Multiplying Fractions

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Lesson Objective

In this lesson, we will learn the basics behind multiplying fractions and will be using some examples to explain how this multiplication works.

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About This Lesson

It is easier to multiply fractions as compared to adding or subtracting fractions. This is because we don't have to worry about the denominators.

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

  • are proper fractions
  • a proper fraction and a mixed fraction.

The study tips and math video below will explain more.

multiplying fractions

Study Tips

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Tip #1

When multiplying fractions, the denominators don't have to be the same.

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Tip #2 - How to Multiply Fractions

Below are steps to multiply two fractions:

  1. Multiply the numerators:
    Multiply the numerators (2 x 1 = 2)
  2. Multiply the denominators:
    Multiply the denominators (4 x 5 = 20)
  3. Simplify the fraction if possible:
    Simplify the fraction 2/20
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Tip #3 - Multiplying Mixed Fractions

The example below shows how we can multiply two mixed fractions:

Multiply 1 1/2 with 2 1/3
  1. Convert the mixed fractions to improper fractions:
    Convert mixed fractions to improper fractions
  2. After the conversions, we have:
    Multiply 3/2 with 7/3
  3. Now, multiply the fractions as usual. Simplify if possible:
    Multiply the converted fraction, 3/2 with 7/3

Watch the math video below for more explanation.

Math Video

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Lesson Video

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Math Video Transcript

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

Now, compared to adding or subtracting fractions, it is easier to multiply fractions.

This is because when we multiply fractions, we don’t have to make the denominators the same.

For example, let's multiply, 2/3 with 4/5.

To do so, we just need to multiply the numerators together.

Therefore, we multiply 2 with 4. This gives 8.

Next, we multiply the denominators together.

Therefore, we multiply 3 with 5. This gives 15.

So finally, we can see that this fraction multiplication gives 8/15.

Now, let's visually examine how this multiplying fractions work.

We can represent 2/3, with this rectangle. Similarly, we represent 4/5, with this rectangle.

When we multiply these fractions, visually, it means that we are combining these rectangles.

When the green and purple rectangles overlap, they give blue rectangles.

Here, we can see that, these 8 blue rectangles are represented by the numerator 8.

Also, notice that there are total of 15 rectangles, which are represented by the denominator 15.

Alright, let's take a look at more examples on multiplying fractions.

Let's multiply, 7/8, with 2/5.

First we multiply the numerators. So, we multiply 7 with 2. This gives 14.

Next, multiply the denominators. So, we multiply 8 with 5. This gives 40.

Now, we have the fraction, 14/40.

Notice that, we can simplify this fraction. To do so, we divide the numerator and denominator with 2.

This gives the simplified fraction, 7/20.

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

Notice the mixed fraction here?

It is important to change it to an improper fraction before multiplying.

To do so, first, we multiply 2 with 3. This gives 6.

Next, we add 6 with 1. This gives 7. This 7 becomes the improper fraction's numerator.

Hence, we have the improper fraction, 7/2.

We can now multiply these fractions.

First, multiply the numerators. So, we multiply 1 with 7. This gives 7.

Next, we multiply the denominators. So, we multiply 3 with 2. This gives 6.

Notice that, 7/6 is an improper fraction. Now, rather than leaving the answer like this, it is recommended to change it to a mixed fraction, by using long division.

Here's how. 7/6 is the same as, 7 divides 6. Now, this division gives the quotient 1. This quotient is actually the whole number for the mixed fraction.

Next, we multiply 1 with 6. This gives 6. 7 minus 6 gives the remainder as 1.

This remainder, 1, is actually the mixed fraction's numerator.

So here, we have the answer in mixed fraction, 1 1/6.

That is all for this lesson. Try out the practice question to further your understanding.

--End of Multiplying 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 questions on Multiplying Fractions or pick your choice of question below.

  • Question 1 on multiplying two proper fractions
  • Question 2 on multiplying a mixed fraction with a proper fraction
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