Divide.

2 1/3÷2/5
(1 point)
Responses

14/15
14 over 15

9/16
9 over 16

4/5
4 fifths

5 5/6
5 and 5 sixths

1 answer

To divide \( 2 \frac{1}{3} \) by \( \frac{2}{5} \), we first convert \( 2 \frac{1}{3} \) into an improper fraction.

  1. Convert \( 2 \frac{1}{3} \) to an improper fraction: \[ 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \]

  2. Now divide \( \frac{7}{3} \) by \( \frac{2}{5} \). To divide by a fraction, we multiply by its reciprocal: \[ \frac{7}{3} \div \frac{2}{5} = \frac{7}{3} \times \frac{5}{2} \]

  3. Multiply the fractions: \[ \frac{7 \times 5}{3 \times 2} = \frac{35}{6} \]

So, the final result of the division is \( \frac{35}{6} \).

Since this fraction does not match any of the provided responses, it seems that we have a misalignment. However, since \( \frac{35}{6} \) does not fit the list, here's the summary of what we computed and the correct answer:

  • The division results in \( \frac{35}{6} \) (which could also be expressed as \( 5 \frac{5}{6} \)).

Therefore, the closest correct response from your options should be \( 5 \frac{5}{6} \).