Kaplan Nursing Entrance Practice Exam

What is the result of dividing 2 6/7 by 3/4?

1. 20/7

2. 80/21

3. 10/3

4. 24/5

The correct answer is: 80/21

To find the result of dividing \(2 \frac{6}{7}\) by \(\frac{3}{4}\), it is helpful to first convert the mixed number into an improper fraction. The mixed number \(2 \frac{6}{7}\) can be converted as follows: 1. Multiply the whole number (2) by the denominator (7): \(2 \times 7 = 14\). 2. Add the numerator (6) to that result: \(14 + 6 = 20\). 3. Therefore, \(2 \frac{6}{7}\) can be written as the improper fraction \(\frac{20}{7}\). Now, to divide \(\frac{20}{7}\) by \(\frac{3}{4}\), we can multiply by the reciprocal of \(\frac{3}{4}\): \[ \frac{20}{7} \div \frac{3}{4} = \frac{20}{7} \times \frac{4}{3} \] Next, multiply the numerators and the denominators: \[ \frac{20 \times 4}{7 \times 3} = \frac{80}{21}