๐ Understanding Ratios
A ratio is a comparison of two or more quantities. It shows the relative sizes of these quantities. Ratios can be written in several ways, including using a colon, as a fraction, or with the word 'to'.
- ๐ Example: If you have 3 apples and 2 oranges, the ratio of apples to oranges is 3:2, $\frac{3}{2}$, or '3 to 2'.
- ๐งฎ General Form: A ratio comparing quantities $a$ and $b$ can be written as $a:b$ or $\frac{a}{b}$.
- ๐ค Important: Ratios do not necessarily represent a part-to-whole relationship; they simply compare quantities.
โ Demystifying Unit Rates
A unit rate is a ratio that compares a quantity to one unit of another quantity. It tells you how much of something you get for one unit of something else, like cost per item or distance per hour.
- ๐ Example: If you travel 100 miles in 2 hours, your speed (unit rate) is 50 miles per hour.
- ๐ Calculation: To find a unit rate, divide the quantity by the number of units. If you buy 5 items for $20, the unit rate is $\frac{$20}{5 \text{ items}} = $4 \text{ per item}$.
- ๐ก Key Use: Unit rates are very helpful for comparing prices and understanding rates of change.
๐ Unit Rate vs. Ratio: Side-by-Side Comparison
| Feature |
Ratio |
Unit Rate |
| Definition |
Compares two or more quantities. |
Compares a quantity to one unit of another quantity. |
| Form |
$a:b$, $\frac{a}{b}$, or 'a to b' |
Amount per one unit (e.g., miles per hour, cost per item). |
| Purpose |
Shows the relative sizes of different quantities. |
Determines the amount or cost for a single unit of something. |
| Example |
3 apples to 2 oranges (3:2) |
$4 per item |
๐ Key Takeaways
- ๐ฏ Focus: Ratios focus on the relationship between quantities, while unit rates focus on the amount per single unit.
- โ Flexibility: Ratios can compare any quantities, while unit rates typically involve rates like speed, cost, or quantity per unit.
- ๐ก Practical Use: Use ratios for general comparisons and unit rates for finding the value of a single item or unit.