Improper Fractions and Mixed Fractions

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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.

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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.

improper and mixed fractions

Study Tips

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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:

difference betweeen improper and mixed fractions

The math video below will explain more about it.

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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.

converting improper to mixed fractions

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

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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.

converting mixed to improper fractions

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

Math Video

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Math Video Transcript

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

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

Consider this fraction, 3 over 5.

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

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

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

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

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

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

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

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

Here's how.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 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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