Subjects fractions

Ratio Sixths 38D980

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1. **Problem 1: Find the ratio of 3 quarts to 3 gallons.** 2. First, recall the unit conversion: 1 gallon = 4 quarts. 3. Convert 3 gallons to quarts: $$3 \text{ gallons} = 3 \times 4 = 12 \text{ quarts}$$ 4. The ratio of 3 quarts to 3 gallons is the same as the ratio of 3 quarts to 12 quarts. 5. Write the ratio as a fraction: $$\frac{3}{12}$$ 6. Simplify the fraction by dividing numerator and denominator by their greatest common divisor 3: $$\frac{\cancel{3}}{\cancel{12}} = \frac{1}{4}$$ 7. So, the ratio of 3 quarts to 3 gallons is $$\boxed{\frac{1}{4}}$$. 8. **Problem 2: How many sixths are there in $$\frac{4}{5}$$?** 9. To find how many $$\frac{1}{6}$$ parts fit into $$\frac{4}{5}$$, divide $$\frac{4}{5}$$ by $$\frac{1}{6}$$: $$\frac{4}{5} \div \frac{1}{6} = \frac{4}{5} \times \frac{6}{1}$$ 10. Multiply numerators and denominators: $$\frac{4 \times 6}{5 \times 1} = \frac{24}{5}$$ 11. So, there are $$\boxed{\frac{24}{5}}$$ sixths in $$\frac{4}{5}$$. **Final answers:** - Ratio of 3 quarts to 3 gallons: $$\frac{1}{4}$$ - Number of sixths in $$\frac{4}{5}$$: $$\frac{24}{5}$$