Simplify the following :
(i) `(-7)+(-6)div2-{(-5)xx(-4)-(3-5)}`
(ii) `121div{17-{15-3(8-5)}]`.

Answer

Let's simplify the given expressions step by step.

### Part (i): Simplify `(-7) + (-6) ÷ 2 - {(-5) × (-4) - (3 - 5)}`

1. **Identify the operations**: We have addition, division, multiplication, and subtraction. According to the order of operations (BODMAS/BIDMAS), we need to solve brackets first, then division/multiplication from left to right, and finally addition/subtraction.

2. **Solve the inner brackets**: Start with `(3 - 5)`.
\[ 3 - 5 = -2 \]
Now, substitute this back into the expression:
\[ (-7) + (-6) ÷ 2 - {(-5) × (-4) - (-2)} \]

3. **Calculate the multiplication inside the curly brackets**:
\[ (-5) × (-4) = 20 \]
Substitute this back:
\[ (-7) + (-6) ÷ 2 - {20 - (-2)} \]

4. **Solve the subtraction inside the curly brackets**:
\[ 20 - (-2) = 20 + 2 = 22 \]
Substitute this back:
\[ (-7) + (-6) ÷ 2 - 22 \]

5. **Perform the division**:
\[ (-6) ÷ 2 = -3 \]
Substitute this back:
\[ (-7) + (-3) - 22 \]

6. **Now perform the addition/subtraction from left to right**:
\[ (-7) + (-3) = -10 \]
Then,
\[ -10 - 22 = -32 \]

So, the final answer for part (i) is:
\[ \text{Answer (i)} = -32 \]

### Part (ii): Simplify `121 ÷ {17 - {15 - 3(8 - 5)}}`

1. **Identify the operations**: Again, we have brackets, subtraction, and multiplication. We will follow the BODMAS/BIDMAS rules.

2. **Solve the innermost brackets**: Start with `(8 - 5)`.
\[ 8 - 5 = 3 \]
Substitute this back into the expression:
\[ 121 ÷ {17 - {15 - 3 × 3}} \]

3. **Calculate the multiplication**:
\[ 3 × 3 = 9 \]
Substitute this back:
\[ 121 ÷ {17 - {15 - 9}} \]

4. **Solve the subtraction inside the curly brackets**:
\[ 15 - 9 = 6 \]
Substitute this back:
\[ 121 ÷ {17 - 6} \]

5. **Now solve the subtraction**:
\[ 17 - 6 = 11 \]
Substitute this back:
\[ 121 ÷ 11 \]

6. **Perform the division**:
\[ 121 ÷ 11 = 11 \]

So, the final answer for part (ii) is:
\[ \text{Answer (ii)} = 11 \]

### Summary of Answers:
- (i) = -32
- (ii) = 11