Addition of Fractions 3

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We will now see a few special cases in faction addition.

Fractions Adding to More Than a Whole

Let us take &frac12; +3/4. This is difficult to demonstrate using paper because the &ldquo;whole&rsquo; gets &ldquo;destroyed&rdquo; when one of the fractions is taken out. So we need to keep the &ldquo;whole&rdquo; as a reference without directly working on it. Let us see a way of doing it.

We can see that 4 is a convenient whole for performing this operation. Let us think of a medicine tablet which is normally sold in a strip of 4 tablets. So the whole is a &ldquo;strip&rdquo; of tablets.

If we ask the shopkeeper for &frac12; a strip then she gives us 2 tablets. If we ask for &frac34; of a strip then we get 3 tablets. Hence together we have 5 tables. This can also be seen as 5/4 of a strip or 1 strip &amp; &frac14; of a strip. Hence we can say that &frac12; + &frac34; is 5/4. We can frame a word problem as below.

&ldquo;A particular tablet is sold in strips. If we buy &frac12; the strip in the morning and &frac34; of the strip in the evening, what is the total amount of the medicine we have bought on that day?&rdquo;

&ldquo;A Whole&rdquo; instead of &ldquo;The Whole&rdquo;

We see that for understanding fraction additions &amp; subtractions, discrete representations of fractions are more suitable. But it is also a more abstract idea than using continuous representations.

Hence as soon as children are comfortable with the idea of fractions &amp; part &amp; whole it is better to shift to the idea of &ldquo;a whole&rdquo; in place of &ldquo;the whole&rdquo;. &ldquo;A Whole&rdquo; can be seen as a independent entity which can be kept separately for reference.

Some Simple cases

We will now see some simple variations in fractions additions &amp; subtractions.

2 + 5 = 2 + 5 + +  = 7
 * 1) Addition of a whole number and a fraction can be directly written down. 2 + &frac34; can be directly written as 2.
 * 2) Addition of 2 mixed fractions. The whole numbers &amp; the fractions can be added separately and then combined. There is no need to convert each mixed fraction into an improper fraction.

 				#However, while applying this idea to subtraction of mixed fractions, we have to be careful.  For example in 4 - 2, we need to observe that &frac12; cannot be subtracted from 1/3. Here converting both to improper fractions would be a better option.


 * 1) In some cases, one of the denominators itself would be the LCM. For example +.

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