Comparing Quantities: Ratios & Percentages

🔹 Understanding Ratios

A ratio is a way to compare two or more quantities of the same kind. It tells us “how many times one quantity is compared to another.”

📌 Example:
A basket contains 20 apples and 5 oranges.

• Ratio of oranges to apples = 5 : 20

• Simplifying by dividing both terms by 5:

  5:20=1:4

  ✅ This means that for every 1 orange, there are 4 apples.

• Ratio of apples to oranges = 20 : 5

  • Simplify by dividing by 5:
  • 20:5=4:1

  ✅ This means apples are 4 times the number of oranges.

🔹 Ratios as Fractions

A ratio can also be written as a fraction, helping us understand the relationship between two quantities.

🔸 For oranges to apples:

520=14​

✅ This means the number of oranges is 14 of the number of apples.

🔹 Converting Ratios to Percentages

A percentage expresses a number out of 100 and helps in easier comparisons.

To find the percentage of oranges:

525×100=20%

✅ Oranges make up 20% of the total fruits.

Since there are only apples and oranges, the percentage of apples is:

100%−20%=80%

✅ Apples make up 80% of the total fruits.

🎯 Key Takeaways

🔹 Ratios show comparisons in simplest form (e.g., 1:4).
🔹 Fractions help understand proportions (e.g., 1/4).
🔹 Percentages express the part out of 100 (e.g., 20% oranges, 80% apples).
🔹 Conversions:

• Ratio → Fraction (e.g., 1:4 → 14
• Fraction → Percentage (e.g., 14×100=25%)

💡 Why Is This Useful?

Ratios and percentages are used in real life for:
✔ Discounts & sales (50% off!)
✔ Recipe ingredients (2:1 ratio of flour to sugar)
✔ Population studies (70% urban, 30% rural)
✔ Sports statistics (win/loss ratios)