1. **Ratio**: A ratio compares two quantities showing how many times one value contains or is contained within the other. It is written as $a:b$ or $\frac{a}{b}$. For example, if there are 2 apples and 3 oranges, the ratio of apples to oranges is $2:3$. 2. **Proportion**: A proportion states that two ratios are equal. If $\frac{a}{b} = \frac{c}{d}$, then $a$, $b$, $c$, and $d$ are in proportion. This means the relationship between $a$ and $b$ is the same as between $c$ and $d$. 3. **Indices (Exponents)**: Indices show how many times a number (the base) is multiplied by itself. For example, $a^n$ means multiply $a$ by itself $n$ times. Important rules include: - $a^m \times a^n = a^{m+n}$ - $\frac{a^m}{a^n} = a^{m-n}$ - $(a^m)^n = a^{mn}$ - $a^0 = 1$ (if $a \neq 0$) 4. **Logarithms**: A logarithm answers the question: to what power must the base be raised to get a number? If $b^x = y$, then $\log_b y = x$. Important properties: - $\log_b (xy) = \log_b x + \log_b y$ - $\log_b \left(\frac{x}{y}\right) = \log_b x - \log_b y$ - $\log_b (x^n) = n \log_b x$ These concepts are fundamental in algebra and help solve equations involving multiplication, division, powers, and roots.