1. **State the problem:** A container holds 0.7 liters of a mixture of oil and vinegar. Three-fourths ($\frac{3}{4}$) of the mixture is vinegar. We need to find how many liters of oil are in the container, expressed as both a fraction and a decimal. 2. **Identify the formula and important rules:** - Total mixture volume = 0.7 liters - Fraction of vinegar = $\frac{3}{4}$ - Fraction of oil = $1 - \frac{3}{4} = \frac{1}{4}$ (since the mixture is only oil and vinegar) 3. **Calculate the volume of oil:** $$\text{Oil volume} = \text{Total volume} \times \text{Fraction of oil} = 0.7 \times \frac{1}{4}$$ 4. **Show intermediate work:** $$0.7 \times \frac{1}{4} = \frac{0.7}{1} \times \frac{1}{4} = \frac{0.7 \times 1}{1 \times 4} = \frac{0.7}{4}$$ 5. **Convert 0.7 to a fraction:** $$0.7 = \frac{7}{10}$$ 6. **Substitute and multiply fractions:** $$\frac{7}{10} \times \frac{1}{4} = \frac{7 \times 1}{10 \times 4} = \frac{7}{40}$$ 7. **Final answer in fraction form:** $$\frac{7}{40}$$ 8. **Convert fraction to decimal:** $$\frac{7}{40} = 7 \div 40 = 0.175$$ 9. **Check answer in fraction form:** - Vinegar volume = $0.7 \times \frac{3}{4} = 0.7 \times 0.75 = 0.525$ liters - Oil volume = $0.7 - 0.525 = 0.175$ liters, which matches our decimal answer. **Answer:** There are $\frac{7}{40}$ liters or 0.175 liters of oil in the container.