Question

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

Answer 1

To compare the widths of the stamps, we first need to convert each measurement into improper fractions or decimals for easier comparison.

1. **1 and 5/8 inches:**
\[
1 + \frac{5}{8} = \frac{8}{8} + \frac{5}{8} = \frac{13}{8}
\]

2. **1 and 11/16 inches:**
\[
1 + \frac{11}{16} = \frac{16}{16} + \frac{11}{16} = \frac{27}{16}
\]

3. **1 and 3/4 inches:**
\[
1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4} = \frac{14}{8} \text{ (to make comparison easier)}
\]

4. **1 and 1/2 inches:**
\[
1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} = \frac{12}{8} \text{ (to make comparison easier)}
\]

Now let's convert these fractions so they have a common denominator for easy comparison. The common denominator can be 16.

1. **1 and 5/8 inches:**
\[
\frac{13}{8} = \frac{13 \times 2}{8 \times 2} = \frac{26}{16}
\]

2. **1 and 11/16 inches:**
\[
\frac{27}{16} \text{ (remains the same)}
\]

3. **1 and 3/4 inches:**
\[
\frac{7}{4} = \frac{7 \times 4}{4 \times 4} = \frac{28}{16}
\]

4. **1 and 1/2 inches:**
\[
\frac{3}{2} = \frac{3 \times 8}{2 \times 8} = \frac{24}{16}
\]

Now we have all the measurements converted to the same denominator:

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

Now we compare the numerators:

- \( \frac{26}{16} \) (1 and 5/8)
- \( \frac{27}{16} \) (1 and 11/16)
- \( \frac{28}{16} \) (1 and 3/4)
- \( \frac{24}{16} \) (1 and 1/2)

The widest stamp is \( 1\frac{3}{4} \) inches or \( \frac{28}{16} \).

**Thus, the width of the widest stamp is 1 and 3/4 inches.**