Adding Fractions

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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.

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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.

Adding fractions with like denominators

Study Tips

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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.

multiply to find equivalent fraction
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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:

Add both the numerator together

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

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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.

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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:

Multiply the denominators

Step 1

Multiply both the denominators. This gives 10.

Multiply numerator with denominator

Step 2

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

Multiply numerator with denominator

Step 3

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

Add these fractions

Step 4

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

Math Video

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Lesson Video

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Math Video Transcript

This lesson shows you the basics behind adding fractions.

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

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

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

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

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

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

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

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

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

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

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.

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.

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

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

Notice that, these 2 fractions have unlike denominators.

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

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

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

This means that, these fractions must have like denominators.

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

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.

This gives the fraction, 4/6.

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.

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

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

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

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

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

We can do so, by using equivalent fractions.

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

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.

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

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

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

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

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.

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

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

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

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

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

That is all for this lesson. Try out the practice question to further 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 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
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