Monique measured the widths of several stamps in her collection of world stamps. The measurements are 1 5/8 in., 1 11/16 in., 1 3/4 in., and 1 1/2 in. What is the width of the widest stamp?

1 answer

To determine the widest stamp from the measurements provided, we need to convert all the mixed numbers into improper fractions or decimals for easier comparison.

  1. For \(1 \frac{5}{8}\): \[ 1 \frac{5}{8} = \frac{8}{8} + \frac{5}{8} = \frac{13}{8} \]

  2. For \(1 \frac{11}{16}\): \[ 1 \frac{11}{16} = \frac{16}{16} + \frac{11}{16} = \frac{27}{16} \]

  3. For \(1 \frac{3}{4}\): \[ 1 \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4} = \frac{14}{8} \]

  4. For \(1 \frac{1}{2}\): \[ 1 \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} = \frac{12}{8} \]

Next, we will compare all the fractions in terms of eighths:

  • \(1 \frac{5}{8} = \frac{13}{8}\)
  • \(1 \frac{11}{16} = \frac{27}{16} = \frac{54}{32}\) (converting to sixteenths)
  • \(1 \frac{3}{4} = \frac{7}{4} = \frac{14}{8}\)
  • \(1 \frac{1}{2} = \frac{3}{2} = \frac{12}{8}\)

To compare \(1 \frac{11}{16}\) to \(1 \frac{3}{4}\) and \(1 \frac{1}{2}\), we can convert \(1 \frac{3}{4}\) and \(1 \frac{1}{2}\) to sixteenths as well:

  • \(1 \frac{3}{4} = \frac{7}{4} = \frac{28}{16}\)
  • \(1 \frac{1}{2} = \frac{3}{2} = \frac{24}{16}\)

Now we can compare in terms of sixteenths:

  • \(1 \frac{5}{8} = \frac{13}{8} = \frac{26}{16}\)
  • \(1 \frac{11}{16} = \frac{27}{16}\)
  • \(1 \frac{3}{4} = \frac{28}{16}\)
  • \(1 \frac{1}{2} = \frac{24}{16}\)

Now we can see which is the largest:

  • \(1 \frac{1}{2} = \frac{24}{16}\) (smallest)
  • \(1 \frac{5}{8} = \frac{26}{16}\)
  • \(1 \frac{11}{16} = \frac{27}{16}\)
  • \(1 \frac{3}{4} = \frac{28}{16}\) (largest)

Thus, the width of the widest stamp is:

\[ \boxed{1 \frac{3}{4} \text{ in.}} \]