1. **Problem statement:** Arrange the given rivet or drill sizes in order from smallest to largest. 2. **Key idea:** To compare fractions, convert them to decimals or find a common denominator. 3. **Example for c) ½" or 17/32": - Convert ½ to decimal: $\frac{1}{2} = 0.5$ - Convert 17/32 to decimal: $\frac{17}{32} = 0.53125$ - Since $0.5 < 0.53125$, ½" is smaller than 17/32". 4. **Problem 6: Arrange 3/4", 7/8", 13/16", 49/64", 27/32" from smallest to largest.** - Convert each to decimal: - $\frac{3}{4} = 0.75$ - $\frac{7}{8} = 0.875$ - $\frac{13}{16} = 0.8125$ - $\frac{49}{64} = 0.765625$ - $\frac{27}{32} = 0.84375$ - Order: 3/4" (0.75), 49/64" (0.765625), 13/16" (0.8125), 27/32" (0.84375), 7/8" (0.875) 5. **Problem 7: Arrange 5/16", 3/8", 9/32", 21/64", ¼" from smallest to largest.** - Convert each to decimal: - $\frac{5}{16} = 0.3125$ - $\frac{3}{8} = 0.375$ - $\frac{9}{32} = 0.28125$ - $\frac{21}{64} = 0.328125$ - $\frac{1}{4} = 0.25$ - Order: ¼" (0.25), 9/32" (0.28125), 5/16" (0.3125), 21/64" (0.328125), 3/8" (0.375) 6. **Problem 8: Arrange 57/64", 7/8", 3/4", 29/32", 13/16" from smallest to largest.** - Convert each to decimal: - $\frac{57}{64} = 0.890625$ - $\frac{7}{8} = 0.875$ - $\frac{3}{4} = 0.75$ - $\frac{29}{32} = 0.90625$ - $\frac{13}{16} = 0.8125$ - Order: 3/4" (0.75), 13/16" (0.8125), 7/8" (0.875), 57/64" (0.890625), 29/32" (0.90625) 7. **Problem 9: Arrange 45/64", 7/8", 3/4", 11/16", 23/32" from smallest to largest.** - Convert each to decimal: - $\frac{45}{64} = 0.703125$ - $\frac{7}{8} = 0.875$ - $\frac{3}{4} = 0.75$ - $\frac{11}{16} = 0.6875$ - $\frac{23}{32} = 0.71875$ - Order: 11/16" (0.6875), 45/64" (0.703125), 23/32" (0.71875), 3/4" (0.75), 7/8" (0.875) 8. **Problem 10: Arrange drill sizes 1/4", 5/16", 1/16", 17/64", 9/32", 3/4", ¼, 3/2, 7/8, 7/2, ½, 23/64 from smallest to largest.** - Convert each to decimal: - $\frac{1}{16} = 0.0625$ - $\frac{1}{4} = 0.25$ - $\frac{¼}{1} = 0.25$ (same as 1/4) - $\frac{23}{64} = 0.359375$ - $\frac{5}{16} = 0.3125$ - $\frac{17}{64} = 0.265625$ - $\frac{9}{32} = 0.28125$ - $\frac{1}{2} = 0.5$ - $\frac{5}{16} = 0.3125$ - $\frac{7}{8} = 0.875$ - $\frac{3}{4} = 0.75$ - $\frac{3}{2} = 1.5$ - $\frac{7}{2} = 3.5$ - Order: 1/16" (0.0625), 1/4" or ¼ (0.25), 17/64" (0.265625), 9/32" (0.28125), 5/16" (0.3125), 23/64" (0.359375), 1/2" (0.5), 3/4" (0.75), 7/8" (0.875), 3/2" (1.5), 7/2" (3.5) **Final answers:** - c) ½" < 17/32" - 6) 3/4", 49/64", 13/16", 27/32", 7/8" - 7) ¼", 9/32", 5/16", 21/64", 3/8" - 8) 3/4", 13/16", 7/8", 57/64", 29/32" - 9) 11/16", 45/64", 23/32", 3/4", 7/8" - 10) 1/16", 1/4" or ¼, 17/64", 9/32", 5/16", 23/64", 1/2", 3/4", 7/8", 3/2", 7/2"