📐 Day 2 Math: Ratios (比率)
🎧 Listen to the Lesson (听讲解)
Hello, Sisi! Today we’re learning about Ratios（比率）. Ratios are very important in PSLE Math!
📚 Key Vocabulary (重点词汇)
🔹 Part 1: What is a Ratio? (什么是比率？)
A ratio（比率） compares two or more quantities. We write it using a colon :.
For example: If there are 3 boys（3个男孩） and 5 girls（5个女孩） in a class:
- The ratio of boys to girls is 3 : 5
- Total students = 3 + 5 = 8
📌 Key Rule (关键规则)
✅ Always simplify ratios to their simplest form（最简形式）.
Example: 6 : 8 = 3 : 4 (divide both by 2)
🎮 Interactive Demo: See Ratios! (比率可视化)
Boys (男孩)
Girls (女孩)
🔹 Part 2: Simplifying Ratios (化简比率)
To simplify（化简） a ratio, divide both sides by their highest common factor (HCF)（最大公约数）.
💡 Example 1 (例题1)
Q: Simplify the ratio 12 : 18
A:
- HCF of 12 and 18 = 6
- 12 ÷ 6 = 2, 18 ÷ 6 = 3
- Simplified ratio = 2 : 3
💡 Example 2 (例题2)
Q: Simplify the ratio 15 : 25 : 35
A:
- HCF of 15, 25, and 35 = 5
- 15 ÷ 5 = 3, 25 ÷ 5 = 5, 35 ÷ 5 = 7
- Simplified ratio = 3 : 5 : 7
🎮 Interactive Demo: Simplify This Ratio! (化简练习)
🔹 Part 3: Ratio Problems (比率应用题)
Problem Type 1: Ratio & Total (比率与总和)
💡 Example (例题)
Q: The ratio of apples to oranges is 3 : 4. There are 28 fruits in total. How many apples are there?
A:
- Total ratio units = 3 + 4 = 7 units
- 1 unit = 28 ÷ 7 = 4
- Apples = 3 units = 3 × 4 = 12
Problem Type 2: Ratio Change (比率变化)
💡 Example (例题)
Q: The ratio of boys to girls in a class is 2 : 3. After 5 more boys join, the ratio becomes 3 : 4. How many girls are there?
A:
- Boys = 2u, Girls = 3u (before)
- After 5 boys: Boys = 2u + 5, Girls = 3u
- New ratio: (2u + 5) : 3u = 3 : 4
- 4(2u + 5) = 3(3u) → 8u + 20 = 9u
- u = 20
- Girls = 3u = 3 × 20 = 60
🔹 Part 4: Practice Questions (练习题)
Q1: Simplify the ratio 10 : 15
Q2: The ratio of red balls to blue balls is 4 : 5. There are 36 balls in total. How many red balls?
Q3: The ratio of X to Y is 2 : 5. If X = 12, what is Y?
📝 Summary (本节总结)
- ✅ A ratio（比率） compares quantities using :
- ✅ Always simplify（化简） ratios to simplest form
- ✅ Use ratio units（比率单位） to solve problems
- ✅ Total ratio units = sum of all parts