📚 Topic Summary
Mathematical proportions show the relationship between two ratios. If two ratios are equal, they are said to be in proportion. Proportions are often used to solve problems involving scaling, comparing quantities, and converting units. Understanding proportions is essential for various real-world applications, from cooking and construction to finance and science.
A proportion can be written as $\frac{a}{b} = \frac{c}{d}$, where $a$, $b$, $c$, and $d$ are numbers, and $b$ and $d$ are not zero. In a proportion, the cross products are equal: $a \times d = b \times c$. This property allows us to solve for an unknown value in a proportion.
🧠 Part A: Vocabulary
Match the term with its definition:
- Term: Ratio
- Term: Proportion
- Term: Cross Product
- Term: Direct Proportion
- Term: Inverse Proportion
- Definition: A statement that two ratios are equal.
- Definition: A comparison of two quantities by division.
- Definition: A relationship where one quantity increases as the other decreases.
- Definition: The product of the means equals the product of the extremes in a proportion.
- Definition: A relationship where one quantity increases as the other increases.
📝 Part B: Fill in the Blanks
Complete the following paragraph using the words: ratio, proportion, equal, quantities, cross product.
A ______ is a comparison of two ______. A ______ is a statement that two ratios are ______. To solve a proportion, we often use the ______ property.
💡 Part C: Critical Thinking
Explain how proportions are used in everyday life. Give at least two specific examples.