### Adding Fractions

#### Lesson Objective

In this lesson, we will learn the basics behind adding fractions with like denominators. We also will learn how to add fractions with unlike denominators.

#### About This Lesson

It is quite easy to add fractions after we have understood the basic ideas behind it.

This lesson will show you the important ideas that you need to know when adding fractions. We will be dealing with fractions with:

- Like denominators
- Unlike denominators

Here, you will able to see how Equivalent Fractions plays an important role when we add fractions with unlike denominators.

### Study Tips

#### Tip #1 - Understand Equivalent Fractions

The idea behind equivalent fractions enables us to change the denominator of a fraction. If you are not very sure about it, click here to watch the math video.

#### Tip #2 - Adding fractions with like denominators

It is quite simple to add fractions that have like denominators. To do so, we simply add the numerators together while keeping the denominator the same.

This is illustrated in the picture below:

The math video below will explain why we can do so.

#### Tip #3 - Adding fractions with unlike denominators

To add fractions with unlike denominators, we need to:

- Make the denominators the same (like denominators)
- Then add the fractions, using the same way as shown in Tip #2

Now, we can make the denominators of these fractions to be the same by using the idea behind equivalent fractions. Scroll down to the math video below for more explanation.

#### Tip #4 - Shortcut to add fractions with unlike denominators

Fortunately, there is a short-cut to add fractions with unlike denominators. Below are the steps:

#### Step 1

Multiply both the denominators. This gives 10.

#### Step 2

Multiply 1 with the other fraction's denominator. This gives 5.

#### Step 3

Multiply 3 with the other fraction's denominator. This gives 6.

#### Step 4

Adding 5 with 6 gives 11. Hence, the resulting fraction is 11/10 . That is all.

### Math Video

#### Math Video Transcript

00:00:03.050

This lesson shows you the basics behind adding fractions.

00:00:07.220

Let's consider these 2 fractions, 1/5, and 2/5.

00:00:14.060

Now, we can visually represent these fractions using these 2 bars.

00:00:20.210

The denominator 5, means that, each bar is divided into 5 parts.

00:00:28.050

The numerator 1 here, means that 1 part of this bar is colored green.

00:00:33.200

Similarly, the numerator 2, means that 2 parts of this bar are colored green.

00:00:40.050

Alright, let us now understand the basics behind adding fractions.

00:00:46.030

We can see that, these fractions have like denominators, which make all these parts to have the same size.

00:00:54.060

This means that, it is possible to add these 2 fractions, because all the parts match perfectly.

00:01:01.150

So, when we add these two fractions, it is like placing this green part on the empty part here.

00:01:09.080

Now, let's focus on this bar, by analyzing it here.

00:01:14.200

From this, we can see that by adding fractions, it will result in a new fraction with the numerator of 3, and the denominator of 5.

00:01:27.170

Using this observation, we can get the same result through calculation, by just adding both the numerators together, 1 plus 2, which gives 3. And, by keeping the denominator the same.

00:01:43.000

Now, we can see that, by calculating this way, we get back the same fraction, 3/5.

00:01:54.040

Next example, let's add these fractions together, 2/3, and 1/6.

00:02:01.120

Notice that, these 2 fractions have unlike denominators.

00:02:08.030

This means that, the size of the parts are not the same, as you can see right here.

00:02:17.140

Because of this, we can visually see that, we cannot add these 2 fractions as they are.

00:02:26.140

Therefore, the only way to add these fractions, is to make all the parts to have the same size.

00:02:33.210

This means that, these fractions must have like denominators.

00:02:40.040

To do so, we need to use Equivalent Fractions that we learned from the last lesson.

00:02:45.190

Notice that, by using equivalent fractions, we can change this denominator to 6, by multiplying both the numerator and denominator of this fraction with 2.

00:02:57.220

This gives the fraction, 4/6.

00:03:02.180

Now, we can see that the fractions have like denominators. This means that, all the parts have the same size. As you can see here.

00:03:16.060

With this, we can now add these two fractions together just like the previous example. By doing so, we get, (4+1)/6.

00:03:28.040

Now, 4 plus 1 gives 5. Finally, we have the fraction, 5/6.

00:03:39.170

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

00:03:45.190

Again, notice that these fractions have unlike denominators. Hence, the size of these parts are not the same, as we can see here.

00:03:58.210

Therefore, in order to add these fractions, we need to make these fractions to have like denominators.

00:04:05.080

We can do so, by using equivalent fractions.

00:04:10.100

Note that, unlike previous example, we can only get like denominators here, by finding the equivalent fractions for both of these fractions.

00:04:20.060

Here's how. We can make both the denominator the same by multiplying 2/3, with the other fraction's denominator, 2, and multiply 1/2 with, the other fraction's denominator, 3.

00:04:35.160

Let's do it. Multiplying 2/3, with 2, and multiplying 1/2, with 3

00:04:43.030

This gives the equivalent fractions, 4/6, and 3/6 respectively. With this, now these 2 fractions have like denominators.

00:04:56.130

Alright, we now add these two fractions together like the previous examples. This gives, (4+3)/6.

00:05:07.230

Now, 4 plus 3, gives 7. So, we have the fraction, 7/6.

00:05:17.010

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.

00:05:29.030

Here's how, 7/6 is the same as, 7 divide by 6. Now, this division gives the quotient 1.

00:05:40.170

This quotient is actually the whole number for the mixed fraction.

00:05:45.200

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

00:05:57.110

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

00:06:03.180

So here, we have successfully converted 7/6 to mixed fraction form, 1 1/6.

00:06:12.160

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 Adding Fractions or pick your choice of question below.

- Question 1 on adding fractions with like denominators
- Question 2 on adding fractions with unlike denominators

#### Site-Search and Q&A Library

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