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To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of 3/5 is 5/3.
Therefore, 1/8 divided by 3/5 becomes (1/8) * (5/3).
Multiplying the numerators together and the denominators together, we get (1 * 5) / (8 * 3).
Simplifying, we have 5/24 as the quotient of 1/8 divided by 3/5.