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In this video we will look at how to calculate fractions by adding and subtracting.
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We will be using the following methods:
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We extend/shorten the fraction, which is the same as multiply/divide the fraction, in order to get a common denominator. After that, since the denominator is the same, we are able to add the two fractions together and then, if possible, simplifying the fraction further.
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We first need to look at how to extend/shorten the fractions by using division or multiplication, in order to find a common denominator.
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When extending a fraction, you multiplying the numerator and the denominator by the same number.
When shortening a fraction, you then divide the numerator and the denominator by the same number.
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We will do two examples.
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We have 3/8 and we will extend this fraction by 2
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This will give us the fraction 6/16
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The fractions 3/8 and 6/16 are equal and have the exact same value. To show this we can use an image.
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We have a circle that is divided into 8 equal pieces.
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Let's highlight three of these, i.e. 3/8
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If we then divide the circle into 16 equal parts, we can see that the marked area now covers 6 out of the 16 pieces.
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Because of this 3/8 is equal to 6/16
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Let's also do an example on how to shorten, or simplify, a fraction.
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We have the fraction 18/24 and we will shorten it by 6. To do this, we divide both the numerator and the denominator by 6
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This will give us 3/4, which means that 18/24 is the exact same as 3/4
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We will also look at how to find a common denominator
and most preferably the smallest common denominator.
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The idea here is to extend or shorten the fractions so that they
have the same denominator. We will do an example.
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We have the two fractions 1/3 and 2/5
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These two fractions have the smallest common denominator at
15 since we can extend the denominators 3 and 5 to 15
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We can extend the fraction 1/3 by 5 so that we get
5/15, and fraction 2/5 can be extended by 3 so that we get 6/15
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Now both fractions have the same denominator, and they can now be added or subtracted by each other.
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We will continue this video by doing three examples. First we are going to calculate 2/5 + 1/2
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When it comes to the denominators 5 and 2, the lowest common denominator will be 10
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When adding these two fractions together, we then first have to extend 2/5 by 2, and 1/2 by 5. This will give us 4/10 + 5/10
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Now both fractions have the same denominator. We are now able to write them as one single fraction, i.e. (4 + 5) / 10
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4 + 5 = 9, thereby this will be equal to 9/10
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In the next example we will calculate 1/3 - 1/4 + 1/5
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Here it may be a bit more tricky to immediately see what the lowest common denominator is.
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What we can do is to extend the fractions by the denominators in the two other fractions.
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When doing this we will for sure get a common denominator, even though it might not be the smallest.
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But as long as we have the same denominator, we are able to add and subtract
them. If needed, we can shorten, or simplify, the fraction afterwards.
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Back to the problem (1/3 - 1/4 + 1/5). Let us multiply every fraction by the denominators in the two remaining fractions, in order to create one common denominator.
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We then multiply 1/3 by 4 and 5, 1/4 is multiplied by 3 and 5 and 1/5
by 3 and 4
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Then we have 3·4·5 in all denominators, the denominators will then be 60 in all tree denominators.
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The entire calculation will now look like: 20/60 - 15/60 + 12/60, and since the denominator is the same, the numerators can be added together and written as one single fraction: (20-15+12) / 60 = 17/60
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We will finish this by calculating 2 + 2/3 - 1/12
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Here, we can re-write 2 as 2/1. This will make it easier to show every step in our process of finding a common denominator.
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The denominators in this calculation are 1, 3 and 12 and the smallest common denominator will thereby be 12
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Now we multiply, or lengthen, 2/1 by 12 and 2/3 by 4, in order to change the calculation to 24/12 + 8/12 - 1/12
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We can now add the numerators together and write them over the same denominator: (24+8-1) / 12 = 31/12
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We can also write this fraction in mixed form: 2 and 7/12