How to Divide Fractions? Explain It to a 5th Grader

Jan 23, 2025 | 4S Ranch
Mathnasium tutor explaining fractions to a young girl.

Dividing fractions, which are already parts of a whole, might sound like a lot of math. But don’t worry—thanks to a little help from multiplication, it’s easier than you think. 

Multiplication? Yes, you read that right! 

To divide fractions, we will need to multiply. 

We’ve put together this guide for everyone—from 5th graders still discovering fractions to test-takers, and even older students looking to refresh their skills. Inside, you'll find clear definitions, step-by-step methods, solved examples, practice exercises, and answers to frequently asked questions.

Visit Mathnasium of 4S Ranch, a Top-Rated Math Learning Center

Let’s Review: What Are Fractions?

Simply put, a fraction is a part of a whole. It’s written as two numbers, one over the other, separated by a line, like so: \( \Large \frac{1}{2}\).

  • The top number in a fraction is called the numerator. It tells us how many parts we have.
  • The bottom number in a fraction is called the denominator. It tells us how many equal parts the whole is divided into.

For example, in the fraction \( \Large \frac{3}{4}\), the 3 (numerator) means we have 3 parts, and the 4 (denominator) shows that the whole is divided into 4 equal parts.

Types of Fractions

There are four types of fractions:

  1. Proper Fractions: The numerator (top number) is always smaller than the denominator (bottom number), such as \( \Large \frac{2}{4}\).
  2. Improper Fractions: The numerator is equal to or greater than the denominator, such as \( \Large \frac{7}{2}\).
  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 \( \Large \frac{1}{8}\).

Now that we've refreshed our memory, let's divide fractions!

How to Divide Fractions

When dividing fractions, there are a few different situations we might come across:

  • Dividing one fraction and another fraction, like \( \Large \frac{3}{4}\)÷\( \Large \frac{2}{5}\).
  • Dividing a fraction by a whole number and vice versa, like \( \Large \frac{3}{4}\) ÷ 2 or 2 ÷ \( \Large \frac{3}{4}\).
  • Dividing a fraction and a mixed number and vice versa, like \( \Large \frac{3}{4}\) ÷ 1\( \Large \frac{1}{2}\) or 1\( \Large \frac{1}{2}\)÷\( \Large \frac{3}{4}\).

Even though all these look different, they all follow the same, simple principle.

To show you this principle, we’ll start with the first case—dividing one fraction by another—and then build on that to cover the other scenarios.

How to Divide Fractions by Fractions

At Mathnasium, we love using examples to make math concepts clear and easy to understand. 

Instead of listing all the steps for dividing fractions and asking you to memorize them, we’ll work through one together so you can easily follow along.

Let’s say we want to divide \( \Large \frac{3}{4}\) ÷ \( \Large \frac{1}{2}\).

What we’re doing here is similar to dividing whole numbers. We’re figuring out how many \( \Large \frac{1}{2}\) parts fit into \( \Large \frac{3}{4}\).

Let’s break it down in steps.

Step 1: Keep, Change, Flip

This step may come at different points in fraction division, but remember, it’s the most important step and we use it every time.

  • Keep: Keep the first fraction exactly as it is. In our case, that’s \( \Large \frac{3}{4}\).
  • Change: Change the division to multiplication. So, \( \Large \frac{3}{4}\) will be followed by x.
  • Flip: Flip the second fraction to its reciprocal. So, \( \Large \frac{1}{2}\) will become \( \Large \frac{2}{1}\).

A reciprocal, as you may have noticed, is when we swap the numerator and denominator of a fraction.

Now, our division becomes \( \Large \frac{3}{4}\) x \( \Large \frac{2}{1}\).

Step 2: Multiply

Now, we multiply:

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

Since the result we got, \( \Large \frac{6}{4}\), is an improper fraction (its numerator is larger than its denominator), we have to simplify it some more.

Step 3: Simplify

To simplify the fraction \( \Large \frac{6}{4}\), we have to find the greatest common denominator (GCD) for 6 and 4. 

That would be 2. 

We divide both 6 and 4 by their GCD or 2:

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

Since \( \Large \frac{3}{2}\) is an improper fraction (its numerator is larger than its denominator), we can convert it to a mixed number.

Step 4: Convert the Fraction to a Mixed Number

Time to brush up on how to convert fractions into mixed numbers!

To convert the \( \Large \frac{3}{2}\) to a mixed number, we first need to divide the numerator (3) by the denominator (2). 

3 goes into 2 only 1 time and leaves a remainder of 1.

3 ÷ 2=1R1

Now, we can convert the result into a mixed number (a whole number + a fractional part).

  • Our whole number in the mixed number is 1
  • The remainder is also 1 and it becomes the numerator of the fractional part
  • The denominator stays 2, just as in \( \Large \frac{3}{2}\) (the improper fraction we simplified).

So, \( \Large \frac{3}{2}\) is simplified to 1\( \Large \frac{1}{2}\).

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

Why do we keep, change, and flip?

Well, fractions are basically division problems. \( \Large \frac{1}{4}\) means that you’re dividing 1 by 4, right? And if we multiply a number by \( \Large \frac{1}{4}\), it’s just the same as dividing it by 4.

For instance: 

12 x \( \Large \frac{1}{4}\) = \( \Large \frac{12}{12}\) x \( \Large \frac{1}{4}\) = \( \Large \frac{12}{4}\) = 3

When you divide something by 4, it’s really like dividing it by \( \Large \frac{4}{1}\) because every whole number can be expressed as a fraction (2=\( \Large \frac{2}{1}\), 3=\( \Large \frac{3}{1}\), etc.) 

But dividing by a fraction, like \( \Large \frac{4}{1}\), is the same as multiplying by its reciprocal, which is \( \Large \frac{4}{1}\). 

For instance: 

12 ÷ \( \Large \frac{4}{1}\) = \( \Large \frac{12}{1}\) x \( \Large \frac{1}{4}\) = \( \Large \frac{12}{4}\) = 3

So, to make division by fractions easier, we flip the fraction and switch to multiplication.

How to Divide Fractions by Whole Numbers

Now that we know the main principle for dividing fractions, let’s see how it works when we divide a fraction by a whole number (or a whole number by a fraction).

We’ll take this example: \( \Large \frac{3}{4}\) ÷ 2.

Step 1: Convert the Whole Number to a Fraction

Before we start dividing, we have to convert the whole number into a fraction. Any number can be turned into a fraction if we just place it over 1.

Why? Because dividing anything by 1 doesn't change its value.

So 2 becomes \( \Large \frac{2}{1}\).

We’re dividing: \( \Large \frac{3}{4}\) ÷ \( \Large \frac{2}{1}\).

Step 2: Keep, Change, Flip

  • Keep: We keep \( \Large \frac{3}{4}\) as is.
  • Change: We change the operation from division (÷) to multiplication (x).
  • Flip: We flip the second fraction to its reciprocal. So, \( \Large \frac{2}{1}\) becomes \( \Large \frac{1}{2}\).

Step 3: Multiply

Now, we multiply:

\( \Large \frac{3}{4}\) x \( \Large \frac{1}{2}\) = \( \Large \frac{3×1}{4×2}\) = \( \Large \frac{3}{8}\)

Since the fraction is already in its simplest form, our work is done. 

\( \Large \frac{3}{4}\) ÷ 2 = \( \Large \frac{3}{8}\)

What if we had to divide a whole number by a fraction instead? 

No problem! 

We’d use the same method: convert the whole number to a fraction, then keep, change, and flip.

How to Divide Fractions by Mixed Numbers

Next, we’ll see how to divide a fraction by a mixed number. 

For this purpose, we can solve \( \Large \frac{3}{4}\) ÷ 1\( \Large \frac{1}{2}\).

Step 1: Convert the Mixed Number to a Fraction

To make the division simpler, we have to convert the mixed number 1\( \Large \frac{1}{2}\) into a fraction.

To convert a mixed number into a fraction, we need to:

  1. Multiply the whole number (1) by the denominator (2):
    1. 1 x 2 = 2
  2. Add the numerator of the fraction (1) to this result:
    1. 2 + 1 = 3
  3. Write the result as the numerator, and keep the original denominator (2):
    1. 1\( \Large \frac{1}{2}\) = \( \Large \frac{3}{2}\)

After the conversion, we are dividing \( \Large \frac{3}{4}\) ÷ \( \Large \frac{3}{2}\).

You May Also Like: How to Convert Mixed Numbers to Fractions

Step 2: Keep, Change, Flip

Now, our most important step.

  • Keep: We keep \( \Large \frac{3}{4}\) as is.
  • Change: We change the operation from division (÷) to multiplication (x).
  • Flip: We flip the second fraction to its reciprocal. So, \( \Large \frac{3}{4}\) becomes \( \Large \frac{2}{3}\).

Step 3: Multiply

Now, we can multiply easily:

\( \Large \frac{3}{4}\) x \( \Large \frac{2}{3}\) = \( \Large \frac{3×2}{4×3}\) = \( \Large \frac{6}{12}\).

The result we got from multiplying is \( \Large \frac{6}{12}\).

This fraction can be simplified, so we need one final step.

Step 4: Simplify

To simplify \( \Large \frac{6}{12}\), we need to find the greatest common denominator of 6 and 12. This would be 6. We divide both the numerator and the denominator by that number.

\( \Large \frac{6}{12}\) ÷ \( \Large \frac{6}{6}\) = \( \Large \frac{1}{2}\)

Since the fraction is in its simplest form, we’re all done. 

So, \( \Large \frac{3}{4}\) ÷ 1\( \Large \frac{1}{2}\) = \( \Large \frac{1}{2}\)

And that’s how we divide fractions by mixed numbers. 

If the mixed number was divided by a fraction, we would follow the same steps:

  1. Convert the mixed number to a fraction
  2. Keep, change, flip
  3. Multiply
  4. Simplify if needed

Solved Examples of Dividing Fractions

Dividing fractions gets easier the more we practice! Let’s work through some examples together so you’ll feel confident solving any fraction division in the future.

Example 1: Divide Fraction by Fraction

Let’s solve \( \Large \frac{2}{3}\) ÷ \( \Large \frac{4}{5}\).

Step 1: Keep, Change, Flip

  • Keep the first fraction as is: \( \Large \frac{2}{3}\)
  • Change from division (÷) to multiplication (×).
  • Flip the second fraction (\( \Large \frac{4}{5}\)) to its reciprocal (\( \Large \frac{5}{4}\))

Step 2: Multiply

Now, we multiply: \( \Large \frac{2}{3}\) x \( \Large \frac{5}{4}\)

\( \Large \frac{2}{3}\) x \( \Large \frac{5}{4}\) = \( \Large \frac{2x5}{3x4}\) = \( \Large \frac{10}{12}\)

This fraction can be simplified, so we need one final step.

Step 3: Simplify

To simplify \( \Large \frac{10}{12}\), we find the greatest common factor (GCF) of 10 and 12. That’s 2.

Divide both numerator and denominator by 2:

\( \Large \frac{10}{12}\) ÷ \( \Large \frac{2}{2}\) = \( \Large \frac{5}{6}\)

The final answer: \( \Large \frac{2}{3}\) ÷ \( \Large \frac{4}{5}\) = \( \Large \frac{5}{6}\)

Example 2: Divide Fraction by Whole Number

Now, let’s solve: \( \Large \frac{3}{8}\) ÷ 2.

Step 1: Convert the Whole Number

Convert 2 to a fraction \( \Large \frac{2}{1}\).

Now, we’re dividing \( \Large \frac{3}{8}\) ÷ \( \Large \frac{2}{1}\).

Step 2: Keep, Change, Flip

  • Keep the first fraction as is: \( \Large \frac{3}{8}\)
  • Change from division (÷) to multiplication (×).
  • Flip the second fraction (\( \Large \frac{2}{1}\)) to its reciprocal (\( \Large \frac{1}{2}\)).

Step 3: Multiply

Now, we can multiply:

\( \Large \frac{3}{8}\) x \( \Large \frac{1}{2}\) = \( \Large \frac{3×1}{8×2} \) = \( \Large \frac{3}{16}\)

Since the fraction is in its simplest form, we stop dividing. 

The final answer: \( \Large \frac{3}{8}\) ÷ 2 = \( \Large \frac{3}{16}\)

Example 3: Divide Mixed Number by Fraction

Now, let’s solve 1\( \Large \frac{3}{4}\) ÷ \( \Large \frac{2}{5}\).

Step 1: Convert the Mixed Number

Convert 1\( \Large \frac{3}{4}\) ÷ \( \Large \frac{2}{5}\) to an improper fraction:

  • Multiply the whole number by the denominator: 1 × 4 = 4.
  • Add the numerator to the result: 4 + 3 = 7.
  • Write the result (7) as the numerator over the original denominator (4): 1\( \Large \frac{3}{4}\) = \( \Large \frac{7}{4}\) 

The division becomes: \( \Large \frac{7}{4}\) ÷ \( \Large \frac{2}{5}\).

Step 2: Keep, Change, Flip

Keep the first fraction as is: \( \Large \frac{7}{4}\)

Change from division (÷) to multiplication (×).

Flip the second fraction (\( \Large \frac{2}{5}\)) to its reciprocal (\( \Large \frac{5}{2}\)).

Step 3: Multiply

Now, we can multiply: \( \Large \frac{7}{4}\) x \( \Large \frac{5}{2}\).

\( \Large \frac{7}{4}\) x \( \Large \frac{5}{2}\) = \( \Large \frac{7×5}{4×2}\) = \( \Large \frac{35}{8}\)

This fraction can’t be simplified. However, since \( \Large \frac{35}{8}\) is an improper fraction, we have to convert it to a mixed number.

Step 4: Convert the Fraction to a Mixed Number

To convert \( \Large \frac{35}{8}\) to a mixed number, we first have to divide the numerator by the denominator. 

Since 35 isn’t divisible by 4, we look for the next lower number that is.

32 ÷ 8 = 4

So, 8 goes into 35 a total of 4 times, leaving a remainder of 3.

35 ÷ 8=4 R3

  • Our whole number in the mixed number is 4
  • The remainder is 3 and it becomes the numerator of the fractional part
  • The denominator stays 8, just as in the original fraction.

So, we get: 4\( \Large \frac{3}{8}\)

The final answer: 1\( \Large \frac{3}{4}\) ÷ \( \Large \frac{2}{5}\) = 4\( \Large \frac{3}{8}\)

Your Turn: Divide These Fractions

Ready to test your skills? Divide the following fractions:

  1. \( \Large \frac{5}{6}\) ÷ \( \Large \frac{2}{3}\)
  2. \( \Large \frac{4}{9}\) ÷ \( \Large \frac{2}{5}\)
  3. \( \Large \frac{3}{10}\) ÷ 2\( \Large \frac{1}{4}\)

When you finish solving the exercises, check your answers at the bottom of the guide.

Master Fractions with Mathnasium of 4S Ranch

Mathnasium of 4S Ranch 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 dividing fractions. 

Discover our approach to elementary school tutoring.

Students start their Mathnasium journey with a diagnostic assessment that allows us to understand their specific 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 4S Ranch today! 

Schedule a Free Assessment at Mathnasium of 4S Ranch

Pssst! Check Your Answers Here

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

  1. 1\( \Large \frac{1}{4}\)
  2. \( \Large \frac{4}{27}\)
  3. \( \Large \frac{2}{15}\)