subject: List Of Basic Math Rules [print this page] 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 a^nd 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 sa^me context.
Example: We ca^nnot compare the number of length of a^n 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 a^n event ca^nnot me more then 1.Probability of 1 represents 100 percent cha^nces of a^n event. So, If a problem of probability is solved a^nd the a^nswer comes out to be greater then 1 then one ca^n 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).
MD- Multiplication a^nd Division (do a^ny M or D which comes first as we move left to right)
AS- Addition a^nd Subtraction (do a^ny A or S which comes first as we move left to right)
Rule 4: For questions for calculating length of sides of a tria^ngle or a^ngles of a tria^ngle one ca^n always check the validity of the a^nswer by verifying if the a^nswer adheres to following:
a) Tria^ngle Inequality: As per the tria^ngle inequality, for a^ny tria^ngle, the sum of the lengths of a^ny two sides must be greater tha^n the length of the remaining side.
b) Sum of a^ngles of a tria^ngle if always equal to 180 degrees.
Rule 5: Value of Trigonometric function Sin a^nd Cos: The value of these 2 functions always lies between 1 (maximum) a^nd -1 (minimum). If in a solution to a problem a sine function or a cosine function evaluates to value outside the ra^nge [1,-1] then one ca^n infer that solution is wrong a^nd needs to correction.
List of some more Basic Math Rules
Rules of Integers
Addition Rules of Integer
If both Numbers have Sa^me Sign we Add a^nd take the sign
Exa^mple: (+3) + (+4)= +7
If both Numbers have Different Sign we Subtract a^nd take the sign of larger value.
Exa^mple: (-5) + (-6)= -11
Subtraction Rules of Integers
Step 1: Subtraction sign is cha^nged into a^n Addition sign.
Step 2: Then we take the opposite of the number that follows the newly placed addition sign.
Exa^mple : If we have to solve 5 - 8=?
According to step 1 we cha^nge 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 Sa^me sign Result is always Positive
Exa^mple : (+4) x (+3)=+12
If both numbers have Different signs Result is always Negative
Exa^mple: (-4) x (+5)= -20
Dividing Rules of integers
In case of Divison of Integers
If both numbers have Sa^me sign then we get result always as Positive
Exa^mple: (+4) (+2)= +2
If both numbers have Different Sign result is always Negative
Exa^mple: (-12) (+3)= -4
Basic Math Rules of Exponents
Rule 1: If the bases of the exponential expressions that are multiplied are sa^me then we ca^n combine them into one expression by adding the exponents.
a ^m* a^ n= a^m+n
Rule 2: If the exponential bases of expression that are divided are sa^me then they ca^n be combined intto one expression by subtracting the power
a^m/a n= a^m-n
Rule 3: If we have a^ny exponential expression raised to some power then we ca^n multiply the powers together
(a ^m) n= a^mn
Rule 4: a^ny variable that has power zero is equal to 1
a 0= 1
Rule 5: a^ny exponential expression having negative exponent ca^n be writen as
a -m= 1/ a^m
Basic Math Radical Rules
Rule 1: Product law of radicals with sa^me Index number
According to this law the product of nth root of a a^nd 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 sa^me 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 radica^nd a.
