1. **Problem statement:** Use method 2 to complete the number sentences by finding the unknown multiplier □ such that the sum of two fractions equals the product of one fraction and □. 2. **Step-by-step solutions:** **a.** $\frac{3}{4} + \frac{1}{2} = \frac{3}{4} \times \Box$ - Find sum: $\frac{3}{4} + \frac{1}{2} = \frac{3}{4} + \frac{2}{4} = \frac{5}{4}$ - Set equation: $\frac{5}{4} = \frac{3}{4} \times \Box$ - Solve for $\Box$: $\Box = \frac{5}{4} \div \frac{3}{4} = \frac{5}{4} \times \frac{4}{3} = \frac{5}{3}$ **b.** $\frac{2}{3} + \frac{1}{3} = \frac{5}{3} \times \Box$ - Sum: $\frac{2}{3} + \frac{1}{3} = \frac{3}{3} = 1$ - Equation: $1 = \frac{5}{3} \times \Box$ - Solve: $\Box = 1 \div \frac{5}{3} = \frac{3}{5}$ **c.** $\frac{7}{10} + \frac{1}{4} = \frac{7}{10} \times \Box$ - Sum: $\frac{7}{10} + \frac{1}{4} = \frac{14}{20} + \frac{5}{20} = \frac{19}{20}$ - Equation: $\frac{19}{20} = \frac{7}{10} \times \Box$ - Solve: $\Box = \frac{19}{20} \div \frac{7}{10} = \frac{19}{20} \times \frac{10}{7} = \frac{19}{14}$ **d.** $\frac{3}{10} + \frac{2}{5} = \frac{1}{2} \times \Box$ - Sum: $\frac{3}{10} + \frac{4}{10} = \frac{7}{10}$ - Equation: $\frac{7}{10} = \frac{1}{2} \times \Box$ - Solve: $\Box = \frac{7}{10} \div \frac{1}{2} = \frac{7}{10} \times 2 = \frac{7}{5}$ **e.** $\frac{3}{10} + \frac{1}{10} = \frac{4}{10} \times \Box$ - Sum: $\frac{3}{10} + \frac{1}{10} = \frac{4}{10}$ - Equation: $\frac{4}{10} = \frac{4}{10} \times \Box$ - Solve: $\Box = 1$ **f.** $1 + \frac{1}{10} = 1 \times \Box$ - Sum: $1 + \frac{1}{10} = \frac{10}{10} + \frac{1}{10} = \frac{11}{10}$ - Equation: $\frac{11}{10} = 1 \times \Box$ - Solve: $\Box = \frac{11}{10}$ **g.** $\frac{1}{5} + \frac{5}{10} = \frac{3}{10} \times \Box$ - Sum: $\frac{1}{5} + \frac{1}{2} = \frac{2}{10} + \frac{5}{10} = \frac{7}{10}$ - Equation: $\frac{7}{10} = \frac{3}{10} \times \Box$ - Solve: $\Box = \frac{7}{10} \div \frac{3}{10} = \frac{7}{10} \times \frac{10}{3} = \frac{7}{3}$ **h.** $\frac{1}{5} + \frac{1}{5} = \frac{2}{5} \times \Box$ - Sum: $\frac{1}{5} + \frac{1}{5} = \frac{2}{5}$ - Equation: $\frac{2}{5} = \frac{2}{5} \times \Box$ - Solve: $\Box = 1$ 3. **Use either method to find the basic fraction sums:** **a.** $\frac{3}{4} + \frac{1}{4} = \frac{4}{4} = 1$ **b.** $\frac{2}{3} + \frac{1}{3} = \frac{3}{3} = 1$ **c.** $\frac{7}{10} + \frac{1}{4} = \frac{14}{20} + \frac{5}{20} = \frac{19}{20}$ **Final answers:** - a: $\Box = \frac{5}{3}$ - b: $\Box = \frac{3}{5}$ - c: $\Box = \frac{19}{14}$ - d: $\Box = \frac{7}{5}$ - e: $\Box = 1$ - f: $\Box = \frac{11}{10}$ - g: $\Box = \frac{7}{3}$ - h: $\Box = 1$ Basic fraction sums: - a: $1$ - b: $1$ - c: $\frac{19}{20}$