Consider the following fractions. \[ \frac{5}{21}, \frac{8}{15} \] Step 2 of 2 : How much larger is the larger fraction? Express your answer in simplest form.

To find out how much larger the larger fraction is, we first need to compare the two fractions: \(\frac{5}{21}\) and \(\frac{8}{15}\). We can do this by finding a common denominator. The least common multiple of 21 and 15 is 105. Now we convert both fractions to have the same denominator: For \(\frac{5}{21}\): \[ \frac{5}{21} = \frac{5 \times 5}{21 \times 5} = \frac{25}{105} \] For \(\frac{8}{15}\): \[ \frac{8}{15} = \frac{8 \times 7}{15 \times 7} = \frac{56}{105} \] Now that we have both fractions as \(\frac{25}{105}\) and \(\frac{56}{105}\), we can see that \(\frac{56}{105}\) is larger. To find out how much larger, we subtract the smaller fraction from the larger one: \[ \frac{56}{105} - \frac{25}{105} = \frac{56 - 25}{105} = \frac{31}{105} \] Thus, the larger fraction is \(\frac{31}{105}\) larger than the smaller fraction. This fraction is already in its simplest form.