subject: List Of Basic Math Rules [print this page] List of basic math rules,Basic Math Rules of Exponents
The article (List of Basic Math rules) is about the basic rules of mathematics which should be followed while working on problems. The agenda of the article is to help the readers to perform the problems correctly and logically evaluate the accuracy of the results.
List of Basic Rules in Math
Rule 1: Always compare the equivalent things or object. That is to say that when doing comparison in mathematics, one should always take care that the objects/variable being compared is in same context.
Example: We cannot compare the number of length of an object A to weight of object B that is to say that either weight of object A should be compared with weight of object B or length of object A should be compared with length of object B, if the comparison has to be meaningful.
Rule 2: Probability of an event cannot me more then 1.Probability of 1 represents 100 percent chances of an event. So, If a problem of probability is solved and the answer comes out to be greater then 1 then one can easily figure out that there should be some mistake with the working of problem.
Rule 3: In Algebra, when calculating expressions one should follow the basic Rule of PEMDAS. As per this rule while evaluating expression, the calculation should be done in following order (left to right).
P- Parentheses first
E- Exponents (like Powers and Square Roots, etc.)
MD- Multiplication and Division (do any M or D which comes first as we move left to right)
AS- Addition and Subtraction (do any A or S which comes first as we move left to right)
Rule 4: For questions for calculating length of sides of a triangle or angles of a triangle one can always check the validity of the answer by verifying if the answer adheres to following:
a) Triangle Inequality: As per the triangle inequality, for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
b) Sum of angles of a triangle if always equal to 180 degrees.
Rule 5: Value of Trigonometric function Sin and Cos: The value of these 2 functions always lies between 1 (maximum) and -1 (minimum). If in a solution to a problem a sine function or a cosine function evaluates to value outside the range [1,-1] then one can infer that solution is wrong and needs to correction.
List of some more Basic Math Rules
Rules of Integers
Addition Rules of Integer
If both Numbers have Same Sign we Add and take the sign
Example: (+3) + (+4)= +7
If both Numbers have Different Sign we Subtract and take the sign of larger value.
Example: (-5) + (-6)= -11
Subtraction Rules of Integers
Step 1: Subtraction sign is changed into an Addition sign.
Step 2: Then we take the opposite of the number that follows the newly placed addition sign.
Example : If we have to solve 5 - 8=?
According to step 1 we change the negative sign to addition
According to step 2 we have to take opposite of 8 which is (-8)
Using the rules for Addition we get 5 + (-8)= -3
Multiplication Rules
If both numbers have Same sign Result is always Positive
Example : (+4) x (+3)=+12
If both numbers have Different signs Result is always Negative
Example: (-4) x (+5)= -20
Dividing Rules of integers
In case of Divison of Integers
If both numbers have Same sign then we get result always as Positive
Example: (+4) (+2)= +2
If both numbers have Different Sign result is always Negative
Example: (-12) (+3)= -4
Basic Math Rules of Exponents
Rule 1: If the bases of the exponential expressions that are multiplied are same then we can combine them into one expression by adding the exponents.
a m* a n= am+n
Rule 2: If the exponential bases of expression that are divided are same then they can be combined intto one expression by subtracting the power
a m/a n= a m-n
Rule 3: If we have any exponential expression raised to some power then we can multiply the powers together
(a m) n= a mn
Rule 4: Any variable that has power zero is equal to 1
a 0= 1
Rule 5: Any exponential expression having negative exponent can be writen as
a -m= 1/ a m
Basic Math Radical Rules
Rule 1: Product law of radicals with same Index number
According to this law the product of nth root of a and nth root of b is equal to the nth root of ab
root(n)(a) xx root(n)(b) = root (n)(ab)
Rule 2: Quotient rule of Radical with same Index number
According to this law the nth root of a over nth root of b is equal to nth root of a/b
(root(n)(a))/root(n)(b)= root (n)(a/b)
Rule 3: The mth root of nth root of a number is a is given as mnth root of radicand a.
