Final answer:
To find the missing factor using the inverse operation, apply the given scale or conversion factor to the actual value, simplify the terms, and check if the result is reasonable. For example, to convert an actual distance of 80 meters to the distance on Calvin's 1/800 scale map, you would find it to be 10 centimeters.
Step-by-step explanation:
The subject in question involves using the inverse operation to find the missing factor in a given problem. This is often applied in the context of unit conversions or scale factors in mathematics, where we multiply by conversion factors that have the effect of '1' to change units seamlessly. This technique can be used in unit conversions within math problems.
For example, when Calvin drew a map of his neighborhood using a scale factor of 1/800, and the actual distance between his house and Frank's house is 80 meters, we would use the scale factor to find the corresponding distance on the map. Since 1 meter is 100 centimeters, we compute the distance on the map in centimeters by multiplying 80 meters by the scale factor (1/800), and then convert the result to centimeters by multiplying by 100 cm/meter: (80 meters) x (1/800) x (100 cm/meter) = 10 centimeters. This shows us that on Calvin's scale drawing, the distance between the two houses should be 10 centimeters.
- Identify the scale factor or conversion factor given in the problem.
- Multiply the actual value by the scale factor to find the scaled value.
- Eliminate terms wherever possible to simplify the algebra.
- Substitute the known quantities along with their units into the formula.
- Check the answer to ensure it is reasonable and makes sense.