Multiply the fractions, ^{5}/_{6} and ^{3}/_{10}. Give the answer in the simplest form.

Let's write down these fractions:

First, we multiply the numerators (5 x 3). Next, multiply the denominators (6 x 10).

Notice that, 5 and 10 can be divided with the common factor 5. This gives 1 and 2 respectively.

Next, 3 and 6 can be divided with the common factor 3. This gives 1 and 2 respectively.

Since there is no more common factor. We can continue with the multiplication.

Here, we have the resulting fraction as ^{1}/_{4}. Clearly, the answer is C.

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