Can someone explain to me the general procedure used to identify and set up a proportion problem?
Repost with a specific problem, so we can use it as an example.
I hope this helps a little. Thanks for asking.
The following ratios:
Map scale - distance between two points
75 miles (real): 2 inches (map)
=
n (actual distance between two points) : 3.4 inches(distance on the map between the 2 points)
I understand the equation and the solution, but need more formal way of explaining the general procedure used to identify and set up the proportion problem. Ex. why 75 is the numerator and 2 is the denominator same with n/3.4... 75/2=n/3.4
To identify and set up a proportion problem, you need to understand the relationship between the given values and the unknown value you are trying to find. Here is the general procedure:
1. Identify the given values: In the example you provided, the given values are the map scale (75 miles:2 inches) and the distance on the map between the two points (3.4 inches).
2. Determine what you are trying to find: In this case, you are trying to find the actual distance between the two points (n miles).
3. Set up the proportion: You can set up a proportion by equating the given ratios. In this example, the map scale ratio is 75 miles:2 inches, and the unknown ratio is n miles:3.4 inches. Therefore, we can set up the proportion as follows:
75 miles / 2 inches = n miles / 3.4 inches
4. Cross-multiply: Multiply the numerator of the first ratio with the denominator of the second ratio, and vice versa. In this case, cross-multiplying gives:
(75 miles) x (3.4 inches) = (2 inches) x (n miles)
5. Solve for the unknown value: Simplify the equation by multiplying and dividing as needed. In this example, you would have:
255 miles * inches = 2 inches * n miles
Simplifying further:
255 miles * inches / 2 inches = n miles
n = (255 miles * inches) / (2 inches)
6. Calculate the unknown value: Finally, calculate the unknown value using the equation you derived in the previous step. In this case, you would have:
n = (255 miles * inches) / (2 inches)
Simplifying:
n = 127.5 miles
Therefore, the actual distance between the two points is 127.5 miles.
In summary, the general procedure to identify and set up a proportion problem involves identifying the given values, determining the unknown value, setting up the proportion using the given ratios, cross-multiplying, solving for the unknown value, and calculating the answer.