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- Dictionaryarithmetic
noun
- 1. the branch of mathematics dealing with the properties and manipulation of numbers: "the laws of arithmetic"
adjective
- 1. relating to arithmetic: "arithmetic calculations"
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Arithmetic is the study of numbers and their basic operations, such as addition, subtraction, multiplication and division. Learn the history, properties, examples and solved problems of arithmetic with Byju's Maths.
- Arithmetic is one of the branches of mathematics which deals with different types of numbers like odd numbers, whole numbers, even numbers, etc. an...
- The four basic arithmetic operators are addition (+), subtraction (-), multiplication (×) and division (÷).
- There are four main properties of operations which include: Commutative Property Associative Property Distributive Property Additive Identity
- The BODMAS or PEMDAS rule is followed to order any operation involving +, −, ×, and ÷. The order of operation is: B: Brackets O: Order D: Division...
Arithmetic is the branch of mathematics that studies numbers and their operations, such as addition, subtraction, multiplication, and division. Learn about the origin, development, and types of arithmetic, as well as its applications and related fields.
Arithmetic is a branch of mathematics that deals with real numbers and their operations. Learn the synonyms, examples, history, and related phrases of arithmetic from Merriam-Webster dictionary.
Arithmetic is the part of mathematics that involves the adding and multiplying, etc. of numbers. Learn more about arithmetic, its synonyms, collocations, and translations from Cambridge Dictionary.
- Overview
- Natural numbers
- Addition and multiplication
- Integers
- Exponents
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arithmetic, branch of mathematics in which numbers, relations among numbers, and observations on numbers are studied and used to solve problems.
Arithmetic (a term derived from the Greek word arithmos, “number”) refers generally to the elementary aspects of the theory of numbers, arts of mensuration (measurement), and numerical computation (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots). Its meaning, however, has not been uniform in mathematical usage. An eminent German mathematician, Carl Friedrich Gauss, in Disquisitiones Arithmeticae (1801), and certain modern-day mathematicians have used the term to include more advanced topics. The reader interested in the latter is referred to the article number theory.
In a collection (or set) of objects (or elements), the act of determining the number of objects present is called counting. The numbers thus obtained are called the counting numbers or natural numbers (1, 2, 3, …). For an empty set, no object is present, and the count yields the number 0, which, appended to the natural numbers, produces what are known as the whole numbers.
If objects from two sets can be matched in such a way that every element from each set is uniquely paired with an element from the other set, the sets are said to be equal or equivalent. The concept of equivalent sets is basic to the foundations of modern mathematics and has been introduced into primary education, notably as part of the “new math” (see the figure) that has been alternately acclaimed and decried since it appeared in the 1960s. See set theory.
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Define It: Math Terms
Combining two sets of objects together, which contain a and b elements, a new set is formed that contains a + b = c objects. The number c is called the sum of a and b; and each of the latter is called a summand. The operation of forming the sum is called addition, the symbol + being read as “plus.” This is the simplest binary operation, where binary refers to the process of combining two objects.
From the definition of counting it is evident that the order of the summands can be changed and the order of the operation of addition can be changed, when applied to three summands, without affecting the sum. These are called the commutative law of addition and the associative law of addition, respectively.
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If there exists a natural number k such that a = b + k, it is said that a is greater than b (written a > b) and that b is less than a (written b < a). If a and b are any two natural numbers, then it is the case that either a = b or a > b or a < b (the trichotomy law).
From the above laws, it is evident that a repeated sum such as 5 + 5 + 5 is independent of the way in which the summands are grouped; it can be written 3 × 5. Thus, a second binary operation called multiplication is defined. The number 5 is called the multiplicand; the number 3, which denotes the number of summands, is called the multiplier; and the result 3 × 5 is called the product. The symbol × of this operation is read “times.” If such letters as a and b are used to denote the numbers, the product a × b is often written a∙b or simply ab.
Subtraction has not been introduced for the simple reason that it can be defined as the inverse of addition. Thus, the difference a − b of two numbers a and b is defined as a solution x of the equation b + x = a. If a number system is restricted to the natural numbers, differences need not always exist, but, if they do, the five basic laws of arith...
Just as a repeated sum a + a + ⋯ + a of k summands is written ka, so a repeated product a × a × ⋯ × a of k factors is written ak. The number k is called the exponent, and a the base of the power ak.
The fundamental laws of exponents follow easily from the definitions (see the Click Here to see full-size tabletable), and other laws are immediate consequences of the fundamental ones.
Arithmetic is the branch of mathematics that studies and uses numbers, relations, and operations. Learn about the fundamental definitions, laws, and history of arithmetic, from natural numbers to integers, from ancient to modern times.
Arithmetic is the branch of mathematics that deals with numerical calculations, such as addition, subtraction, multiplication, and division. Learn the origin, history, and examples of arithmetic from Dictionary.com.
Arithmetic is the act of calculating numbers, for example by multiplying or adding. Find out how to say arithmetic in different languages, such as Chinese, Spanish, Portuguese and more.
