number becomes \(\frac { 171 }{ 1 } \).

Multiply these numbers \(\frac { 234 * 171 }{ 26 * 1 } \)

The result will be 1539.

Hence, the result obtained by multiplying the whole number 171 and factional number \(\frac { 234 }{ 26 } \) is 1539.

### Multiplying a Mixed Fraction with a Whole Number

In order to multiply the mixed fractions with a whole number, first, change the mixed fraction to a normal fraction which helps us to solve the problem with the same process as a normal fraction.

#### How to Multiply Mixed Fractional Numbers with Whole Numbers?

We follow simple few steps to multiply fractional numbers with whole numbers

Step 1: Change the mixed fraction to a normal fraction.

Step 2: Here, we observe that the whole number does not have a denominator. So, we need to put the denominator as 1.

Step 3: When you multiply the whole number and the mixed fractional number, you should multiply the numerator with a numerator and a denominator with a denominator.

Step 4: The solution will be either a fraction or a whole number and this gives us the final result.

Here are few examples that help you to understand the multiplication of mixed fractions with whole numbers.

### Multiplication of Mixed Fractions with Whole Numbers Examples

**Example 1: **

Multiply the mixed fraction 2 \(\frac { 2 }{ 5 } \) with a whole number 6?

**Solution:**

2 \(\frac { 2 }{ 5 } \) is a mixed fraction. So, we cannot use it for simple multiplication. Change it to a simple fraction.

The Simple fraction is \(\frac { 12 }{ 5 } \).

For a whole number, we only have a numerator and no denominator. So, here we take the denominator as 1.

The multiplication of fractional numbers is done by multiplying the numerators and denominators.

Here, the fraction is \(\frac { 12 }{ 5 } \) and the whole number is 6.

We do not have a denominator for 6. So, put the denominator as 1.

Now, the whole number becomes \(\frac { 6 }{ 1 } \).

Multiply these numbers \(\frac { 12 * 6 }{ 5 * 1 } \)

The result will be \(\frac { 72 }{ 5 } \).

Hence, the result obtained by multiplying the whole number 6 with fractional number 2 \(\frac { 2 }{ 5 } \)is \(\frac { 72 }{ 5 } \).

**Example 2: **

Multiply the mixed fraction 7 \(\frac { 12 }{ 15 } \) with a whole number 9?

**Solution:**

7 \(\frac { 12 }{ 15 } \) is a mixed fraction. So, we cannot use it for simple multiplication. Change it to a simple fraction.

The Simple fraction is \(\frac { 117 }{ 15 } \).

The multiplication of fractional numbers is done by multiplying the numerators and denominators.

Here, the fraction is \(\frac { 117 }{ 15 } \) and the whole number is 9.

We do not have a denominator for 9. So, put the denominator as 1.

Now, the whole number becomes \(\frac { 9 }{ 1 } \).

Multiply these numbers \(\frac { 117 * 9 }{ 15 * 1 } \)

The result will be \(\frac { 1053 }{ 15 } \).

Hence, the result obtained by multiplying the whole number 9 with fractional number 7 \(\frac { 12 }{ 15 } \) is \(\frac { 1053 }{ 15 } \)