### Examples on How to Add Fractions

#### Lesson Objective

In this lesson, we will see a few more examples on how to add fractions...

#### About This Lesson

Once you have understood the basics behind adding fractions, it is time to look at several more examples.

In this lesson, we will learn how to add the following fractions:

- Whole number + proper fraction
- Mixed fraction + proper fraction with like denominator
- Mixed fraction + proper fraction with unlike denominator

The study tips and math video below will explain more.

### Study Tips

#### Tip #1

By now, you should know that we can add two fractions directly only if these fractions have like denominators.

If these fractions have unlike denominators, it is important to change these fractions (e.g. using equivalent fractions) so that the denominators are the same.

#### Tip #2

When we add two fractions, one of the fraction can be a mixed fraction. Now, generally speaking, it is better to convert this fraction into an improper fraction before adding. This is illustrated below:

If you are not sure how to do this conversion, click here for the lesson.

#### Tip #3

We may come across adding a whole number with a fraction. For example:

Now, we can easily get the answer by combining the whole number and the fraction together as shown below:

The math video will show some examples...

### Math Video

#### Lesson Video

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#### Math Video Transcript

Transcript on How to Add Fractions

00:00:02.210

This video shows some more examples on adding fractions.

00:00:06.180

Let's add 2, and 1/3 together.

00:00:10.160

First, let's change 2, into a fraction before adding. We know that, 2 is equals to 2 divides 1.

00:00:20.030

So, when we change it into the form of fraction, it becomes 2/1. Therefore, we can change this to 2/1.

00:00:31.070

Notice that, we cannot add these 2 fractions because they have unlike denominators.

00:00:37.080

Therefore, the only way to add these fractions, is to make them to have like denominators.

00:00:43.160

So, how to add fractions? We can do so, by using equivalent fractions.

00:00:48.100

Using equivalent fractions, we can change this denominator to 3, by multiplying the numerator and denominator of this fraction with 3.

00:00:57.230

This gives the fraction, 6/3.

00:01:02.150

Now, with like denominators, we can just add these 2 fractions. This gives 6 plus 1/3.

00:01:12.030

Now, 6 plus 1 gives 7. Finally, we have the fraction, 7/3.

00:01:20.190

Notice that, 7/3 is an improper fraction. So, rather than leaving the answer like this, it is recommended to change it to a mixed fraction using long division. Here's how.

00:01:33.070

7/3 is the same as, 7 divides by 3. Now, this division gives the quotient 2. This quotient is actually the whole number for the mixed fraction.

00:01:48.120

Next, we multiply 2 with 3. This gives 6. 7 minus 6 gives the remainder as 1.

00:01:59.020

This remainder, 1, becomes the mixed fraction numerator.

00:02:04.160

So here, we have the answer in mixed fraction, 2 1/3.

00:02:11.150

Now, there something interesting that we should take note.

00:02:17.040

Next time, if we have similar question like this, we can quickly get the answer by just combining the whole number, with the fraction.

00:02:29.170

Next example, let's add 1 2/3 with, 1/3. How to add fractions? Notice that, this fraction is a mixed fraction.

00:02:40.080

So, it is advisable to first convert this fraction to an improper fraction, before we add these fractions. This is to minimize mistakes.

00:02:50.020

To do so, we just multiply 3 with 1. This gives 3.

00:02:57.090

Now, we add 3 with 2. This gives 5, which becomes the improper fraction's numerator. Now, we have the improper fraction, 5/3.

00:03:12.090

Now, since these fractions have like denominators, we can start adding them together.

00:03:18.150

This gives 5 plus 1/3. Adding 5 with 1, gives 6. Now, we have the fraction as 6/3.

00:03:31.130

Notice that, we can simplifying this fraction by dividing 6 with 3. This gives the answer, 2.

00:03:41.240

Next example on how to add fractions, 1 1/2 with 1/3.

00:03:48.030

Notice that, this fraction is a mixed fraction. Again, it is advisable to convert it to an improper fraction.

00:03:56.060

To do so, we just multiply 2 with 1. This gives 2.

00:04:02.210

Now, we add 2 with 1. This gives 3, which becomes the improper fraction's numerator. Now, we have the improper fraction, 3/2.

00:04:17.100

Notice that, we cannot add these 2 fractions because they have unlike denominators. Therefore, how to add fractions?

00:04:23.140

Therefore, the only way to add these fractions, is to make them to have like denominators. We can do so, by using equivalent fractions.

00:04:34.180

Here's how to add fractions. We can make the denominators the same by multiplying 3/2, with the other fraction's denominator 3, and multiplying 1/3, with the other fraction's denominator 2.

00:04:49.100

Let's do so. Multiplying 3/2 with 3, and multiplying 1/3 with 2. This gives the equivalent fractions, 9/6, and 2/6 respectively.

00:05:04.220

The denominators are now the same.

00:05:08.100

Hence, we can now add these two fractions together. This gives 9 plus 2/6.

00:05:17.160

Adding 9 with 2, gives 11. With this, we have the fraction, 11/6.

00:05:26.090

Notice that, 11/6 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.

00:05:38.220

Here's how. 11/6 is the same as 11 divides 6. Now, this division gives the quotient as 1.

00:05:49.220

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

00:05:54.170

Next, we multiply 1 with 6. This gives 6. 11 minus 6 gives the remainder as 5.

00:06:05.120

This remainder, 5, is actually the mixed fraction's numerator.

00:06:11.170

So here, we have the final answer as, 1 5/6.

00:06:18.240

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

End of Transcript on How to Add Fractions

### 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 how to add fractions or pick your choice of question below.

- Question 1 on adding a whole number with a proper fraction
- Question 2 on adding a mixed fraction with a proper fraction

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