1. The problem states: For every $\frac{1}{4}$ mile Pascal walks, Lucien runs $\frac{2}{3}$ mile. We want to find how many miles Pascal walks for every 1 mile Lucien runs. 2. To find this, we set up the ratio of Pascal's distance to Lucien's distance and solve for Pascal's distance when Lucien runs 1 mile. 3. The ratio given is $\frac{1}{4}$ (Pascal) to $\frac{2}{3}$ (Lucien). We want to find $x$ such that: $$\frac{1}{4} : \frac{2}{3} = x : 1$$ 4. This means: $$x = \frac{1}{4} \div \frac{2}{3}$$ 5. Dividing fractions means multiplying by the reciprocal: $$x = \frac{1}{4} \times \frac{3}{2}$$ 6. Multiply numerators and denominators: $$x = \frac{1 \times 3}{4 \times 2} = \frac{3}{8}$$ 7. So, Pascal walks $\frac{3}{8}$ miles for every 1 mile Lucien runs. Answer to the blanks: 5. $\frac{1}{4} \div \frac{2}{3} = \frac{1}{4}$ divided by $\frac{2}{3}$ = $\frac{1}{4} \times \frac{3}{2}$ = $\frac{3}{8}$