Examples on How to Divide Fractions

Lesson Objective

In this lesson, we will see more examples on how to divide fractions. We will also see how we can use common factors to simplify the division.

About This Lesson

After learning the basics, let's take a look at some more example questions. This will help us to gain better understanding on how to divide fractions.

Each of these examples will have the following fractions respectively:

2 proper fractions
1 proper and 1 mixed fractions
2 mixed fractions.

The study tips and math video below will explain more.

$dividing fractions examples$

Study Tips

Tip #1 - The basics

The previous lesson had explained the basics behind dividing fractions. Here is the summary:

Know how to find the reciprocal of a fraction
To find the reciprocal of a fraction, we just need to swap the numerator and denominator of that fraction.
Steps to divide fractions
We can divide fractions by:

1) First, change the division sign to multiplication sign

2) Then, change the divisor to its reciprocal.

The math video will show some examples...

Math Video

Lesson Video

Math Video Transcript

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In this lesson, we will see more examples on how to divide fractions.

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Let's divide, 5/8 with 3/4. Here's how to divide fractions.

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First, we change the division sign to multiplication sign. 

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We can do so, provided that we also swap the numerator and denominator of the divisor, 3/4, to get its reciprocal, 4/3.

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By doing so, we now have 5/8 multiply by 4/3.

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By multiplying these fractions, we have 5 multiply by 4, over, 8 multiply by 3.

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Notice that, we can simplify this before multiplying by dividing 4 and 8 with the common factor, 4.

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This gives, 1 and 2 respectively.

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Since there is no more common factor, we can continue to multiply.

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5 multiply by 1, gives 5. 2 multiply by 3, gives 6.

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Finally, we have the fraction, 5/6.

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Next example, let's divide 1/2, with 2 1/3.

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Notice that, 2 1/3 is a mixed fraction.

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We need to change it into an improper fraction before we can continue.

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Multiply 3 with 2. This gives 6.

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Now, 6 plus 1, gives 7. This 7 becomes the improper fraction's numerator.

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Hence, we have the improper fraction, 7/3. Now, we can start dividing these fractions.

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First, we change the division sign to multiplication sign.

00:01:53.150
We can do so, provided that we swap the numerator and denominator of the divisor, 7/3, to get its reciprocal, 3/7.

00:02:04.060
After doing so, we have, 1/2 multiply by 3/7.

00:02:10.150
Multiplying these fractions give, 1 multiply 3, over, 2 multiply 7.

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Now, 1 multiply 3, gives 3. 

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2 multiply 7, gives 14.

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So now, we have the fraction, 3/14.

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Final example, let's divide 1 1/2, with 2 1/4. Here's how to divide fractions.

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Since these are mixed fractions, we have to convert them into improper fractions before dividing.

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Let's start with 1 1/2. 2 multiply with 1, gives 2.

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Now, 2 plus 1, gives 3. This 3 becomes the improper fraction's numerator.

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With this, we have the improper fraction, 3/2.

00:03:09.030
Similarly, let's convert 2 1/4 to an improper fraction.  4 multiply 2, gives 8.

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8 plus 1, gives 9. This 9 becomes the improper fraction's numerator.

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So now, we have the improper fraction, 9/4.

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Alright, we can start dividing these fractions.

00:03:38.230
First, change the division sign to multiplication sign.

00:03:43.240
We can do so, provided that we swap the numerator and denominator of the divisor, 9/4, to get its reciprocal, 4/9.

00:03:54.130
Now, we have 3/2, multiply by 4/9.

00:04:00.040
By multiplying these fractions, we have 3 multiply 4, over, 2 multiply 9.

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Here, notice that we can simplify this, by dividing 4 and 2 with the common factor, 2.

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This gives 2 and 1 respectively.

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Similarly, we can divide 3 and 9 with the common factor, 3.

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This gives 1 and 3 respectively.

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Since there are no more common factors, let's continue the multiplication.

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Multiply 1 with 2, gives 2. Multiply 1 with 3, gives 3.

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Finally, we have the fraction, 2/3.

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That is all for this lesson. Try out the practice questions to test your understanding.

--End of How to Divide Fractions Transcript--

Practice Questions & More

Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on how to divide fractions or pick your choice of question below.

Question 1 on dividing a proper fraction with a mixed fraction

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