v) \( \frac{8}{7}: \frac{1}{23}-\frac{14}{21}: 23 \)

To solve the expression \( \frac{8}{7}: \frac{1}{23}-\frac{14}{21}: 23 \), we will first interpret the colons (:) as division. The expression can be rewritten as: \[ \frac{8}{7} \div \frac{1}{23} - \frac{14}{21} \div 23 \] Now, we will calculate each division separately. 1. **Calculating \( \frac{8}{7} \div \frac{1}{23} \)**: Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{8}{7} \div \frac{1}{23} = \frac{8}{7} \times 23 = \frac{8 \times 23}{7} = \frac{184}{7} \] 2. **Calculating \( \frac{14}{21} \div 23 \)**: Again, we will multiply by the reciprocal: \[ \frac{14}{21} \div 23 = \frac{14}{21} \times \frac{1}{23} = \frac{14}{21 \times 23} = \frac{14}{483} \] Now we can substitute these results back into the expression: \[ \frac{184}{7} - \frac{14}{483} \] To perform this subtraction, we need a common denominator. The least common multiple of 7 and 483 can be calculated. Since \( 483 = 7 \times 69 \), the common denominator is \( 483 \). Now we convert \( \frac{184}{7} \) to have a denominator of 483: \[ \frac{184}{7} = \frac{184 \times 69}{7 \times 69} = \frac{12696}{483} \] Now we can perform the subtraction: \[ \frac{12696}{483} - \frac{14}{483} = \frac{12696 - 14}{483} = \frac{12682}{483} \] Thus, the final result is: \[ \frac{12682}{483} \] This fraction can be simplified if necessary, but it appears to be in its simplest form. Therefore, the final answer is: \[ \frac{12682}{483} \]