In statistics, the mode is the value that appears most often in a set of data values. If X is a discrete random variable, the mode is the value x at which the probability mass function takes its maximum value (i.e., x=argmaxxi P(X = xi)). In other words, it is the value that is most likely to be sampled. (Full article...)
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The
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In
fraction
of two
denominator
q. For example, is a rational number, as is every integer (e.g., ). The set of all rational numbers, also referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by boldface Q, or blackboard bold (Full article...)
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In
divides
each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted . For example, the GCD of 8 and 12 is 4, that is, gcd(8, 12) = 4. (Full article...)
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In mathematics, a divisor of an integer also called a factor of is an integer that may be multiplied by some integer to produce In this case, one also says that is a multiple of An integer is divisible or evenly divisible by another integer if is a divisor of ; this implies dividing by leaves no remainder. (Full article...)
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. (Full article...)
A mean is a numeric quantity representing the center of a collection of numbers and is intermediate to the extreme values of a set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statistics. Each attempts to summarize or typify a given group of data, illustrating the magnitude and sign of the data set. Which of these measures is most illuminating depends on what is being measured, and on context and purpose. (Full article...)
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, etc., possibly excluding 0. Some define the natural numbers as the non-negative integers0, 1, 2, 3, ..., while others define them as the positive integers1, 2, 3, .... Some authors acknowledge both definitions whenever convenient. Some texts define the whole numbers as the natural numbers together with zero, excluding zero from the natural numbers, while in other writings, the whole numbers refer to all of the integers (including negative integers). The counting numbers refer to the natural numbers in common language, particularly in primary school education, and are similarly ambiguous although typically exclude zero. (Full article...)
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In mathematics, the irrational numbers (in- + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning that they share no "measure" in common, that is, there is no length ("the measure"), no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself. (Full article...)
The following are images from various arithmetic-related articles on Wikipedia.
Image 1Hieroglyphic numerals from 1 to 10,000 (from Arithmetic)
Image 2Example of modular arithmetic using a clock: after adding 4 hours to 9 o'clock, the hand starts at the beginning again and points at 1 o'clock. (from Arithmetic)
Image 3Calculations in
mental arithmetic are done exclusively in the mind without relying on external aids. (from Arithmetic
)
Image 4Abacuses are tools to perform arithmetic operations by moving beads. (from Arithmetic)
Image 5If of a cake is to be added to of a cake, the pieces need to be converted into comparable quantities, such as cake-eighths or cake-quarters. (from Fraction)
Image 6Example of modular arithmetic using a clock: after adding 4 hours to 9 o'clock, the hand starts at the beginning again and points at 1 o'clock. (from Arithmetic)
Image 7Example of
long multiplication. The black numbers are the multiplier and the multiplicand. The green numbers are intermediary products gained by multiplying the multiplier with only one digit of the multiplicand. The blue number is the total product calculated by adding the intermediary products. (from Arithmetic
)
Image 8The
Warring States era decimal multiplication table of 305 BC (from Multiplication table
)
Image 9Example of addition with carry. The black numbers are the addends, the green number is the carry, and the blue number is the sum. In the rightmost digit, the addition of 9 and 7 is 16, carrying 1 into the next pair of the digit to the left, making its addition 1 + 5 + 2 = 8. Therefore, the addition of 59 + 27 gives the result 86. (from Elementary arithmetic)
Image 10Leibniz's stepped reckoner was the first calculator that could perform all four arithmetic operations. (from Arithmetic)
Image 11Example of addition with carry. The black numbers are the addends, the green number is the carry, and the blue number is the sum. (from Arithmetic)
Image 12Different types of numbers on a number line. Integers are black, rational numbers are blue, and irrational numbers are green. (from Arithmetic)
Image 13Hieroglyphic numerals from 1 to 10,000 (from Arithmetic)
Image 14Abacuses are tools to perform arithmetic operations by moving beads. (from Arithmetic)
Image 15Example of addition with carry. The black numbers are the addends, the green number is the carry, and the blue number is the sum. (from Arithmetic)
Image 16Leibniz's stepped reckoner was the first calculator that could perform all four arithmetic operations. (from Arithmetic)
Image 17Example of
long multiplication. The black numbers are the multiplier and the multiplicand. The green numbers are intermediary products gained by multiplying the multiplier with only one digit of the multiplicand. The blue number is the total product calculated by adding the intermediary products. (from Arithmetic
)
Image 18Some historians interpret the Ishango bone as one of the earliest arithmetic artifacts. (from Arithmetic)
Image 19Irrational numbers are sometimes required to describe magnitudes in geometry. For example, the length of the hypotenuse of a right triangle is irrational if its legs have a length of 1. (from Arithmetic)
Image 21A cake with one quarter (one fourth) removed. The remaining three fourths are shown by dotted lines and labeled by the fraction 1/4 (from Fraction)
Image 22The main arithmetic operations are addition, subtraction, multiplication, and division. (from Arithmetic)
Image 23Using the number line method, calculating is performed by starting at the origin of the number line then moving five units to right for the first addend. The result is reached by moving another two units to the right for the second addend. (from Arithmetic)
Image 24Different types of numbers on a number line. Integers are black, rational numbers are blue, and irrational numbers are green. (from Arithmetic)
Image 25Calculations in
mental arithmetic are done exclusively in the mind without relying on external aids. (from Arithmetic
)
Image 26The main arithmetic operations are addition, subtraction, multiplication, and division. (from Arithmetic)
Image 27Using the number line method, calculating is performed by starting at the origin of the number line then moving five units to right for the first addend. The result is reached by moving another two units to the right for the second addend. (from Arithmetic)
Image 28The symbols for elementary-level math operations. From top-left going clockwise: addition, division, multiplication, and subtraction. (from Elementary arithmetic)
Image 29Irrational numbers are sometimes required to describe magnitudes in geometry. For example, the length of the hypotenuse of a right triangle is irrational if its legs have a length of 1. (from Arithmetic)
Image 30Multiplication table from 1 to 10 drawn to scale with the upper-right half labeled with prime factorisations (from Multiplication table)
Image 31Some historians interpret the Ishango bone as one of the earliest arithmetic artifacts. (from Arithmetic)
Image 32Cycles of the unit digit of multiples of integers ending in 1, 3, 7 and 9 (upper row), and 2, 4, 6 and 8 (lower row) on a telephone keypad (from Multiplication table)
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Do you have a question about Arithmetic that you can't find the answer to?
Khaṇḍakhādyaka ("edible bite", dated 665), a more practical text.
In 628 CE, Brahmagupta first described gravity as an attractive force, and used the term "gurutvākarṣaṇam (गुरुत्वाकर्षणम्)" in Sanskrit to describe it. He is also credited with the first clear description of the quadratic formula (the solution of the quadratic equation) in his main work, the Brāhma-sphuṭa-siddhānta. (Full article...