In this lesson, we will learn the basics behind adding fractions that have like and unlike denominators.
About This Lesson
It is quite straight forward to add fractions after we understand the basic ideas behind it.
This lesson shows you the important ideas that you should know when adding fractions. We will be dealing with fractions that have:
Also, you will able to see why
plays an important role when we have fractions with unlike denominators.
Tip #1 - Understand Equivalent Fractions
The idea behind Equivalent Fractions enables us to change a fraction's denominator. If you are not very sure about it,
to watch the math video lesson.
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 visually explain why we can do so.
Tip #3 - Adding fractions with unlike denominators
To add fraction with unlike denominators, we need to:
Make the denominators the same (like denominators)
Then, just add the same way as shown in Tip #2
Now, we can make the denominators the same by using the ideas 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:
Multiply both the denominators. This
Multiply 1 with the other fraction's
denominator. This gives 5.
Multiply 3 with the other fraction's
denominator. This gives 6.
Adding 5 with 6 gives 11. Hence, the resulting fraction is
. That is all.
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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.
on adding fractions with like denominators
on adding fractions with unlike denominators
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