Evaluate (36 - 8 x 4 - 15 / 3)/(-3 x 3 - 8(-6 + 2))

Here are the solutions to the problems:

1. Evaluate $\frac{36 - 8 \times 4 - 15 \div 3}{-3 \times 3 - 8(-6 + 2)}$

Step 1: Evaluate the numerator using the order of operations (BODMAS/PEMDAS).

$$36 - 8 \times 4 - 15 \div 3 = 36 - 32 - 5 = 4 - 5 = -1$$

Step 2: Evaluate the denominator using the order of operations.

$$-3 \times 3 - 8(-6 + 2) = -3 \times 3 - 8(-4) = -9 - (-32) = -9 + 32 = 23$$

Step 3: Divide the numerator by the denominator.

$$\frac{-1}{23}$$

The evaluated expression is $\boxed{-\frac{1}{23}}$.

2. Simplify $a + b - 2a$

Step 1: Combine the like terms involving $a$.

$$a - 2a + b = -a + b$$

The simplified expression is $\boxed{b - a}$.

3. Find the greatest number which divides 181 and 236 and leaves a remainder of 5 in each case.

Step 1: Subtract the remainder from each number to find the numbers that are perfectly divisible.

$$181 - 5 = 176$$ $$236 - 5 = 231$$

Step 2: Find the Greatest Common Divisor (GCD) of 176 and 231.
Prime factorization of $176 = 2^4 \times 11$
Prime factorization of $231 = 3 \times 7 \times 11$

Step 3: Identify the common prime factors and multiply them.
The only common prime factor is 11.
The GCD is 11.
The greatest number is $\boxed{11}$.

4. A rectangle measures 20cm by 15cm. If each dimension is increased by 2.5cm, by what percentage is:

• Original length ($L_1$) = 20 cm
• Original width ($W_1$) = 15 cm
• New length ($L_2$) = $20 + 2.5 = 22.5$ cm
• New width ($W_2$) = $15 + 2.5 = 17.5$ cm