Final answer:
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. After simplifying, the quotient is 6.
Step-by-step explanation:
To calculate this quotient, we need to divide the fraction 9/4 by the fraction 3/8. When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction. So, we can rewrite the problem as: 9/4 * 8/3. Multiplying the numerators (9 * 8) gives us 72, and multiplying the denominators (4 * 3) gives us 12.
Therefore, the quotient is 72/12. To simplify this fraction, we find the greatest common factor (GCF) of 72 and 12, which is 12. Dividing 72 and 12 by 12 gives us 6 and 1 respectively. So, the simplified quotient is 6/1, which is equal to 6.