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This lesson shows you the basics behind adding fractions.

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

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

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

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

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

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

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

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

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

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

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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.

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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.

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

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

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Notice that, these 2 fractions have unlike denominators.

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

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

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

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This means that, these fractions must have like denominators.

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

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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.

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This gives the fraction, 4/6.

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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.

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

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

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

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

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

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We can do so, by using equivalent fractions.

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

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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.

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

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

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

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

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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.

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

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

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

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

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

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