TopAlgebra is the branch of Mathematics which deals not only in Numbers but also in variables which are given by the English alphabets. We have already learnt about forming algebraic expressions as well as equations & also about the techniques of solving Algebraic Equations. We will learn here how to do Algebra problems.
Before we proceed to the topic let us recall some important points related to formation of algebraic equations & their solution. Whenever we form an algebraic equation, we should be very careful about the language being used in the statements & also carefully do with the mathematical Relations being expressed therein, especially in case of subtraction & division of the different values involved in a particular problem.
Another Point to remember is about the rules of transposing while solving the equation formed. In transposition, + & - are interchanged; * & / are also interchanged. Also , while solving the equation, we try to leave the variable alone on one side & take away all the numbers associated with the variable one by one, thus getting its value .
Also, it is worth nothing to assume some consecutive Natural Numbers, we take n, n + 1, n + 2….
Consecutive Even Numbers, assume 2n, 2n + 2, 2n + 4……, while for Odd Numbers we take 2n + 1, 2n + 3, 2n + 5….
A two digit number with some relation in digits is also given, the digits be a, b & number: 10a + b.
For example: 2/3 of a number is less than the original number by 20. Here in the problem, the number is unknown, and if the number is known, the problem can be solved easily. Let the number be ‘n’.
Now, it is given that 2/3 of the number, which means 2n/3; is less than the number by 20 means we have to subtract 20 from the number to make two values equal.
Thus, we get 2n/3 = n - 20.
2n = 3(n - 20),
2n = 3n – 60,
60 = 3n - 2n,
n = 60,
So, number is 60.