1. **Problem statement:** Arrange the given fractions (rivet sizes) in order from smallest to largest. 2. **Method:** To compare fractions, convert each to a decimal or find a common denominator. 3. **Example for problem 6:** - Convert each fraction to decimal: - $\frac{3}{4} = 0.75$ - $\frac{7}{8} = 0.875$ - $\frac{13}{16} = 0.8125$ - $\frac{49}{64} = 0.765625$ - $\frac{27}{32} = 0.84375$ 4. **Order from smallest to largest:** $\frac{3}{4} (0.75), \frac{49}{64} (0.765625), \frac{13}{16} (0.8125), \frac{27}{32} (0.84375), \frac{7}{8} (0.875)$ 5. **Repeat for problem 7:** - Convert: - $\frac{5}{16} = 0.3125$ - $\frac{3}{8} = 0.375$ - $\frac{9}{32} = 0.28125$ - $\frac{21}{64} = 0.328125$ - $\frac{1}{4} = 0.25$ - Order: $\frac{1}{4} (0.25), \frac{9}{32} (0.28125), \frac{5}{16} (0.3125), \frac{21}{64} (0.328125), \frac{3}{8} (0.375)$ 6. **Problem 8:** - Convert: - $\frac{57}{64} = 0.890625$ - $\frac{7}{8} = 0.875$ - $\frac{3}{4} = 0.75$ - $\frac{29}{32} = 0.90625$ - $\frac{13}{16} = 0.8125$ - Order: $\frac{3}{4} (0.75), \frac{13}{16} (0.8125), \frac{7}{8} (0.875), \frac{57}{64} (0.890625), \frac{29}{32} (0.90625)$ 7. **Problem 9:** - Convert: - $\frac{45}{64} = 0.703125$ - $\frac{5}{8} = 0.625$ - $\frac{3}{4} = 0.75$ - $\frac{11}{16} = 0.6875$ - $\frac{23}{32} = 0.71875$ - Order: $\frac{5}{8} (0.625), \frac{11}{16} (0.6875), \frac{45}{64} (0.703125), \frac{23}{32} (0.71875), \frac{3}{4} (0.75)$ 8. **Problem 10:** - Convert: - $\frac{1}{4} = 0.25$ - $\frac{5}{16} = 0.3125$ - $\frac{1}{16} = 0.0625$ - $\frac{17}{64} = 0.265625$ - $\frac{9}{32} = 0.28125$ - $\frac{7}{64} = 0.109375$ - $\frac{3}{8} = 0.375$ - $\frac{7}{32} = 0.21875$ - $\frac{1}{2} = 0.5$ - $\frac{23}{64} = 0.359375$ - Order: $\frac{1}{16} (0.0625), \frac{7}{64} (0.109375), \frac{7}{32} (0.21875), \frac{1}{4} (0.25), \frac{17}{64} (0.265625), \frac{9}{32} (0.28125), \frac{5}{16} (0.3125), \frac{23}{64} (0.359375), \frac{3}{8} (0.375), \frac{1}{2} (0.5)$ **Final answers:** 6. $\frac{3}{4}, \frac{49}{64}, \frac{13}{16}, \frac{27}{32}, \frac{7}{8}$ 7. $\frac{1}{4}, \frac{9}{32}, \frac{5}{16}, \frac{21}{64}, \frac{3}{8}$ 8. $\frac{3}{4}, \frac{13}{16}, \frac{7}{8}, \frac{57}{64}, \frac{29}{32}$ 9. $\frac{5}{8}, \frac{11}{16}, \frac{45}{64}, \frac{23}{32}, \frac{3}{4}$ 10. $\frac{1}{16}, \frac{7}{64}, \frac{7}{32}, \frac{1}{4}, \frac{17}{64}, \frac{9}{32}, \frac{5}{16}, \frac{23}{64}, \frac{3}{8}, \frac{1}{2}$