Express `frac(-8)(11)` as a rational number with denominator
(i) 22,
(ii) -55.

Answer

To express \(-\frac{8}{11}\) as a rational number with different denominators, we will follow these steps:

### Step 1: Express \(-\frac{8}{11}\) with a denominator of 22
To convert \(-\frac{8}{11}\) to have a denominator of 22, we need to multiply the denominator (11) by 2.

\[ \text{New denominator} = 11 \times 2 = 22 \]

Since we multiplied the denominator by 2, we must also multiply the numerator by the same factor to keep the value of the fraction the same.

\[ \text{New numerator} = -8 \times 2 = -16 \]

Thus, we can express \(-\frac{8}{11}\) as:

\[ -\frac{8}{11} = -\frac{16}{22} \]

### Step 2: Express \(-\frac{8}{11}\) with a denominator of -55
Next, we want to express \(-\frac{8}{11}\) with a denominator of -55. To do this, we need to multiply the denominator (11) by -5.

\[ \text{New denominator} = 11 \times -5 = -55 \]

Again, since we multiplied the denominator by -5, we must multiply the numerator by -5 as well.

\[ \text{New numerator} = -8 \times -5 = 40 \]

Thus, we can express \(-\frac{8}{11}\) as:

\[ -\frac{8}{11} = \frac{40}{-55} \]

### Final Answers
1. \(-\frac{8}{11} = -\frac{16}{22}\)
2. \(-\frac{8}{11} = \frac{40}{-55}\)

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