The scale of a ratio often refers to the relationship between two quantities, and finding it usually involves simplifying or comparing ratios. The specific method depends on the context. Here are a few common scenarios:
1. Simplifying a Ratio:
Often, "finding the scale" means simplifying a ratio to its simplest form. This is done by dividing all parts of the ratio by their greatest common factor (GCF).
- Example: The ratio 20:100. The GCF of 20 and 100 is 20. Dividing both sides by 20 gives us 1:5. Therefore, the simplified scale (or simplified ratio) is 1:5.
2. Comparing Ratios to Determine Scale Factor:
If you have two related ratios (e.g., representing a scaled drawing), you can find the scale factor between them.
- Example: A map has a scale of 1:100,000. A second map of the same area has a scale of 1:50,000. To find the scale factor between the maps, you can divide the second scale by the first: (1/50,000) / (1/100,000) = 2. This means the second map is twice the scale of the first map (or twice as zoomed in).
3. Converting Between Ratio Scales:
This involves multiplying or dividing all parts of the ratio by the same number to change the scale while maintaining the proportion.
- Example: You have a ratio of 1:100 and you want to convert it to 1:50. To do this, you need to halve the second number in the ratio. To keep the ratio proportional, you need to multiply both sides by a factor of 2, which is essentially dividing both sides by 0.5. The operation performed is dividing 100 by 2 to get 50, so to keep the ratio the same, you must perform the same operation to the other number in the ratio, making the adjusted ratio of scale 0.5:50.
4. Finding Scale in Scale Drawings/Maps:
The scale in a scale drawing or map represents the relationship between a distance on the drawing/map and the corresponding distance in reality. It's often expressed as a ratio. To "find" the scale in this context usually means determining this ratio. This can be done if you know a distance on the drawing and the corresponding real-world distance.
- Example: A line on a map is 5 cm long and represents 10 km in reality. First, convert both to the same units: 10 km = 1,000,000 cm. The ratio is then 5 cm : 1,000,000 cm. Simplify by dividing both sides by 5: 1:200,000. The scale of the map is 1:200,000.
In summary, finding the scale of a ratio depends on the context and can involve simplification, comparison, conversion, or calculation based on real-world measurements.
