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Now that you understand what fractions are, let's learn to add them.
This is the basic concept of adding fractions with the same denominator:
Example:
Three-fifths means three parts out of five. One-fifth means one part out of five.
So,
More examples:
When we add fractions with the same denominator, we add only the numerators (top numbers).
If the resulting answer has the numerator equal to the denominator, this means the answer is 1 whole.
If the resulting answer has the numerator bigger than the denominator, this means the answer is an improper fraction.
An improper fraction is more than 1 whole so we must re-write it as a mixed fraction or a mixed number.
When adding fractions with the same denominators, it is similar to the idea of cutting something into smaller pieces then adding the individual pieces.
When it comes to adding fractions with different denominators, we encounter a problem.
Since the denominators are different, it means that we cut the whole into different sizes.
Example:
From the diagram we can see that the 1/3 piece and the 1/5 piece are of different sizes. If we just add the 2 pieces together, what size should the remainder of the pieces be, the smaller size or the bigger size? The way to accomplish this is to further divide each piece of the 1/3 fraction into 5 pieces to get 5/15. And further divide each of the 1/5 piece into 3 pieces to get 3/15 as shown below: |
Now we can add fractions with different denominators:
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