Final answer:
In mathematics, working with ratios and proportions involves setting two ratios equal to one another and ensuring units are consistent for calculations. To calculate proportions, convert all measurements to the same unit, set up the proportion, and solve for the unknown variable. Correct unit cancellation is crucial when multiplying fractions to arrive at the desired units.
Step-by-step explanation:
When working with ratios and proportions in mathematics, it is often necessary to write proportions by setting two ratios equal to one another. For example, if you know that one half of one-half is one quarter, you could represent this mathematically as (1/2) * (1/2) = 1/4. This can be applied to units of measurement as well. If you have a ratio such as Length is to Width, and you know the scale (for example, 1:50), you could write a proportion like Length = w/30 = 0.5/. Similarly, if working with different units such as centimeters and meters, you need to convert them to the same unit before setting up the proportion, like 500 mm = 50 cm.
It is also important to remember that when you are multiplying fractions, you multiply the numerators together and the denominators together. Ensure that units cancel out properly so that you end up with the desired units for your answer. For instance, when calculating how many inches are in 75 miles if 0.5 inch equals 3 miles, you would write the proportion 0.5 inches/75 miles = 3 inches/x miles to solve for x.