To determine the width of the widest stamp, let's first convert all the measurements into improper fractions for easier comparison:
- \( 1 \frac{5}{8} \) in = \( \frac{8 \times 1 + 5}{8} = \frac{13}{8} \)
- \( 1 \frac{11}{16} \) in = \( \frac{16 \times 1 + 11}{16} = \frac{27}{16} \)
- \( 1 \frac{3}{4} \) in = \( \frac{4 \times 1 + 3}{4} = \frac{7}{4} = \frac{14}{8} \) (to have the same denominator as the first measurement)
- \( 1 \frac{1}{2} \) in = \( \frac{2 \times 1 + 1}{2} = \frac{3}{2} = \frac{12}{8} \)
Now we have the following measurements:
- \( \frac{13}{8} \) in
- \( \frac{27}{16} \) in
- \( \frac{14}{8} \) in
- \( \frac{12}{8} \) in
Now, let's convert all of these to a common denominator (16 works well):
- \( \frac{13}{8} = \frac{26}{16} \)
- \( \frac{27}{16} \) (remains the same)
- \( \frac{14}{8} = \frac{28}{16} \)
- \( \frac{12}{8} = \frac{24}{16} \)
Now, the widths in terms of sixteenths are:
- \( \frac{26}{16} \)
- \( \frac{27}{16} \)
- \( \frac{28}{16} \)
- \( \frac{24}{16} \)
Among these fractions, \( \frac{28}{16} \) is the largest.
Thus, the widest stamp measures \( 1 \frac{3}{4} \) inches.
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