### Understanding Fractions

#### Lesson Objective

Need help in understanding fractions? This lesson will show you the basic idea on fractions and the common terms used in describing fractions...

#### About This Lesson

To begin understanding fractions, this lesson introduces you the basic ideas behind fractions.

This lesson will also show the common terms used in describing fractions. These terms are:

- Numerator
- Denominator
- Proper Fractions
- Improper Fractions
- Mixed Fractions

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

### Study Tips

#### Tip #1 - Numerator and Denominator

When we divide two with five, we will usually write the expression in this way:

2รท5

Now, the above expression can also be written in the form of fraction as shown in the picture on the right.

Notice that, the fraction is divided into 2 parts. The upper part is the numerator and the lower part is the denominator.

The math video below will explain more.

#### Tip #2 - Proper Fractions

When a fraction's numerator is lesser than its denominator, this fraction is a proper fraction. Below are some examples:

^{5}/_{20 }, ^{3}/_{8 }, ^{7}/_{8}

#### Tip #3 - Improper Fractions & Mixed Fractions

A fraction is considered as an improper fraction when its numerator is greater or equals to its denominator. Below are some examples:

^{8}/_{7 }, ^{2}/_{1 }, ^{20}/_{6} , ^{5}/_{5}

Note that, an improper fraction can be changed into a mixed fraction and these two fractions are equivalent. The difference is only at the way they are written.

The picture on the right illustrates this. The math video below will explain more on this.

### Math Video

#### Lesson Video

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Understanding Fractions Transcript

00:00:03.020

This lesson shows you basic ideas behind in understanding fractions.

00:00:07.230

Let's say that we are given the expression, 2 divide 5.

00:00:12.190

Now, we should know that, 2 divide 5 can be changed into the form of fraction, which is, 2 over 5.

00:00:21.110

In this form, the upper part of the fraction is called, numerator, and the lower part is called, denominator.

00:00:30.030

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

00:00:36.220

Next, let's try to understand what does fraction means.

00:00:42.070

To do so, consider this long piece of bar.

00:00:46.190

When the fraction has a denominator of 5, this means that this bar is divided into, one, two, three, four, five small equal parts.

00:00:57.240

When the numerator is 2, it means that we selected 2 out of 5 parts of the bar, shown by the yellow colored parts.

00:01:07.010

Now, when we increase the numerator to three, four, five, observe the number of the yellow parts increase as well.

00:01:15.240

Here, notice that the numerator, and the denominator, are now the same.

00:01:21.080

This kind fraction means that, we are dividing 5 with 5, which gives 1.

00:01:28.050

We can visualize this by seeing the entire bar as 1 yellow piece.

00:01:35.050

Let's examine further, when we increase the numerator from 5 to 6, the numerator is now greater than the
denominator.

00:01:43.160

Here, we can visualize the fraction, 6 over 5, by seeing this yellow bar as 1, and the next bar has 1 of the 5 parts as yellow.

00:01:54.050

Now, let's further elaborate this fraction. By now, we should know that 6 over 5 is the same as 6 divides 5.

00:02:04.060

Also, from what we have seen here, 6 over 5 is also the same as one, one over five.

00:02:12.150

The next thing that we should know, since the numerator is greater than the denominator, this fraction is an improper fraction.

00:02:20.220

Also, when 6 over 5 is written in this way, this fraction is called a mixed fraction.

00:02:29.110

Alright, let us continue to increase this numerator . Observe how the improper fraction and mixed fraction changes.

00:02:37.210

The improper fraction, 7 over 5, will have the mixed fraction as 1, 2 over 5.

00:02:45.080

The improper fraction, 8 over 5, will have the mixed fraction as 1, 3 over 5.

00:02:52.110

The improper fraction, 9 over 5, will have the mixed fraction as 1, 4 over 5.

00:03:00.000

The improper fraction, 10 over 5 is the same as 10 divided by 5, which gives 2.

00:03:07.050

The improper fraction, 11 over 5, will have the mixed fraction as 2, 1 over 5.

00:03:15.060

Alright, that is all for this lesson. Try out the practice question to further 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 understanding fractions or pick your choice of question below.

- Question 1 on the basics terms needed in understanding fractions

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