A ratio compares two numbers, while the scale factor is a specific value derived from a ratio that indicates how much quantities are being enlarged or reduced.
Understanding Ratios and Scale Factors
Based on the provided reference, a scale factor is obtained from a specific type of ratio called a unit ratio. A unit ratio is a ratio where one side of the comparison is equal to one (e.g., 1:5 or 8:1).
- Ratio: A comparison of two quantities (e.g., 2:7).
- Unit Ratio: A ratio where one term is 1 (e.g., 1:3.5).
- Scale Factor: The number on the other side of the "one" in a unit ratio.
Comparing a Ratio to Its Scale Factor
A general ratio compares two quantities directly. To compare it with its corresponding scale factor, you must first convert the ratio into a unit ratio. The scale factor is the value you get on the second side once the first side of the ratio becomes one.
Think of it this way: the ratio provides the relationship between two quantities, and the scale factor quantifies this relationship when comparing one unit of the first quantity to the corresponding amount of the second quantity.
Example: Ratio 2:7
Let's use the example from the reference to see how a ratio compares to its scale factor.
| Description | Value | Calculation |
|---|---|---|
| Original Ratio | 2:7 | - |
| Convert to Unit Ratio | 1:3.5 | Divide both sides by 2 |
| Scale Factor | 3.5 | The second number in the unit ratio |
As shown, the ratio 2:7 is equivalent to a scale factor of 3.5. The scale factor represents the second term of the unit ratio (1:3.5) that is derived from the original ratio (2:7) by making one side equal to 1. Therefore, a ratio provides the basis from which its corresponding scale factor is calculated.
In summary, a ratio is a comparison, and its associated scale factor is the numerical value found opposite the "one" in the equivalent unit ratio, quantifying the scaling relationship.
