Subjects algebra

Ratio Comparison D83C9D

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

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.