📚 What is a Ratio?
A ratio is a comparison of two or more quantities. It shows how much of one thing there is compared to another. Ratios can be written in a few different ways:
- 🍎 Using a colon: For example, if you have 3 apples and 2 oranges, the ratio of apples to oranges is 3:2.
- ➗ As a fraction: The same ratio can be written as \(\frac{3}{2}\).
- ✍️ Using the word 'to': You can also say the ratio is 3 to 2.
🧮 What is a Unit Rate?
A unit rate is a special type of ratio that compares a quantity to one unit of another quantity. It tells you how much of something you get for one of something else. Think of it like finding the price for just one item.
- 💰 Examples: Price per pound, miles per hour, or words per minute are all unit rates.
- 📝 Calculating: To find a unit rate, you usually divide the first quantity by the second quantity to get a denominator of 1.
- ✍️ Formula: If you travel 120 miles in 2 hours, the unit rate (speed) is \(\frac{120 \text{ miles}}{2 \text{ hours}} = 60 \text{ miles per hour}\).
🆚 Ratio vs. Unit Rate: The Key Differences
| Feature |
Ratio |
Unit Rate |
| Definition |
Compares two or more quantities. |
Compares a quantity to one unit of another quantity. |
| Units |
Can have the same or different units. |
Always has different units, with the second unit being one. |
| Form |
Expressed as a:b, a fraction, or 'a to b'. |
Expressed as 'a per b', where b = 1. |
| Example |
3 apples : 2 oranges |
$5 per pound |
💡 Key Takeaways
- 🔑 Ratios compare any two quantities, while unit rates compare a quantity to one unit of another.
- ➕ Unit rates are a specific type of ratio. Not all ratios are unit rates!
- ➗ To find a unit rate, divide to get the denominator (the second quantity) equal to 1.
- ✍️ Think of unit rates as "for each one" or "per one".