1. The problem involves comparing two ratios: $4:30$ and $5:14$ minutes.
2. To compare ratios, convert each ratio to a fraction and simplify if possible.
3. First ratio: $\frac{4}{30}$. Simplify by dividing numerator and denominator by their greatest common divisor (GCD), which is 2.
$$\frac{4}{30} = \frac{\cancel{2} \times 2}{\cancel{2} \times 15} = \frac{2}{15}$$
4. Second ratio: $\frac{5}{14}$. The GCD of 5 and 14 is 1, so it is already in simplest form.
5. To compare $\frac{2}{15}$ and $\frac{5}{14}$, find a common denominator or cross-multiply.
6. Cross-multiplying:
$$2 \times 14 = 28$$
$$5 \times 15 = 75$$
7. Since $28 < 75$, we conclude that $\frac{2}{15} < \frac{5}{14}$.
8. Therefore, the ratio $4:30$ is less than the ratio $5:14$ when expressed in minutes.
Ratio Comparison D83C9D
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