Step \(1\)
Find the irreducible fraction in each ratio
case 1) \(\frac{40}{64}\)
Divide by \(8\) boths numerator and denominator
\(\frac{40}{64}=\frac{5}{8}\)
case 2) \(\frac{5}{75}\)
Divide by \(5\) boths numerator and denominator
\(\frac{5}{75}=\frac{1}{15}\)
case 3) \(\frac{14}{35}\)
Divide by \(7\) boths numerator and denominator
\(\frac{14}{35}=\frac{2}{5}\)
case 4) \(\frac{24}{64}\)
Divide by \(8\) boths numerator and denominator
\(\frac{24}{64}=\frac{3}{8}\)
case 5) \(\frac{6}{15}\)
Divide by \(3\) boths numerator and denominator
\(\frac{6}{15}=\frac{2}{5}\)
case 6) \(\frac{65}{104}\)
Divide by \(13\) boths numerator and denominator
\(\frac{65}{104}=\frac{5}{8}\)
case 7) \(\frac{66}{176}\)
Divide by \(22\) boths numerator and denominator
\(\frac{66}{176}=\frac{3}{8}\)
case 8) \(\frac{12}{30}\)
Divide by \(6\) boths numerator and denominator
\(\frac{12}{30}=\frac{2}{5}\)
case 9) \(\frac{15}{225}\)
Divide by \(15\) boths numerator and denominator
\(\frac{15}{225}=\frac{1}{15}\)
case 10) \(\frac{6}{16}\)
Divide by \(2\) boths numerator and denominator
\(\frac{6}{16}=\frac{3}{8}\)
case 11) \(\frac{15}{24}\)
Divide by \(3\) boths numerator and denominator
\(\frac{15}{24}=\frac{5}{8}\)
case 12) \(\frac{48}{128}\)
Divide by \(16\) boths numerator and denominator
\(\frac{48}{128}=\frac{3}{8}\)
Step \(2\)
Sort the ratios into bins
1) First Bin
\(Ratio=\frac{5}{8}\)
\(\frac{40}{64}\)
\(\frac{65}{104}\)
\(\frac{15}{24}\)
2) Second Bin
\(Ratio=\frac{1}{15}\)
\(\frac{5}{75}\)
\(\frac{15}{225}\)
3) Third Bin
\(Ratio=\frac{2}{5}\)
\(\frac{14}{35}\)
\(\frac{6}{15}\)
\(\frac{12}{30}\)
4) Fourth Bin
\(Ratio=\frac{3}{8}\)
\(\frac{24}{64}\)
\(\frac{66}{176}\)
\(\frac{6}{16}\)
\(\frac{48}{128}\)
