ARITHMETIC

 Arithmetic 

           Arithmetic is an elementary part of mathematics that consist of the study of the properties of the traditional operations on numbers  such as addition , subtraction, multiplication, division, expontiation, extraction of roots. Arithmetic also includes more advanced operation such as manipulation of percentage, square roots, Logrithmic function and trignometric function . 

        Arithmetic operaters perform mathematical operation such as addition and subtraction with operands. There are two types of mathematical operation . 

  1. Unary
  2. Binary. 
History of Arithmetic:

      The arithmetic comes from arithmos, the greek word for number ; but people began doing arithmetic log before the greeks invented numbers, historians believe that as early as 10,000 year ago forming, they began to uws arithmetic. 

  Rules of Arithmetic: 

  Step I :- 

The nth term of an arithmetic sequence is given by  an = a+(n -1) d  so, to find the nth term, substitute the given values a=3 and d=4 into the formula. 

  Step II :- 

Now, to find the sixth term substituate n= 6 into th equation for the nth term. 

BASIC ARITHMETIC OPERATION 

    1. Addition  

      Addition is one of the four basic operation of arithmetic. Addition is process of combining two or more numbers. In addition process order does not matter. It means that addition process id commutative. It is denoted by "+" sign.  And it can involve any number like real number, complex number, fraction or decimal.    Ex.,   2+4=6  or  4+2=6 . 

Rules of Addition :

  1. Addition of two positive integer is a positive integer ex, 3+4=7 . 
  2. Addition two negative integers is a negative integers ex, (-3) +(-4) = -7. 
  3. Addition of positive and negative integers is, subtract the integers and and use the sign of largest integers number ex, 3-7=-4.
2. Subtraction:

       The operation or process of finding the difference between two numbers or quantities is know as subtraction. To subtract the number from another number.  It is denoted by "-" sign. Ex, 8-2=6.

 Types of subtraction 

  • Taking away
  • Part -whole
  • Comparison
  Rules of Subtraction :

  1. If both integers are positive then answer is positive. Ex, 3+4=7
  2. If the both integers are negative then the answer is negative. Ex, -4-5=-9
  3. If the signs of integers are different, subtract the number and use the sign of largest number. 6-8=-2.

3. Multiplication:

     Multiplication is the method of finding the product of two numbers. Multiplication is used when we need to combine groups of equal size. It is denoted by "×" sign. The multiplication process involve Multiplicant and multiplier and their multiplication result is called the productproduct

 Ex, 3×5=15                                                    3 is a multiplier, 5 is Multiplicant and 15 is a product. 

Rules of Multiplication:

  1. The product of two positive integers is positive. 
  2. The product of two negative integers is positive. 
  3. The product of  positive and negative integers is negative integers.
 4.Division:

  Division is a process of sharing a collection in equal parts. It is opposite from multiplication. It is denoted by "÷" sign. The division process involves dividend and divisor, where the dividend is divided by divisor to get a single term value and dividend  is greater than divisor then the result  obtain is grater than 1 or less than 1. ex, 8÷4=2                                                       here, 8 is dividend, 4 is divisor and 2 is quotient. 

Rules of Division : 

  1. If both integers are positive then answer is positive. 
  2. If both number are negative then answer is positive. 
  3. If both integers are different then answer is negative. 
BASIC ARITHMETIC PROPERTY 

 There are three basic property, 

  1. Commutative property
  2. Associative property
  3. Distributive property
1. Commutative property: 

      Commutative property is applicable only for addition and multiplication. This not apply for subtraction and division. 

Suppose A and B are two real numbers then,  

  • A+B=B+A  ex, 2+3=3+2=5 
  • A×B=B×A  ex, 2×3=3×2=6
2. Associative property: 

      The associative property is a property of some binary operation which means that rearranging the parentheses in an expression will not change the result. It applicable for addition and multiplication. 

  Suppose A , B and C are real nber then 

  • A+(B+C) = (A+B) +C                                EX,   2+(3+4) =(2+3) +4 . 
  • A×(B×C) =(A×B) ×C                                  EX, 4×(3×2) =(4×3) ×2 . 
3. Distributive property:

     According to distributive property multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the product togather. Suppose A, B and C are real numbers then,  

  • A×(B+C)  = (A×B) +(A×C) 
Ex, 

         3×(4+6) = (3×4) +(3×6)                                 3× (10) = (12) +(18)                                       30     =   30   

Hence proved. 

 

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