1. **Problem:** Calculate the average of the numbers 4, 8, and 12. 2. **Formula:** The average (mean) of $n$ numbers $x_1, x_2, ..., x_n$ is given by: $$\text{Average} = \frac{x_1 + x_2 + ... + x_n}{n}$$ 3. **Calculation:** $$\text{Average} = \frac{4 + 8 + 12}{3} = \frac{24}{3} = 8$$ 4. **Explanation:** Add all numbers together and divide by how many numbers there are. 1. **Problem:** Find the ratio of 10 to 25. 2. **Formula:** Ratio of $a$ to $b$ is written as $a:b$ or $\frac{a}{b}$. 3. **Calculation:** $$10:25 = \frac{10}{25} = \frac{2}{5}$$ 4. **Explanation:** Simplify the fraction by dividing numerator and denominator by their greatest common divisor. 1. **Problem:** A car travels 150 kilometers in 3 hours. Find its speed. 2. **Formula:** Speed = $\frac{\text{Distance}}{\text{Time}}$ 3. **Calculation:** $$\text{Speed} = \frac{150}{3} = 50$$ 4. **Explanation:** Divide total distance by total time to get speed. 1. **Problem:** Convert 0.75 to a percentage. 2. **Formula:** Percentage = number $\times 100$% 3. **Calculation:** $$0.75 \times 100 = 75\%$$ 4. **Explanation:** Multiply decimal by 100 to get percentage. 1. **Problem:** Find the surface area of a cube with side length 4 units. 2. **Formula:** Surface area of cube = $6 \times \text{side}^2$ 3. **Calculation:** $$6 \times 4^2 = 6 \times 16 = 96$$ 4. **Explanation:** Each face is a square; multiply area of one face by 6.