Question

Which is greater 1 5/8 in , 1 11/16 in 1 3/4 in or 1 1/2 inches

Answer 1

To compare the fractions, let's convert all the mixed numbers to improper fractions:

1. \(1 \frac{5}{8} = \frac{8}{8} + \frac{5}{8} = \frac{13}{8}\)
2. \(1 \frac{11}{16} = \frac{16}{16} + \frac{11}{16} = \frac{27}{16}\)
3. \(1 \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4} = \frac{14}{8}\) when expressed in eighths.
4. \(1 \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} = \frac{12}{8}\) when expressed in eighths.

Now, let's compare these fractions:

- \( \frac{13}{8} \) (1 5/8)
- \( \frac{27}{16} \) (1 11/16)
- \( \frac{14}{8} \) (1 3/4)
- \( \frac{12}{8} \) (1 1/2)

To compare \( \frac{27}{16} \) with the others, we can convert \( \frac{13}{8} \) and \( \frac{14}{8} \) to sixteenths:

- \( \frac{13}{8} = \frac{26}{16} \)
- \( \frac{14}{8} = \frac{28}{16} \)

Now, the fractions we have in sixteenths are:

- \( \frac{26}{16} \) (1 5/8)
- \( \frac{27}{16} \) (1 11/16)
- \( \frac{28}{16} \) (1 3/4)
- \( \frac{12}{8} = \frac{24}{16} \) (1 1/2)

Now comparing, we can determine:

- \( \frac{24}{16} < \frac{26}{16} < \frac{27}{16} < \frac{28}{16} \)

Thus, the greatest value among them is **1 3/4 inches (or \( \frac{28}{16} \)).**