Dividing Fractions

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Lesson Objective

In this lesson, we will use some examples to explain the basics behind dividing fractions.

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About This Lesson

It is quite easy to divide fractions after we have learned to multiply fractions. This is because dividing fractions is closely related to multiplying fractions.

This relation lies in the step needed to convert the division to multiplication. The picture on the right will give you a rough idea on this.

The study tips and math video will explain more.

convert fraction division to fraction multiplication

Study Tips

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Tip #1 - Reciprocal of a fraction

We need to know how to find the reciprocal of a fraction before we can proceed. The example below shows how:

  1. Find the reciprocal of the following fraction:

    find the reciprocal of 3/4
  2. To do so, we simply swap the numerator and denominator:

    swap 3 and 4
  3. Hence, the reciprocal of 3/4 is:

    reciprocal of 3/4 is 4/3
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Tip #2 - Dividing Fractions

The following example shows the steps required to divide fractions:

  1. First, we change the division to multiplication. Then, we change the divisor 3/4, to its reciprocal, 4/3.

    changing to multiplication
  2. After doing so, we can continue by multiplying these fractions:

    multiply the fractions

The math video below will give more explanation on this. Also, we will see some examples it.

Math Video

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Lesson Video

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Math Video Transcript

In this lesson, we will learn the basics behind dividing fractions.

Let's divide, 1/5 with 3/4.

We can do so, by changing this division sign to multiplication sign, provided that we swap the numerator and denominator of the divisor, 3/4, to get its reciprocal, 4/3.

To explain this, let's take a look at the division again. Note that, 1/5 divides by 3/4, can be written in the form of fraction, 1/5, over, 3/4.

Now, 1/5 is the numerator, and 3/4 is the denominator.

Next, let's multiply the denominator with 4/3.

To keep this fraction equivalent, we must multiply the numerator with 4/3 as well.

Next, notice that these terms cancel off. This is because, 4 divides by 4, and 3 divides by 3 gives 1.

Now, we are left with the numerator. Dividing this numerator with 1, gives back itself, 1/5 multiply by 4/3.

Here, notice something interesting. By comparing these 2 terms, we observe that this fraction division is the same as fractions multiplication, provided that we change the divisor, 3/4 to its reciprocal, 4/3.

Knowing this, let's continue the division by multiplying these fractions.

First, multiply the numerators. 1 multiply by 4, gives 4.

Next, multiply the denominators. 5 multiply by 3, gives 15.

Finally, we have the fraction, 4/15.

Next example, let's divide 2/3, with 5/7.

We can do so, by changing this division sign to multiplication sign, provided that we swap the numerator and denominator of the divisor, 5/7, to get its reciprocal, 7/5.

Now, we can proceed by multiplying these fractions.

First, multiply the numerators. 2 multiply by 7, gives 14.

Next, multiply the denominators. 3 multiply by 5, gives 15.

Finally, we have the fraction, 14/15.

This is all for this lesson, try out the practice questions to further your understanding.

--End of Dividing Fractions Transcript--

Practice Questions & More

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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 Dividing Fractions or pick your choice of question below.

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