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 problem 6:** Arrange 3/4", 7/8", 13/16", 49/64", 27/32" from smallest to largest. 4. Convert each fraction to decimal: - $\frac{3}{4} = 0.75$ - $\frac{7}{8} = 0.875$ - $\frac{13}{16} = 0.8125$ - $\frac{49}{64} = 0.765625$ - $\frac{27}{32} = 0.84375$ 5. Order decimals: 0.75, 0.765625, 0.8125, 0.84375, 0.875 6. So, order is: $\frac{3}{4}$, $\frac{49}{64}$, $\frac{13}{16}$, $\frac{27}{32}$, $\frac{7}{8}$ 7. Repeat the same for other problems: **Problem 7:** 5/16, 3/8, 9/32, 21/64, 1/4 - $\frac{5}{16} = 0.3125$ - $\frac{3}{8} = 0.375$ - $\frac{9}{32} = 0.28125$ - $\frac{21}{64} = 0.328125$ - $\frac{1}{4} = 0.25$ Order: $\frac{1}{4}$, $\frac{9}{32}$, $\frac{5}{16}$, $\frac{21}{64}$, $\frac{3}{8}$ **Problem 8:** 57/64, 7/8, 3/4, 29/32, 13/16 - $\frac{57}{64} = 0.890625$ - $\frac{7}{8} = 0.875$ - $\frac{3}{4} = 0.75$ - $\frac{29}{32} = 0.90625$ - $\frac{13}{16} = 0.8125$ Order: $\frac{3}{4}$, $\frac{13}{16}$, $\frac{7}{8}$, $\frac{57}{64}$, $\frac{29}{32}$ **Problem 9:** 45/64, 5/8, 3/4, 1/16, 23/32 - $\frac{45}{64} = 0.703125$ - $\frac{5}{8} = 0.625$ - $\frac{3}{4} = 0.75$ - $\frac{1}{16} = 0.0625$ - $\frac{23}{32} = 0.71875$ Order: $\frac{1}{16}$, $\frac{5}{8}$, $\frac{45}{64}$, $\frac{23}{32}$, $\frac{3}{4}$ **Problem 10:** 1/4, 5/16, 1/16, 17/64, 9/32, 3/4, 1/64, 3/2, 7/8, 7/32, 1/2, 23/64 - $\frac{1}{4} = 0.25$ - $\frac{5}{16} = 0.3125$ - $\frac{1}{16} = 0.0625$ - $\frac{17}{64} = 0.265625$ - $\frac{9}{32} = 0.28125$ - $\frac{3}{4} = 0.75$ - $\frac{1}{64} = 0.015625$ - $\frac{3}{2} = 1.5$ - $\frac{7}{8} = 0.875$ - $\frac{7}{32} = 0.21875$ - $\frac{1}{2} = 0.5$ - $\frac{23}{64} = 0.359375$ Order: $\frac{1}{64}$, $\frac{1}{16}$, $\frac{7}{32}$, $\frac{1}{4}$, $\frac{17}{64}$, $\frac{9}{32}$, $\frac{5}{16}$, $\frac{23}{64}$, $\frac{1}{2}$, $\frac{3}{4}$, $\frac{7}{8}$, $\frac{3}{2}$ 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. $\frac{1}{16}$, $\frac{5}{8}$, $\frac{45}{64}$, $\frac{23}{32}$, $\frac{3}{4}$ 10. $\frac{1}{64}$, $\frac{1}{16}$, $\frac{7}{32}$, $\frac{1}{4}$, $\frac{17}{64}$, $\frac{9}{32}$, $\frac{5}{16}$, $\frac{23}{64}$, $\frac{1}{2}$, $\frac{3}{4}$, $\frac{7}{8}$, $\frac{3}{2}$