1. Let's start with simplifying algebraic fractions. The problem is to simplify expressions like $$\frac{6x^2}{9x}$$. 2. The formula used is to factor numerator and denominator and cancel common factors: $$\frac{a \times b}{a \times c} = \frac{b}{c}$$. 3. For example, $$\frac{6x^2}{9x} = \frac{6 \times x \times x}{9 \times x}$$. 4. Cancel the common factor $x$ and simplify numbers: $$\frac{6}{9} = \frac{2}{3}$$. 5. So, $$\frac{6x^2}{9x} = \frac{2x}{3}$$. 6. Next, circumference and area of a circle. The formulas are: - Circumference: $$C = 2\pi r$$ - Area: $$A = \pi r^2$$ 7. For example, if radius $r=3$, then circumference is $$2 \times \pi \times 3 = 6\pi$$ and area is $$\pi \times 3^2 = 9\pi$$. 8. Statistics and probability: data collection involves gathering data carefully to avoid bias. 9. Sampling bias occurs when the sample is not representative of the population, leading to incorrect conclusions. 10. Irrational numbers are numbers that cannot be expressed as fractions, like $$\sqrt{2}$$ or $$\pi$$. 11. Area of compound shapes can be found by dividing the shape into rectangles and squares, calculating each area, then adding them. 12. For example, a compound shape made of two rectangles with areas 5 and 7 has total area $$5 + 7 = 12$$. This covers the main points you asked about with examples and formulas.