Final answer:
To simplify (5/8) / (3/4), multiply the first fraction by the reciprocal of the second fraction and simplify the resulting fraction by dividing the numerator and denominator by their greatest common divisor.
Step-by-step explanation:
To simplify the expression (5/8) / (3/4), we can multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping the numerator and denominator. So, (5/8) / (3/4) becomes (5/8) * (4/3). Now, we can multiply the numerators (5 * 4) and the denominators (8 * 3) to get the final answer. This gives us 20/24. To reduce this fraction to its lowest terms, we divide both the numerator and denominator by their greatest common divisor, which is 4. Dividing 20 by 4 gives us 5, and dividing 24 by 4 gives us 6. Therefore, the simplified form of (5/8) / (3/4) is 5/6.