Hi student, let me help you out!

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Part 1 - Adding fractions with unlike denominators

If two fractions have unlike denominators, we first need to give both of them the same denominator, since we know how to add fractions with the same denominators.

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Here we have the following fractions: [tex]\mathrm{\cfrac{5}{8}+\cfrac{1}{2}}[/tex].

First we should find the l.c.m. (least common multiple) of "8" and "2".

The l.c.m. of "8" and "2" is 8. Let's stick it in: [tex]\mathrm{\cfrac{5}{8}+\cfrac{1}{8}}[/tex].

Now let us consider the following: What did we multiply 2 by to get a result of 8?

Since we multiplied 2 by 4 to obtain 8, we also multiply 1 by 4: 4.

As a result, we obtain [tex]\mathrm{\cfrac{5}{8}+\cfrac{4}{8}}[/tex].

Now all we have to do is add the numerators.

This is what we obtain as a result: [tex]\mathrm{\cfrac{5+4}{8}=\cfrac{9}{8}}[/tex].

Notice that the answer is written as an improper fraction, a fraction such that the numerator is larger than the denominator.

Hope this helped you out, ask in comments if any queries arise.

Best Regards!

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