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Numerator
A fraction (from , "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A ''common'', ''vulgar'', or ''simple'' fraction (examples: and ) consists of an integer numerator, displayed above a line (or before a slash like ), and a non-zero integer denominator, displayed below (or after) that line. If these integers are positive, then the numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. For example, in the fraction , the numerator 3 indicates that the fraction represents 3 equal parts, and the denominator 4 indicates that 4 parts make up a whole. The picture to the right illustrates of a cake. Fractions can be used to represent ratios and division. Thus the fraction can be used to represent the ratio 3:4 (the ratio of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rational Fraction
In algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraic expressions. Two examples of algebraic fractions are \frac and \frac. Algebraic fractions are subject to the same laws as arithmetic fractions. A rational fraction is an algebraic fraction whose numerator and denominator are both polynomials. Thus \frac is a rational fraction, but not \frac, because the numerator contains a square root function. Terminology In the algebraic fraction \tfrac, the dividend ''a'' is called the ''numerator'' and the divisor ''b'' is called the ''denominator''. The numerator and denominator are called the ''terms'' of the algebraic fraction. A ''complex fraction'' is a fraction whose numerator or denominator, or both, contains a fraction. A ''simple fraction'' contains no fraction either in its numerator or its denominator. A fraction is in ''lowest terms'' if the only factor common to the numerator and the denominator is 1. An expression which is not in frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rational Number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (for example, The set of all rational numbers is often referred to as "the rationals", and is closed under addition, subtraction, multiplication, and division by a nonzero rational number. It is a field under these operations and therefore also called the field of rationals or the field of rational numbers. It is usually denoted by boldface , or blackboard bold A rational number is a real number. The real numbers that are rational are those whose decimal expansion either terminates after a finite number of digits (example: ), or eventually begins to repeat the same finite sequence of digits over and over (example: ). This statement is true not only in base 10, but also in every other integer base, such as the binary and hexadecimal ones (see ). A real n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Division By Zero
In mathematics, division by zero, division (mathematics), division where the divisor (denominator) is 0, zero, is a unique and problematic special case. Using fraction notation, the general example can be written as \tfrac a0, where a is the dividend (numerator). The usual definition of the quotient in elementary arithmetic is the number which yields the dividend when multiplication, multiplied by the divisor. That is, c = \tfrac ab is equivalent to c \cdot b = a. By this definition, the quotient q = \tfrac is nonsensical, as the product q \cdot 0 is always 0 rather than some other number a. Following the ordinary rules of elementary algebra while allowing division by zero can create a mathematical fallacy, a subtle mistake leading to absurd results. To prevent this, the arithmetic of real numbers and more general numerical structures called field (mathematics), fields leaves division by zero undefined (mathematics), undefined, and situations where division by zero might occur m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oblique Stroke
The slash is a slanting line punctuation mark . It is also known as a stroke, a solidus, a forward slash and several other historical or technical names. Once used as the equivalent of the modern period and comma, the slash is now used to represent division and fractions, as a date separator, or to connect alternative terms. A slash in the reverse direction is known as a backslash. History Slashes may be found in early writing as a variant form of dashes, vertical strokes, etc. The present use of a slash distinguished from such other marks derives from the medieval European virgule (, which was used as a period, scratch comma, and caesura mark. (The first sense was eventually lost to the low dot and the other two developed separately into the comma and caesura mark ) Its use as a comma became especially widespread in France, where it was also used to mark the continuation of a word onto the next line of a page, a sense later taken on by the hyphen . The Fraktur s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ratio
In mathematics, a ratio () shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7). The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be Positive integer, positive. A ratio may be specified either by giving both constituting numbers, written as "''a'' to ''b''" or "''a'':''b''", or by giving just the value of their quotient Equal quotients correspond to equal ratios. A statement expressing the equality of two ratios is called a ''proportion''. Consequently, a ratio may be considered as an ordered pair of numbers, a Fraction (mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Division (mathematics)
Division is one of the four basic operations of arithmetic. The other operations are addition, subtraction, and multiplication. What is being divided is called the ''dividend'', which is divided by the ''divisor'', and the result is called the ''quotient''. At an elementary level the division of two natural numbers is, among other Quotition and partition, possible interpretations, the process of calculating the number of times one number is contained within another. For example, if 20 apples are divided evenly between 4 people, everyone receives 5 apples (see picture). However, this number of times or the number contained (divisor) need not be integers. The division with remainder or Euclidean division of two natural numbers provides an integer ''quotient'', which is the number of times the second number is completely contained in the first number, and a ''remainder'', which is the part of the first number that remains, when in the course of computing the quotient, no further ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slash Mark
The slash is a slanting line punctuation mark . It is also known as a stroke, a solidus, a forward slash and several other historical or technical names. Once used as the equivalent of the modern period and comma, the slash is now used to represent division and fractions, as a date separator, or to connect alternative terms. A slash in the reverse direction is known as a backslash. History Slashes may be found in early writing as a variant form of dashes, vertical strokes, etc. The present use of a slash distinguished from such other marks derives from the medieval European virgule (, which was used as a period, scratch comma, and caesura mark. (The first sense was eventually lost to the low dot and the other two developed separately into the comma and caesura mark ) Its use as a comma became especially widespread in France, where it was also used to mark the continuation of a word onto the next line of a page, a sense later taken on by the hyphen . The Fraktur s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Fraction
A unit fraction is a positive fraction with one as its numerator, 1/. It is the multiplicative inverse (reciprocal) of the denominator of the fraction, which must be a positive natural number. Examples are 1/1, 1/2, 1/3, 1/4, 1/5, etc. When an object is divided into equal parts, each part is a unit fraction of the whole. Multiplying two unit fractions produces another unit fraction, but other arithmetic operations do not preserve unit fractions. In modular arithmetic, unit fractions can be converted into equivalent whole numbers, allowing modular division to be transformed into multiplication. Every rational number can be represented as a sum of distinct unit fractions; these representations are called Egyptian fractions based on their use in ancient Egyptian mathematics. Many infinite sums of unit fractions are meaningful mathematically. In geometry, unit fractions can be used to characterize the curvature of triangle groups and the tangencies of Ford circles. Unit fractions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solidus Mark
The slash is a slanting line punctuation mark . It is also known as a stroke, a solidus, a forward slash and several other historical or technical names. Once used as the equivalent of the modern period and comma, the slash is now used to represent division and fractions, as a date separator, or to connect alternative terms. A slash in the reverse direction is known as a backslash. History Slashes may be found in early writing as a variant form of dashes, vertical strokes, etc. The present use of a slash distinguished from such other marks derives from the medieval European virgule (, which was used as a period, scratch comma, and caesura mark. (The first sense was eventually lost to the low dot and the other two developed separately into the comma and caesura mark ) Its use as a comma became especially widespread in France, where it was also used to mark the continuation of a word onto the next line of a page, a sense later taken on by the hyphen . The Fraktur s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quotient
In arithmetic, a quotient (from 'how many times', pronounced ) is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics. It has two definitions: either the integer part of a division (in the case of Euclidean division) or a fraction or ratio (in the case of a general division). For example, when dividing 20 (the ''dividend'') by 3 (the ''divisor''), the ''quotient'' is 6 (with a remainder of 2) in the first sense and 6+\tfrac=6.66... (a repeating decimal) in the second sense. In metrology (International System of Quantities and the International System of Units), "quotient" refers to the general case with respect to the units of measurement of physical quantities. ''Ratios'' is the special case for dimensionless quotients of two quantities of the same kind. Quotients with a non-trivial dimension and compound units, especially when the divisor is a duration (e.g., "per second"), are known as ''rates''. For example, densi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
