Multiplying Fractions
w/ 15 Step-by-Step Examples!

Did you know that there are two methods for multiplying fractions?

It’s true!

• Table Of Contents
  • 1. Area Model — Multiplication
  • 2. Rules For Multiplying Fractions
  • 3. How To Multiply Mixed Numbers
  • 4. Practice Worksheet
  • 5. Summary
  • 6. Video Tutorial

Area Model — Multiplication

So let’s start with the basics — area models.

Because they help build the foundation when it comes to working with products of fractions.

In this area model, our rectangle’s length and width represent factors, and the area of the overlapping shaded region represents their product.

While this is a great visual representation, drawing rectangles to calculate the product of two fractions is not always practical and can be rather time-consuming.

Rules For Multiplying Fractions

Thankfully, we have fraction rules for dealing with multiplication!

Okay, so now let’s talk about our two methods — both of which are perfectly awesome and easy to use.

Method #1

1. Multiply the Tops (numerator).
2. Multiply the Bottoms (denominator).
3. Reduce the Fraction to Simplest Terms.

Method #2

1. Reduce to simplest terms.
2. Multiply the Tops (numerator).
3. Multiply the Bottoms (denominator).
4. Double-Check that your Fraction is in the Simplest Terms.

You will find that Method #2 is the preferred method for multiplying fractions and is the one that we will use consistently throughout this lesson.

Want to know how to make this process easier?

I know I do…

…it’s to get the greatest common factor before multiplying the fractions.

Remember, the GCF is the greatest factor that both the numerator and the denominator have in common. By dividing both terms by the GCF, we can reduce their values to the lowest form — thus, making our multiplication effortless.

How To Multiply Mixed Numbers

But how do we deal with mixed numbers or whole numbers?

So glad you asked!

All we have to do is first convert our mixed or whole number into an improper fraction — multiply the denominator by the whole number and add the numerator. Then follow the same steps outlined earlier.

These steps include:

1. Reducing the fraction.
2. Multiplying the tops and bottoms.
3. And finally ensuring that it’s in simplest form as discussed on the Prodigy Blog.

Example #1

Example #2

Let’s look at another example, this time with three fractions!

Worksheet (PDF) — Hands on Practice

Put that pencil to paper in these easy to follow worksheets — expand your knowledge!

Multiplying Fractions — Practice Problems
Multiplying Fractions — Step-by-Step Solutions

Final Thoughts

In the video lesson below, we’ll expand on our examples making sure we remember how to find:

• The greatest common factor.
• Change mixed numbers into improper fractions.
• And use our new skill of multiplying to find the product of two or more fractions with ease.

Let’s jump right in!

Video Tutorial — Full Lesson w/ Detailed Examples

1 hr 4 min

• Introduction to Video
• 00:00:33 – Multiplication Notation, Area Models, and Steps for Finds Products of Fractions

• 00:15:30 – Find the product of two fractions and simplify the results (Examples #1-6)
• 00:31:26 – Solve three fractions and leave answer in lowest terms (Example #7-8)
• 00:40:42 – Multiplication of mixed numbers (Examples #9-11)
• 00:50:09 – Multiply the mixed number or whole numbers and simplify (Examples #12-13)
• 00:55:14 – Find the products of three mixed numbers and simplify answers (Examples #14-15)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions