How to Multiply a Fraction by a Whole Number

Jan 24, 2025 | Mason
Mathnasium tutor helping a student with fractions.

Multiplying a fraction by a whole number (or the other way around) might seem like a lot of math, but it’s easier than you may think!

In this guide, we’ll show you how to multiply fractions and whole numbers in a few simple steps.

Read on to find simple definitions, step-by-step instructions, practice problems, and answers to students' most common questions.

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A Quick Refresh: What Are Whole Numbers & Fractions?

Before we multiply fractions by whole numbers, let’s take a moment to revisit what these terms mean.

Whole numbers are numbers without fractions or decimals, such as 1, 2, 3, and so on. They represent complete amounts of something, whether it is a cake, a bottle of water, or the duration of a math class. 

So, if you think of a cake, a whole number would mean an entire cake, with no slices taken out. Or if you think of a math class, a whole number is the duration of your math class from start to finish.

A fraction is a part of a whole. It is written as two numbers separated by a line (e.g. \(\Large\frac{3}{4}\)):

  • The numerator (top number) shows how many parts you have.

  • The denominator (bottom number) shows how many equal parts make up the whole.

For example, if your mom asks you to put \(\Large\frac{3}{4}\) of a cake in a storage container, it means that you should cut the cake into 4 equal slices and pack 3 of them. 

There are four types of fractions we need to know so we can multiply them with whole numbers:

  1. Proper Fractions: The numerator (top number) is always smaller than the denominator (bottom number), such as \(\Large\frac{2}{3}\) and \(\Large\frac{4}{7}\).

  2. Improper Fractions: The numerator is equal to or greater than the denominator, such as \(\Large\frac{3}{2}\) and \(\Large\frac{7}{4}\).

  3. Mixed Numbers: A combination of a whole number and a fraction, such as 1\(\Large\frac{3}{4}\).

  4. Unit Fractions: The numerator is 1, such as \(\Large\frac{1}{2}\) or \(\Large\frac{1}{8}\).

Image of examples of types of fractions.


How to Multiply a Fraction by a Whole Number

At Mathnasium, we love to show how math works using examples! 

Let’s multiply the fraction \(\Large\frac{2}{3}\) by the whole number 4.


Step 1: Rewrite the Whole Number as a Fraction

To multiply a fraction by a whole number, start by writing the whole number as a fraction. This will make it easier to follow the steps.

To write the whole number as a fraction, simply place it over 1:

4 → \(\Large\frac{4}{1}\)

Fractions represent division. For example, \(\Large\frac{4}{1}\) means "4 divided by 1," and dividing any number by 1 doesn’t change its value. 

Now, we’re multiplying:

\(\Large\frac{2}{3}\) × \(\Large\frac{4}{1}\)


Step 2: Multiply the Numerators

Multiply the numerators (the top numbers) together.

In our example:

2 × 4 = 8


Step 3: Multiply the Denominators

Next, multiply the denominators (the bottom numbers) together.

In our example:

3 × 1 = 3

Now our fraction is \(\Large\frac{8}{3}\).


Step 4: Simplify the Fraction (if needed)

\(\Large\frac{8}{3}\) is already in its simplest form, so we can’t simplify it, or reduce the fraction to a smaller one.

However, since \(\Large\frac{8}{3}\) is an improper fraction–a fraction where the numerator is larger than the denominator–we can convert it to a mixed number.

To convert \(\Large\frac{8}{3}\) to a mixed number:

1. Divide the numerator (8) by the denominator (3).

8 ÷ 3 = 2 R2

2. Write the result as a mixed number:

  • The quotient (2) becomes the whole number.

  • The remainder (2) becomes the new numerator.

  • The denominator (3) stays the same.

So, \(\Large\frac{8}{3}\) converts to the mixed number 2\(\Large\frac{2}{3}\).

The final result of our multiplication is:

\(\Large\frac{2}{3}\) × 4 = 2\(\Large\frac{2}{3}\)

And there you have it! That’s how we multiply fractions by whole numbers.

What if the whole number came first, like 4 × \(\Large\frac{2}{3}\)? 

You would follow the exact same steps! 

Multiplication works the same way no matter the order of the numbers–this is called the commutative property of multiplication.  

You Might Also Like: How to Divide Fractions?


How to Multiply a Mixed Number by a Whole Number

Multiplying a mixed number by a whole number is almost the same as multiplying a regular fraction, with one extra step. 

Let’s multiply 1\(\Large\frac{2}{3}\) × 4 to see how this works.


Step 1: Turn the Mixed Number into an Improper Fraction

A mixed number is a whole number and a fraction combined. To make it easier to multiply, we will turn 1\(\Large\frac{2}{3}\) into an improper fraction like so:

1. Multiply the whole number (1) by the denominator (3):

1 × 3 = 3

2. Add the numerator (2) to the result:

3 + 2 = 5

3. Write 5 over the denominator (3):

1\(\Large\frac{2}{3}\) = \(\Large\frac{5}{3}\)

Now, we’re multiplying:

 \(\Large\frac{5}{3}\) × 4


Step 2: Rewrite the Whole Number as a Fraction

Next, change the whole number (4) into a fraction. Just put it over 1:

4 → \(\Large\frac{4}{1}\)

After converting our mixed number and whole number into improper fractions, our multiplication task looks like this:

\(\Large\frac{5}{3}\) × \(\Large\frac{4}{1}\)


Step 3: Multiply the Numerators

Multiply the numerators (the top numbers) together:

5 × 4 = 20


Step 4: Multiply the Denominators

Multiply the denominators (the bottom numbers) together:

3 × 1 = 3

Now we have:

\(\Large\frac{20}{3}\)


Step 5: Simplify the Fraction (if needed)

The numbers 20 and 3 do not have a common factor other than 1, so the resulting fraction \(\Large\frac{20}{3}\) is already in its simplest form.

Since the numerator is bigger than the denominator, we can turn the fraction into a mixed number.

1. Divide the numerator (20) by the denominator (3):

20 ÷ 3 = 6 R2

2. Write the quotient (6) as the whole number.

3. Put the remainder (2) as the numerator over the same denominator (3).

\(\Large\frac{20}{3}\) converts to 6\(\Large\frac{2}{3}\).

The final answer is:

1\(\Large\frac{2}{3}\) × 4 = 6\(\Large\frac{2}{3}\)


Solved Examples of Multiplying Fractions by Whole Numbers

Well done on your work so far!

Let’s work on a few examples to make multiplying fractions by whole numbers second nature.


Example 1: Fraction by Whole Number

Let’s multiply \(\Large\frac{3}{5}\) × 2.

Step 1: Rewrite the Whole Number as a Fraction

To multiply, first rewrite the whole number (2) as a fraction:

2 → \(\Large\frac{2}{1}\)

Now the problem becomes:

\(\Large\frac{3}{5}\) × \(\Large\frac{2}{1}\)

Step 2: Multiply the Numerators

Multiply the numerators (the top numbers) together:

3 × 2  = 6

Step 3: Multiply the Denominators

Multiply the denominators (the bottom numbers) together:

5 × 1 = 5

The result is \(\Large\frac{6}{5}\).

Step 4: Simplify the Fraction

Note that \(\Large\frac{6}{5}\) is already in its simplest form as 6 and 5 have no common factors other than 1.

However, since \(\Large\frac{6}{5}\) is an improper fraction, we can convert it to a mixed number:

1. Divide the numerator (6) by the denominator (5):

6 ÷ 5 = 1  R1

2. Write the quotient (1) as the whole number.

3. Put the remainder (1) over the same denominator (5).

So, \(\Large\frac{6}{5}\) = 1\(\Large\frac{1}{5}\)

The final answer is:

\(\Large\frac{3}{5}\) × 2 = 1\(\Large\frac{1}{5}\)


Example 2: Mixed Number by Whole Number

Let’s multiply 2\(\Large\frac{1}{3}\) × 3

Step 1: Convert the Mixed Number into an Improper Fraction

To make it easier to multiply, first convert 2\(\Large\frac{1}{3}\) into an improper fraction:

  1. Multiply the whole number (2) by the denominator (3):

2 × 3 = 6

  1. Add the numerator (1) to the result:

6 + 1 = 7

  1. Write 7 over the denominator (3):

2\(\Large\frac{1}{3}\) = \(\Large\frac{7}{3}\)

Now, we’re multiplying:

\( \Large \frac{7}{3}\) × 3

Step 2: Rewrite the Whole Number as a Fraction

Rewrite the whole number (3) as a fraction:

3 → \(\Large\frac{3}{1}\)

Now, we’re multiplying:

\( \Large \frac{7}{3}\) × \( \Large \frac{3}{1}\)

Step 3: Multiply the Numerators

Multiply the numerators (the top numbers) together:

7 × 3 = 21

Step 4: Multiply the Denominators

Multiply the denominators (the bottom numbers) together:

3 × 1 = 3

Now we have \(\Large\frac{21}{3}\).

Step 5: Simplify the Fraction

Convert the improper fraction into a whole number.

Divide the numerator (21) by the denominator (3):

21 ÷ 3 = 7

So, our final answer to 2\(\Large\frac{1}{3}\) × 3 is:

\( \Large \frac{21}{3}\) = 7


Your Turn! Multiply These Fractions and Whole Numbers

Ready to practice what you’ve learned? Try working through these tasks on your own.

Task 1: Solve \(\Large\frac{3}{7}\) × 5

Task 2: Solve 6 ×\(\Large\frac{4}{9}\)

Task 3: Solve 2\(\Large\frac{3}{4}\) × 3

Once you’ve worked through these, check your answers at the bottom of the page to see how you did!


FAQs About Multiplying Fractions by Whole Numbers

Learning to multiply fractions by whole numbers doesn’t come without dilemmas. Here are some of the questions students usually have when learning this skill.


1) What if my fractions include negatives?

Multiplying fractions with negative numbers follows the same steps as regular multiplication. The only difference is determining the sign of the answer:

  • If one number is negative and the other is positive, the result will be negative.

  • If both numbers are negative, the result will be positive.

Let’s see an example:

(-\(\Large\frac{3}{4}\)) × 2

Step 1: Rewrite the whole number as a fraction.

2 → \(\Large\frac{2}{1}\)

Now, the problem becomes:

(-\(\Large\frac{3}{4}\)) × \(\Large\frac{2}{1}\)

Step 2: Multiply the numerators.

-3 × 2 = -6

Step 3: Multiply the denominators.

4 × 1 = 4

The result is:

-\(\Large\frac{6}{4}\)

Step 4: Simplify the fraction.

Divide the numerator and denominator by their greatest common factor (2) to simplify:

-\(\Large\frac{6}{4}\) = -\(\Large\frac{3}{2}\)

Final answer:

(-\(\Large\frac{3}{4}\)) × 2 = -\(\Large\frac{3}{2}\)

If both numbers were negative, for example (-\(\Large\frac{3}{4}\)) × (-2), the result would be positive, \(\Large\frac{3}{2}\).


2) What should I do if I get a really big numerator or denominator?

After multiplying, check if your fraction can be simplified. Divide the numerator and denominator by their greatest common factor (GCF).

For example:

\(\Large\frac{12}{16}\) can be simplified to \(\Large\frac{3}{4}\) because both 12 and 16 can be divided by 4.


3) Does the order of multiplication matter?

No, the order doesn’t matter because multiplication is commutative, which means you can multiply numbers in any order, and the result will always be the same.

For example:

3 × \(\Large\frac{2}{5}\) is the same as \(\Large\frac{2}{5}\) × 3.

However, some students find it easier to rewrite the problem with the fraction first to keep things consistent.


Master Fractions at Mathnasium of Mason

Mathnasium of Mason is a math-only learning center for K-12 students of all skill levels.

Using a proprietary teaching approach called the Mathnasium Method™, our specially trained math tutors offer face-to-face instruction in an engaging and supportive group environment to help students master any math class and topic, including multiplication of fractions. 

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Students begin their Mathnasium journey with a diagnostic assessment that allows us to understand their unique strengths and knowledge gaps. Guided by assessment-based insights, we create personalized learning plans that will put them on the best path toward math mastery. 

Whether your student is looking to catch up, keep up, or get ahead in their math class, schedule an assessment, and enroll at Mathnasium of Mason today! 

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Pssst! Check Your Answers Here

If you’ve given our exercises a try, check your answers here:

Task 1: 2\(\Large\frac{1}{7}\)

Task 2: 2\(\Large\frac{2}{3}\)

Task 3: 8\(\Large\frac{1}{4}\)