A ratio is a mathematical expression that compares two quantities, showing the relative size of one quantity to another. Ratios are usually written in the form $a:b$ or $\frac{a}{b}$, where $a$ and $b$ are the quantities being compared. They can be used to represent relationships between numbers, such as proportions, rates, and fractions.

Key Points about Ratios:

1. Simplification: Ratios can be simplified by dividing both terms by their greatest common divisor (GCD).

   • Example: The ratio 8:12 can be simplified to 2:3 by dividing both terms by 4.

2. Equivalent Ratios: Two ratios are equivalent if they express the same relationship between quantities.

   • Example: 1:2 is equivalent to 2:4 and 3:6.

3. Usage: Ratios are used in various fields such as cooking (recipes), finance (interest rates), and science (concentration of solutions).

4. Proportions: When two ratios are equal, they form a proportion.

   • Example: If $\frac{a}{b} = \frac{c}{d}$, then $a:b$ is proportional to $c:d$.

5. Applications: Ratios are essential in understanding scales (maps), constructing models, comparing quantities, and analyzing data.

Would you like more details on any specific aspect of ratios?

Here are 5 questions you might consider asking:

1. How do you simplify a ratio?
2. What are some real-world applications of ratios?
3. Can you explain how to solve problems involving proportions?
4. How are ratios different from fractions?
5. How do you compare ratios to determine which is larger?

Tip:

When working with ratios, always ensure both quantities are in the same units before making comparisons or calculations.