How to Solve Numericals

Solve numerical problems.

Most numerical problems may be solved by applying a similar methodical sequence of steps. Numerical problems appear in a wide range of disciplines, including physics, finance and chemistry. Solving numerical problems is also useful on a personal level; for example, calculating a sale price or the interest on a savings account or a loan. No matter what discipline the problem is for, similar procedures are used to get the solution. Employing a systematic method is efficient and minimizes errors.

Instructions

1. Write down the information that you are given. For example, consider the following problem: If Emma leaves her house at noon and drives 12 miles north at an average speed of 40 miles per hour to visit a friend, at what time does she arrive? Call the distance traveled S, the start time Tstart and the average speed Vave. You have S= 12 miles, Tstart = 12 hours and Vave = 40 miles per hour.

2. Find the appropriate formula. You want a formula that will give you the time of arrival, if you supply the average velocity, distance traveled and start time. The formula for the average velocity will work for this problem. The average velocity is given by the formula Vave = /\\X / /\\T , where /\\X = Xend -- Xstart (the difference between the initial and final positions) and /\\T= Tend -- Tstart (the difference between the initial and final time). The position and velocity are scalars in the one-dimensional problem under consideration.

3. Substitute the known values into the formula that you have. For the current example, you get the following equation: 40 = 12 / (Tend -- 12)

4. Solve for the unknown variable to get your solution. For example:Tend = 12(1 + 1/40) = 12.3 hours. The number of minutes that have elapsed are 0.3 x 60 = 36, which makes Tend equal to 12:36 PM.

Tips & Warnings

• For more complex problems, which may involve using more than one equation to arrive at a solution, always rewrite the current form or state of the solution at each step. For example, if you are substituting one equation into another, rewrite the new combined equation before and after any simplification that may done. This organization minimizes careless errors, and it helps you to see what the next step is.