Question

order from greatest to least:
6 8/15 , 6 1/5 , 6 2/3

Answer 1

To compare the mixed numbers \(6 \frac{8}{15}\), \(6 \frac{1}{5}\), and \(6 \frac{2}{3}\), we can convert them to improper fractions:

1. **Convert \(6 \frac{8}{15}\)**:
\[
6 \frac{8}{15} = \frac{6 \times 15 + 8}{15} = \frac{90 + 8}{15} = \frac{98}{15}
\]

2. **Convert \(6 \frac{1}{5}\)**:
\[
6 \frac{1}{5} = \frac{6 \times 5 + 1}{5} = \frac{30 + 1}{5} = \frac{31}{5}
\]
To compare with \(\frac{98}{15}\), we can convert \(\frac{31}{5}\) to have a denominator of 15:
\[
\frac{31}{5} = \frac{31 \times 3}{5 \times 3} = \frac{93}{15}
\]

3. **Convert \(6 \frac{2}{3}\)**:
\[
6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3}
\]
Again, to compare with \(\frac{98}{15}\), convert \(\frac{20}{3}\):
\[
\frac{20}{3} = \frac{20 \times 5}{3 \times 5} = \frac{100}{15}
\]

Now we can compare all three improper fractions:
- \(6 \frac{8}{15} = \frac{98}{15}\)
- \(6 \frac{1}{5} = \frac{93}{15}\)
- \(6 \frac{2}{3} = \frac{100}{15}\)

Ordering them from greatest to least:
1. \(6 \frac{2}{3} = \frac{100}{15}\)
2. \(6 \frac{8}{15} = \frac{98}{15}\)
3. \(6 \frac{1}{5} = \frac{93}{15}\)

Thus, the final order is:
\[
6 \frac{2}{3}, 6 \frac{8}{15}, 6 \frac{1}{5}
\]