To solve various problems involving measurements, proportions are set up by equating ratios that compare measurements like centimeters, meters, or feet, to an unknown value using a consistent unit scale.
The question revolves around the concept of ratios and proportions, which relate different units of measurement or quantities to each other in a mathematically meaningful way. In the context provided, we need to use the given unit scale to write proportions that compare measurements.
Examples:
To write a proportion using centimeters, if the given ratios are 5/1 and 2.75/1 cm, we set them equal to each other: 5/1 = 2.75/1 cm.
For a proportion involving meters, we compare 1/20 to 1/5.5 by writing 1/20 = 1/5.5 meters.
When dealing with feet, we compare 1/48 to w/16 by setting them equal: 1/48 = w/16 feet.
To write proportions for actual dimensions using a unit scale, compare the scale to actual measurements, for example: Length=14/1 = 1/10.
For scale distances or dimensions, write two proportions by equating the scale length in inches to the actual length in miles: 1 inch/2000 miles = 3 inches/x miles
Note that when setting up proportions, it's essential to keep consistent units and scale factors on each side of the equation to solve for the unknown value.