1. **State the problem:** We need to compare each complex fraction given in items A-F to 1 and determine which are equal to $\frac{1}{2}$ mile per hour. 2. **Recall the rule for dividing fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. That is, $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$$ 3. **Calculate each complex fraction:** A. $\frac{1}{6} \div \frac{1}{3} = \frac{1}{6} \times \frac{3}{1} = \frac{1 \times 3}{6 \times 1} = \frac{3}{6} = \frac{1}{2}$ B. $\frac{1}{3} \div \frac{2}{3} = \frac{1}{3} \times \frac{3}{2} = \frac{1 \times 3}{3 \times 2} = \frac{3}{6} = \frac{1}{2}$ C. $\frac{3}{4} \div 1 \frac{1}{2} = \frac{3}{4} \div \frac{3}{2} = \frac{3}{4} \times \frac{2}{3} = \frac{3 \times 2}{4 \times 3} = \frac{6}{12} = \frac{1}{2}$ D. $\frac{1}{2} \div 1 = \frac{1}{2} \times 1 = \frac{1}{2}$ E. $\frac{3}{4} \div \frac{3}{2} = \frac{3}{4} \times \frac{2}{3} = \frac{6}{12} = \frac{1}{2}$ F. $\frac{4}{9} \div \frac{10}{3} = \frac{4}{9} \times \frac{3}{10} = \frac{12}{90} = \frac{2}{15}$ (which is less than $\frac{1}{2}$) 4. **Classify each fraction compared to 1:** - Fractions equal to $\frac{1}{2}$ are less than 1. - Fractions less than $\frac{1}{2}$ are also less than 1. - Fractions greater than 1 would be those with value more than 1 (none here). So, all except F are exactly $\frac{1}{2}$, and F is less than $\frac{1}{2}$. 5. **Rewrite each complex fraction with denominator 1 by multiplying by the given fraction:** - $\frac{1}{6} \div \frac{1}{3} \times 0$ (given) - $\frac{2}{3} \div \frac{1}{7} \times 7$ - $\frac{3}{4} \div 1 \times 7$ - $\frac{1}{9} \div \frac{1}{16} \times \frac{16}{3}$ - $\frac{1}{2} \div \frac{1}{5} \times \frac{5}{2}$ **Note:** The first multiplication by 0 seems incorrect mathematically (multiplying by zero would zero the fraction), but it is given as is. **Final answer:** - Speeds equal to $\frac{1}{2}$ mile per hour: A, B, C, D, E - Speeds less than 1: A, B, C, D, E, F - Speeds greater than 1: None