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Componendo Dividendo

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  Componendo Dividendo Componendo and dividendo is a theorem on proportions that allows for a quick way to perform calculations and reduce the number of expansions needed. It is particularly useful when dealing with equations involving fractions or rational functions in mathematical Olympiads, especially when you see fractions. The theorem is represented by the following formula: a/(b+c) = (a/b) + (a/c). The theorem is named for its two Latin terms: “componendo,” which means “by combining,” and “dividendo,” which means “by dividing.” The theorem can be applied to any type of number, including fractions, decimals, and negative numbers. Componendo Dividendo Rule Proof So, it can be expressed as a : b = c : d and (a + b ) : (a – b) = (c + d) : (c – d). It is true that if the ratio of a to b = c to d, then the ratio of (a + b) to (a – b) is the same as (c + d) to (c – d). This is termed the componendo and dividendo rule. Also get information from insta handle  @ maths_world61 Question - If
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MATHEMATICAL REASONING

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  MATHEMATICAL REASONING  MATHEMATICAL LOGIC               LOGIC IS THE SUBJECT WHICH DEALS WITH THE PRINCIPLE OF REASONING. Logic is sometimes defines as science of proof.Mathematics and other science subjects deals with the reasoning and the arguments and every student of mathematics and other science should know the principles of logic.  Statement  A sentence is called statement  if it is either true or false but not both . Example-"two plus five is equal to seven"" is a statement because the sentence true. A true statement is called valid statement. A false statement is called invalid statement. Properties of Statements A statement is a mathematical acceptable sentence Mathematical statements are either true or false, they cannot be both Any exclamatory sentences are not mathematical statements An imperative sentence is not a valid mathematical statement An interrogative sentence is not a mathematical valid statement A sentence involving variables such as here, there
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MATHEMATICAL INDUCTION

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 PRINCIPLE OF MATHEMATICAL INDUCTION   The process of drawing a valid general result from particulat result is called the process of induction. The principle of mathematical induction{PMI} is a mathematical process which is used to establish the validity of a general result involving natural numbers.  Statement  A sentence is called statement if it is either true or false but not both . Example-"two plus five is equal to seven"" is a statement because the sentence true. A statement concerning the natural  number 'n'  is generally denoted by (n) Example- If P(n)) denotes the statement : ''n(n+1) is an even number'', then  P(2)=2(2+1)=6 is an even number and                                                                                      P(5)=5(5+1)=30 is an even numer etc..                                                                                      here P(2) & P(5) both true. THE PRINCIPLE OF MATHEMATICAL INDUCTION  If P(n) is a st
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POLYNOMIAL

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 POLYNOMIAL In mathematics, a polynomial is  an expression consisting of indeterminates  (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. ... Polynomials appear in many areas of mathematics and science. In   mathematics , a   polynomial   is an   expression   consisting of   indeterminates   (also called   variables ) and   coefficients , that involves only the operations of   addition ,   subtraction ,   multiplication , and non-negative   integer   exponentiation   of variables. An example of a polynomial of a single indeterminate   x   is   x 2  − 4 x  + 7 . An example in three variables is   x 3  + 2 xyz 2  −  yz  + 1 . Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example,  3x+2x-5  is a polynomial. Introduction to polynomials. This video covers common terminology like terms, degree, standard form, monom
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ADDITION,SUBTRACTION,MULTIPLICATION,DIVISION

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 ADDITION,SUBTRACTION,MULTIPLICATION,DIVISION Addition 3 + 2 = 5 with apples, a popular choice in textbooks Addition   (usually signified by the plus symbol  + ) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or  sum  of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression  "3 + 2 = 5"  (that is, "3  plus  2 is equal to 5"). Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices
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