To solve a problem mathematically, identify the unknown, known variables, use the appropriate equation, and manipulate it to solve for the unknown, checking your solution for accuracy.
To approach a problem that involves using formulas, the steps are crucial for success:
Identify the unknown variable you are trying to solve for.
Identify the known variables that are provided in the problem or can be inferred.
Choose an appropriate equation to solve for the unknown based on the known variables.
Manipulate the equation algebraically if necessary to isolate the unknown variable.
Substitute the known values and their units into the equation to solve for the unknown.
Calculate the answer, ensuring that all units are consistent and correct.
Check the solution to ensure it is reasonable and makes sense within the context of the problem.
To illustrate, let's consider an example involving calculating the area of a rectangle. The formula used for this is A = l \( \times \) w, where A represents the area, l represents the length, and w represents the width of the rectangle. Persons such as students, architects, and engineers might use this formula in various applications.
Here are two example questions where this formula can be applied:
If you know a rectangle has a length of 5 meters and a width of 2 meters, what is its area?
If the area of a rectangle is 50 square meters and its length is 10 meters, what is its width?