Examples on How to Multiply Fractions

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Lesson Objective

In this lesson, we will see more examples on how to multiply fractions. Also, we will learn to make use of common factor to simplify the multiplication.

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About This Lesson

In the previous lesson, we learned about the basics on multiplying fractions. Now, we will see more examples on multiplying two fractions that are:

In this lesson, we will learn how to multiply two fractions that:

  • 2 proper fractions
  • 1 proper and 1 improper fraction
  • 2 mixed fractions

Also, we will learn to make use of common factor to simplify the multiplication whenever possible.

The study tips and math video below will explain more.

divide with the common factor 2

Study Tips

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Tip #1 - The basics on how to multiply fractions

The lesson on multiplying fractions has already explained the basics needed. Please go through it if you are not sure about it.

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Tip #2 - Simplify the multiplication using Common Factor

It is possible to simplify the multiplication if there is at least one common factor in the fractions. For example, let's multiply:

Multiply the fractions, 3/5 with 7/9
  1. Multiplying the fraction gives:
    Multiply the numerators and denominators, (3 x 7)/(5 x 9)
  2. Notice that 3 and 9 have the common factor, 3. Therefore we can divide these two numbers with 3.
    Divide 3 and 9 with the common factor 3
  3. This gives 1 and 3 respectively:
    Simplifying gives (1 x 7)/(5 x 3)
  4. Since we unable to further simplify the fractions, we can continue by multiplying them. This gives:
    The final fraction is 7/15

Math Video

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Lesson Video

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Math Video Transcript

00:00:03:01
In this lesson, we will see more examples on how to multiply fractions.

00:00:08:17
Also, we will learn on how to make the multiplication easier, using common factor.

00:00:15:14
Let's multiply 3/7, with 5/10.

00:00:19:21
Note that, we can make the multiplication easier, by first simplifying 5/10.

00:00:26:22
To do so, we divide the numerator and denominator with the common factor, 5.

00:00:33:05
This gives the fraction, 1/2.

00:00:37:16
Now, we multiply these fractions.

00:00:43:07
First, we multiply the numerators. 3 multiply by 1 gives 3.

00:00:50:24
Next, we multiply the denominators. 7 multiply by 2 gives 14.

00:00:59:02
So finally, we have the fraction, 3/14.

00:01:07:01
Next example, let's multiply 2/5, with 7/4. Let's see how to multiply fractions.

00:01:14:11
First, multiply the numerators. We get 2 multiply by 7.

00:01:23:02
Next, we multiply the denominators. We will get 5 x 4.

00:01:30:02
Before we multiply further , we can simplify this, by dividing 2 and 4 with the common factor, 2.

00:01:38:18
This gives 1, and 2 respectively.


00:01:43:03
Now, we have, 1 multiply 7/5 multiply 2.

00:01:49:11
Since there is no more common factor, let's continue to do the multiplication.

00:01:55:08
1 multiply 7, gives 7. 5 multiply 2, gives 10.

00:02:03:09
So finally, we have the fraction, 7/10.

00:02:11:08
Next example, let's multiply 1 3/5, with 2 1/2. Now, let's see how to multiply fractions.

00:02:19:12
Since these are mixed fractions, we have to convert them into improper fractions, before we can multiply.

00:02:27:06
Let's start with 1, 3/5. Multiplying 5 with 1.

00:02:31:11
This gives 5.

00:02:37:00
Now, adding 5 with 3 gives 8. This 8 becomes the improper fraction's numerator.

00:02:45:01
So now, we have the improper fraction, 8/5.

00:02:50:12
Next, let's convert 2, 1/2. 2 multiply 2, gives 4.

00:02:58:24
Add 4 with 1, gives 5. This 5 becomes the improper fraction's numerator.

00:03:06:15
So now, we have the improper fraction, 5/2.

00:03:12:14
We can now multiply, 8/5, with 5/2.

00:03:18:15
First, we multiply the numerators. This gives, 8 multiply 5.

00:03:26:15
Next, we multiply the denominators. This gives, 5 multiply 2.

00:03:34:10
Notice that, we can make this multiplication easier by dividing 8 and 2 with the common factor 2.

00:03:43:11
This gives 4, and 1 respectively.

00:03:47:21
Again, we can make the multiplication easier, by dividing these two fives with the common factor, 5. This gives 1 for both.

00:03:59:17
Now, we can continue multiplying. 4 multiply with 1 gives 4.

00:04:06:20
Next, 1 multiply with 1, gives 1.

00:04:12:01
Divide 4 with 1. This gives the final answer as 4.

00:04:18:14
That is all for this lesson. Try out the practice question to further your understanding.

--End of 'How to Multiply 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 how to multiply fractions or pick your choice of question below.

  • Question 1 on simplify and multiply two proper fractions
  • Question 2 on simplify and multiply two proper fractions
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