Question

1/13,4 1/6,3 1/2,12/10 arrange in decreasing order with working

Answer 1

To arrange the fractions \( \frac{1}{13}, \, 4 \frac{1}{6}, \, 3 \frac{1}{2}, \, \frac{12}{10} \) in decreasing order, we first convert all the mixed numbers and fractions into improper fractions and have them all in the same format.

1. **Convert mixed numbers:**
- For \( 4 \frac{1}{6} \):
\[
4 \frac{1}{6} = 4 + \frac{1}{6} = \frac{4 \times 6 + 1}{6} = \frac{24 + 1}{6} = \frac{25}{6}
\]
- For \( 3 \frac{1}{2} \):
\[
3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}
\]

2. **Convert \( \frac{12}{10} \) to its simplest form:**
\[
\frac{12}{10} = \frac{6}{5}
\]

Now, we have the following fractions:
- \( \frac{1}{13} \)
- \( \frac{25}{6} \)
- \( \frac{7}{2} \)
- \( \frac{6}{5} \)

Next, we can convert all fractions to have a common denominator to compare them. The least common multiple of the denominators (13, 6, 2, 5) is 390.

3. **Convert each fraction:**
- For \( \frac{1}{13} \):
\[
\frac{1}{13} = \frac{1 \times 30}{13 \times 30} = \frac{30}{390}
\]
- For \( \frac{25}{6} \):
\[
\frac{25}{6} = \frac{25 \times 65}{6 \times 65} = \frac{1625}{390}
\]
- For \( \frac{7}{2} \):
\[
\frac{7}{2} = \frac{7 \times 195}{2 \times 195} = \frac{1365}{390}
\]
- For \( \frac{6}{5} \):
\[
\frac{6}{5} = \frac{6 \times 78}{5 \times 78} = \frac{468}{390}
\]

4. **Now we can compare the numerators:**
- \( \frac{30}{390} \)
- \( \frac{1625}{390} \)
- \( \frac{1365}{390} \)
- \( \frac{468}{390} \)

Arranging these fractions by their numerators in decreasing order gives us:
\[
\frac{1625}{390} > \frac{1365}{390} > \frac{468}{390} > \frac{30}{390}
\]

5. **Thus, the order of the original fractions from greatest to least is:**
\[
4 \frac{1}{6} > 3 \frac{1}{2} > \frac{6}{5} > \frac{1}{13}
\]

Final result in decreasing order:
\[
4 \frac{1}{6}, \, 3 \frac{1}{2}, \, \frac{6}{5}, \, \frac{1}{13}
\]