1. The problem asks to express the fractions $\frac{4}{5}$ and $\frac{1}{6}$ as equivalent fractions with denominator 30. 2. To find an equivalent fraction, multiply numerator and denominator by the same number so that the denominator becomes 30. 3. For $\frac{4}{5}$, find the number to multiply 5 by to get 30: $$5 \times x = 30 \implies x = \frac{30}{5} = 6$$ 4. Multiply numerator and denominator by 6: $$\frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30}$$ 5. So, numerator $a = 24$. 6. For $\frac{1}{6}$, find the number to multiply 6 by to get 30: $$6 \times y = 30 \implies y = \frac{30}{6} = 5$$ 7. Multiply numerator and denominator by 5: $$\frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30}$$ 8. So, numerator $b = 5$. Final answers: $$a = 24, \quad b = 5$$