Write four more rational number in each of the patterns:
`(-1)/(6) , (2)/(-12) , (3)/(-18) , (4)/(-24),...`

Answer

To find four more rational numbers in the given pattern:

**Given Rational Numbers:**
1. \(-\frac{1}{6}\)
2. \(\frac{2}{-12}\)
3. \(\frac{3}{-18}\)
4. \(\frac{4}{-24}\)

**Step 1: Identify the pattern in the numerators and denominators.**

- The numerators are: \(-1, 2, 3, 4\)
- The numerators are increasing by 1 starting from -1.
- The next numerators will be: \(5, 6, 7, 8\).

**Step 2: Identify the pattern in the denominators.**

- The denominators are: \(6, -12, -18, -24\)
- The denominators are multiples of 6:
- \(6 \times 1 = 6\)
- \(6 \times 2 = 12\) (negative)
- \(6 \times 3 = 18\) (negative)
- \(6 \times 4 = 24\) (negative)

- Continuing this pattern, the next denominators will be:
- \(6 \times 5 = 30\) (negative)
- \(6 \times 6 = 36\) (negative)
- \(6 \times 7 = 42\) (negative)
- \(6 \times 8 = 48\) (negative)

**Step 3: Write the next four rational numbers.**

Using the identified patterns, we can write the next four rational numbers as:
1. \(\frac{5}{-30}\)
2. \(\frac{6}{-36}\)
3. \(\frac{7}{-42}\)
4. \(\frac{8}{-48}\)

**Final List of Rational Numbers:**
1. \(-\frac{1}{6}\)
2. \(\frac{2}{-12}\)
3. \(\frac{3}{-18}\)
4. \(\frac{4}{-24}\)
5. \(\frac{5}{-30}\)
6. \(\frac{6}{-36}\)
7. \(\frac{7}{-42}\)
8. \(\frac{8}{-48}\)

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