Day 8: Ratios and Proportions! Middle Stage Mathematics | Apex Institute of Maths and Sciences

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Day 8: Ratios and Proportions! ⚖️

Middle Stage Mathematics | Apex Institute of Maths and Sciences

🎯 1. Concept: Comparing Quantities

Welcome to Week 2! Today we are introducing Ratios and Proportions.

A ratio is simply a mathematical way to compare two or more quantities. It tells us how much of one thing there is compared to another thing.

💡 2. Rules of Ratios

Order matters immensely in ratios!

  • If a bowl has 3 apples and 2 oranges, the ratio of apples to oranges is 3:2.
  • The ratio of oranges to apples is 2:3.
  • Ratios can be written in three ways: 3:2, 3 to 2, or as a fraction 3/2.
  • Just like fractions, ratios should be simplified to their lowest terms (e.g., 4:8 becomes 1:2).

🌍 3. Math in Our Daily Life

Ratios are the secret behind cooking, driving, and even watching videos!

Scenario 1: Baking a Cake. A recipe might call for 2 cups of flour for every 1 cup of sugar (a 2:1 ratio). If you want to make a cake twice as big, you keep the same proportion: 4 cups of flour and 2 cups of sugar (4:2 simplifies back to 2:1!).

Scenario 2: Video Aspect Ratios. When you watch YouTube or movies on your TV, the screen uses an aspect ratio, typically 16:9. This means for every 16 units of width, there are 9 units of height.

📝 4. Home Practice (Observation Task)

Time to be a kitchen mathematician!

  • Task A: The Recipe Scaler: Find a simple recipe at home (like making tea or lemonade). Write down the ratio of the main ingredients (e.g., 1 spoon of sugar to 1 glass of water). Now, calculate exactly how much of each ingredient you need to make enough for 5 people!
  • Task B: Room Ratio: Count the number of chairs and the number of tables in your main living space. What is the ratio of chairs to tables? Can you simplify it?

✅ 5. Day 8 Practice Test

Are you a master of comparisons? Take this quiz to test your ratio skills. Select your answers and click submit to check your score.

Easy
1. What is the main purpose of a ratio?
Solution: A ratio is a mathematical tool used specifically to compare two or more quantities.
Easy
2. If a room has 2 boys and 3 girls, what is the ratio of boys to girls?
Solution: Order matters! Boys come first, then girls. So it is 2 to 3, or 2:3.
Easy
3. Which of the following is another correct way to write the ratio 4:5?
Solution: Ratios can be written using a colon (4:5), using words (4 to 5), or as a fraction (4/5).
Easy
4. Simplify the ratio 10:5 to its lowest terms.
Solution: Divide both sides by 5. 10 ÷ 5 = 2, and 5 ÷ 5 = 1. The simplified ratio is 2:1.
Medium
5. A recipe uses 2 cups of flour and 1 cup of sugar. What is the ratio of flour to sugar?
Solution: Flour is mentioned first (2), then sugar (1). The ratio is 2:1.
Medium
6. A class has 15 boys and 20 girls. What is the ratio of girls to the TOTAL number of students?
Solution: Total students = 15 + 20 = 35. Ratio of girls to total is 20:35. Dividing both by 5 gives the simplified ratio 4:7.
Medium
7. Are the ratios 1:2 and 3:6 equivalent?
Solution: Yes! If you multiply both sides of 1:2 by 3, you get 3:6. They represent the same proportion.
Medium
8. The ratio of cats to dogs at a shelter is 3:4. If there are exactly 12 cats, how many dogs are there?
Solution: 3 units = 12 cats. So 1 unit = 4. To find the dogs, multiply 4 units × 4 = 16 dogs.
Hard
9. You must divide 30 chocolates between two friends in the ratio 1:2. How many chocolates does the person with the larger share get?
Solution: Total parts = 1 + 2 = 3 parts. 30 chocolates ÷ 3 parts = 10 per part. The larger share is 2 parts (2 × 10 = 20 chocolates).
Hard
10. A map scale is 1 cm = 10 km. If two cities are 5 cm apart on the map, how far apart are they in reality?
Solution: The ratio is 1:10. Set up a proportion: 1/10 = 5/x. Multiply 5 × 10 = 50 km.
⚠️ Please answer all 10 questions before submitting!

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