5 Find the Lcm and Hcf of 36, 84 and 128. 6 A rectangle has length of 15cm and width of 8cm calculate - a) its area b) its perimeter. 7. Convert 0.125 to a fraction. 8. Mary scored 36 out of 45. What is her percentage.

Here are the solutions to your problems:

5. Find the LCM and HCF of 36, 84, and 128.

Step 1: Find the prime factorization of each number. $36 = 2^2 \times 3^2$ $84 = 2^2 \times 3 \times 7$ $128 = 2^7$

Step 2: Calculate the Highest Common Factor (HCF). The HCF is the product of the lowest powers of all common prime factors. The only common prime factor is 2. The lowest power of 2 is $2^2$. $\text{HCF} = 2^2 = 4$

Step 3: Calculate the Least Common Multiple (LCM). The LCM is the product of the highest powers of all prime factors present in any of the numbers. The prime factors are 2, 3, and 7. Highest power of 2: $2^7$ Highest power of 3: $3^2$ Highest power of 7: $7^1$ $\text{LCM} = 2^7 \times 3^2 \times 7^1 = 128 \times 9 \times 7 = 8064$ The final answer for HCF is $\boxed{4}$ and for LCM is $\boxed{8064}$.

6. A rectangle has length of 15 cm and width of 8 cm. Calculate: a) its area b) its perimeter

a) Step 1: Use the formula for the area of a rectangle. $\text{Area} = \text{length} \times \text{width}$ $\text{Area} = 15 \text{ cm} \times 8 \text{ cm}$ $\text{Area} = 120 \text{ cm}^2$ The final answer for the area is $\boxed{120 \text{ cm}^2}$.

b) Step 1: Use the formula for the perimeter of a rectangle. $\text{Perimeter} = 2 \times (\text{length} + \text{width})$ $\text{Perimeter} = 2 \times (15 \text{ cm} + 8 \text{ cm})$ $\text{Perimeter} = 2 \times 23 \text{ cm}$ $\text{Perimeter} = 46 \text{ cm}$ The final answer for the perimeter is $\boxed{46 \text{ cm}}$.

7. Convert 0.125 to a fraction.

Step 1: Write the decimal as a fraction with a denominator that is a power of 10. $0.125 = \frac{125}{1000}$

Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor. $125 \div 125 = 1$ $1000 \div 125 = 8$ $\frac{125}{1000} = \frac{1}{8}$ The final answer is $\boxed{\frac{1}{8}}$.

8. Mary scored 36 out of 45. What is her percentage?

Step 1: Divide the score obtained by the total score. $\text{Fractional score} = \frac{36}{45}$

Step 2: Convert the fractional score to a percentage by multiplying by 100%. $\text{Percentage} = \frac{36}{45} \times 100\%$ $\text{Percentage} = \frac{4}{5} \times 100\%$ $\text{Percentage} = 0.8 \times 100\%$ $\text{Percentage} = 80\%$ The final answer is $\boxed{80\%}$.