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Arithmetic

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What is Arithmetic?

Basic Arithmetic is stemmed from ancient and elementary branches of Mathematics. The word originates from the Greek term ‘arithmos’ which symbolizes ‘number’ or ‘numeric’. The root of Arithmetics sprung up from astrologers and wise men of the past seeking a metric system in their daily lives. Arithmetic expands to the realms of numbers using traditional operations to break down complex numerical to simple ones. Although advanced operations are the norm-of-use such as computation of percentages and functions in algebra and logarithms, the basics arise from the concepts of simple addition, subtraction, multiplication, and division.


History of Arithmetic

The historical application of the field of Arithmetics began with the fundamental principle of Number Theory. This theory was proposed by Carl Friedrich Gauss in 1801. This theory states that any integer described as greater than one has a product of their prime numbers. Arithmetic mainly comprises four elementary operations, that is; addition, subtraction, multiplication, and division. 

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Operations Used in Arithmetic

The four basic operations that comprise the field of arithmetic include addition, subtraction, multiplication, and division. These are briefly explained below:


A. Addition

This is one of the most basic and simplistic functions used continuously in Arithmetic. The addition of two or more values leads to a larger value.

For example: 2 + 5 = 7, 6 + 2 = 8. 

The procedure of adding ‘n; the number of values is termed as summation.

Zero is the identity element of addition. This means that adding a  0 to any value gives the same result. The opposite of any value is the inverse element of addition. This means that it forms an additive identity.

For example, the opposite of 5 is -5, 

Hence 5 + (-5) = 0 


B. Subtraction

The inverse of addition is known as subtraction. It describes the difference between two values, that is, the minuend minus the subtrahend. If the minuend is greater than the subtrahend, the difference is positive. If the minuend is less than the subtrahend, the result is negative, and 0 if the numbers are equal.

For example, subtract 43 from 70 will be calculated as 70 - 43 = 27. 


C. Multiplication

The operation that combines two values into a single value or the product is known as multiplication. It is similar to the functions of addition and subtraction. The multiplicand and the multiplier are the two original values used or simply known as factors.

The product of a and b is calculated as a·b or an x b. In computing languages, characters are used and it is often expressed as, a*b (where * is called asterisk).

For example, when we calculate the product for 24 and 5, we get 24 x 5 = 120.

 

D. Division

The inverse of multiplication is known as division. It calculates the quotient of two numbers. The two numbers are termed as the dividend that is divided by the divisor. If the quotient is more than 1, the dividend is greater than the divisor for any well-defined positive number, otherwise, it is smaller than one.

For example,

Divide 12 by 2, we get 12 ÷ 2 = 6 


What is Bodmas?

BODMAS is defined as the set of the order of operations to be followed when calculating a complex numerical problem and simplifying it.

BODMAS is referred to in this sequence of operations namely,

B -  Brackets

O - Orders

D - Division

M - Multiplication

A - Addition

S - Subtraction

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Examples of Arithmetic

When solving complex numerical problems, it is important to note the functions that are used in the process. Applying the operation strategy of BODMAS is highly important to obtain an accurate result. 

For example, calculate the equation 25 + 5(27 ÷ 3) - 9 

25 + 5(27 ÷ 3) - 9

⇒ 25 + 5(9) - 9

⇒ 25 + 45 - 9

⇒ 70 - 9

⇒ 61 

When solving numerical problems related to unknown numerical, it is important to consider arbitrary values termed as ‘x’ or ‘y’.

For example, calculate the sum of two numbers is 50, and their difference is 30. Find the numbers.

Consider the arbitrary values as x and y. 

x + y = 50 ……………………(i)

x - y = 30………………(ii)

Hence, x = 50 - y, from eq. (i),

Put the value of x in eq(ii), 

50 - y - y = 30 

50 - 2y = 30

2y = 50 - 30 = 20y

= \[\frac{20}{2}\]

= 10x

= 50 - y

= 50 - 10

= 40

Therefore, the two numbers are 40 and 10.

FAQ (Frequently Asked Questions)

1.What are the Properties Associated with the Field of Arithmetic?

Arithmetic is a complex field encompassing a wide range of simple functions to computational systems and algorithms. The four basic properties that act as a base for arithmetic are as follows:

  1. Commutative Property - This property states that numbers or values can change their positions or swap with one another. 

  2. Associative Property - This property states that the addition or multiplication of any number of values can be carried out without any change in the result.

  3. Distributive Property - This property deals with sharing a portion of a larger value or simply the concept of dividing is possible from a large quantity.

  4. Additive Identity - This property states that equality is attained when a common value or numeral is added on both sides of the equation.

2. How is Arithmetic Used in Our Daily Life?

Arithmetic is a broad field of Mathematics. It is universally used for any mathematical, physical, and chemical operations. Its applications are vast and have rendered its contribution to society since its inception. It deals with the numerical manipulation of numbers. It uses operations like addition, subtraction, multiplication, division, and square roots to attain a simpler value to a complex equation. It helps us use certain arbitrary values like ‘x’ and/or ‘y’ to carry out algebraic and trigonometric functions. 

 

The arithmetic principles gradually built up momentum after establishing the theory of counting numbers or the Number theory. From shopping at the mall to buying your monthly groceries and retrieving cash from an ATM, these fundamental operations have been used to smoothen out our daily transactions and work all year round.