Final answer:
An equivalent ratio to 20:15 is 4:3 after dividing both terms by the common factor 5. To use ratios for scale models or conversions, we set up proportions where the unit scale is compared with an actual or unknown measurement, taking advantage of the metric system's simplicity.
Step-by-step explanation:
To find a ratio equivalent to 20:15, we need to identify a common factor that can be used to simplify the ratio. Noticing that both numbers are divisible by 5, we divide each part of the ratio by 5. This gives us 20 ÷ 5 = 4 and 15 ÷ 5 = 3, resulting in the simplified ratio of 4:3.
As an example of setting ratios equal to one another in a proportion, if we consider a scale model where the scale to actual length ratio is 1/20 and we have an actual length side comparison to an unknown scaled length represented as scale/actual = 1/5.5, we can set up a proportion like scale/actual = 1/20 = x/5.5 to solve for x, the unknown scaled length.
For conversion, the metric system simplifies the process since all conversions are based on powers of 10 which, when set as ratios equal to 1, allow for straightforward calculations of scale conversions in actual measurements.