Problem solving is not a very tough thing to do. It’s almost like planning a daily budget or tricks to miss school!! The very first step towards problem solving is shunning that fear of Mathematics and looking at every calculation you do in real life as an algebra problem. Never think of mathematics as only bookish numbers and formulas, the main aim of learning mathematics is so that you can apply it in your real life situations.
First and foremost, UNDERSTAND the problem. Analyze what things you know and what exactly is to be calculated. If you do not understand it, then read it again. Never depend on others to explain things. Simplify things yourself. Read the problems enough number of times so that you’re comfortable with the situation. Even if you’re an expert, take your time to analyze the problem, never jump to conclusions.
Secondly, convert the words into numbers, variables and equations. You cannot solve a mathematical problem with phrase or prose. Translate the problem. Choose appropriate number of variables (for unknown and known quantities), find relation between variables and given values and form an equation. Keep variables to the left of “=” as LHS and known values at the right as RHS. Form as many equations as necessary. Usually there should be at least as many number of equations as the number of unknown quantities (variables). This is the most important step in problem solving. If you get this wrong, you will never reach to the right answer. The key is comparing your equations with the problem given. This will help you track points if you did miss any, and also correct your mistakes yourself.
Third and the trickiest step is SOLVING the equations. Many people are scared of this part the most. Arrange your equations in the order where you start with the equation which has least number of unknown quantities and then move on to the others. In the process, keep substituting the values that you have found. Does it sound tricky still? Try a problem. If you’re not able to solve by yourself, try following some hints from the ’solved examples’.
The final step is CROSS-CHECK your answer. Okay, you found an answer, but is it correct. In algebra problems by substituting your answer in the equations and proving LHS=RHS you can confirm your solution.
Example: There are two numbers. One number is 3 less than another number. If the sum of the two numbers is 27, find each number.
Step 1: Given- first number = x, second number = x-3, sum = 27.
Find- both the numbers.
Step 2: sum = 27
x + (x – 3) = 27.
Step 3: 2x – 3 = 27
2x = 27 + 3 = 30.
x = 30/2 = 15.
SOLUTION – one number is 15 and the other is (15 – 3), that is 12.
Step 4: putting 15 as x in Step 2.
LHS: 15 + (15 -3) = 15 + 12 = 27 =RHS. Hence, our answer is correct.
