### Improper Fractions and Mixed Fractions

#### Lesson Objective

In this lesson, we will learn about improper fractions and mixed fractions. Also, we will see how we can convert from improper to mixed fraction and vice versa.

#### About This Lesson

In understanding fractions, we had seen some ideas behind improper fractions and mixed fractions.

This lesson will explain these two types of fractions in detail and show how they are related.

Next, we will learn a method to quickly convert between these two types of fractions.

You can proceed by reading the study tips first or watch the math video. You can try out the practice questions after that.

### Study Tips

#### Tip #1 - Understand the difference

An improper fraction can be converted into a mixed fraction. Note that, these two fractions are equivalent. The only difference is at the way they are written. See the picture below:

The math video below will explain more about it.

#### Tip #2 - Improper to Mixed Fractions

To quickly convert an improper fraction to a mixed fraction, we can use the 'long division' method. The picture below shows an example on converting ^{11}/_{5}.

The math video below and the practice questions will explain this in detail.

#### Tip #3 - Mixed to Improper Fractions

To quickly convert a mixed fraction to an improper fraction, we use the steps shown in the picture below.

Below is an example on converting 2 ^{1}/_{5}.

The math video below and the practice questions will explain this in detail.

### Math Video

#### Click play to watch video

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#### Math Video Transcript

00:00:02.230

In this lesson, we will learn about improper fractions, and mixed fractions.

00:00:08.150

Also, we will see how we can convert improper to mixed fraction, and vice versa.

00:00:17.080

Consider this fraction, 3 over 5.

00:00:21.240

Now, we can visually represent this fraction, with this long piece of bar.

00:00:28.030

Since the denominator is 5, we can divide this bar into 5 equal parts.

00:00:34.100

Next, with the numerator as 3, 3 out of 5 parts can be colored green.

00:00:40.080

Now, since the numerator is smaller than the denominator, this fraction is a proper fraction.

00:00:47.060

Alright, let's increase the numerator from 3, 4, 5.

00:00:52.230

Note that, from 5 onwards, this fraction is now considered as an I.F, because the numerator, is equals or greater than the denominator.

00:01:03.060

Let's further increase the numerator of this improper fraction until 11.

00:01:09.060

Now, if we observe carefully, we can actually use these bars to convert this I.F, to M.F.

00:01:16.210

Here's how.

00:01:18.170

Since, all the parts in this 2 bars are green, these bars can be considered as 2 whole green bars.

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As for the remaining bar, we have 1 out of 5 part colored as green.

00:01:31.210

So here, is the mixed fraction 2, 1 over 5, converted from I.F, 11 over 5.

00:01:39.230

As you can see, using these bars to convert I.F to M.F, is quite tedious.

00:01:46.210

Therefore, we need to learn a quicker way of doing this.

00:01:50.190

Here's how we can quickly convert the I.F, 11 over 5, to a M.F.

00:01:57.150

First, we know that 11 over 5 is the same as 11 divides 5.

00:02:03.120

So, by doing the division, we get the quotient as 2, which is actually the whole number for the mixed fraction.

00:02:12.110

Next, 2 multiply by 5 gives 10. 11 minus 10 gives the remainder as 1.

00:02:20.120

This remainder, 1, becomes the mixed fraction numerator, and it is actually the green part here.

00:02:29.220

Here, we can see that, we had successfully converted this improper fraction to mixed fraction.

00:02:37.060

Next, let's convert this M.F back to I.F.

00:02:42.080

First, we multiply 5 with 2. This gives 10.

00:02:47.170

This multiplication is actually the same as, finding the 10 green colored parts here.

00:02:54.190

Next, notice that, there is 1 more part to include.

00:02:59.170

We can include it by adding, 10 with 1. This gives 11, where it is actually the I.F's numerator.

00:03:09.100

Here, we had successfully done the conversion from M.F to I.F.

00:03:16.210

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

### 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 improper fractions and mixed fractions or pick your choice of question below.

- Question 1 on converting improper to mixed fractions
- Question 2 on converting mixed to improper fractions

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