Fractions (mathematics)

Fractions in mathematics represent a way to express a part of a whole. A fraction consists of two main components: 1. **Numerator**: The number on the top, which indicates how many parts you have. 2. **Denominator**: The number on the bottom, which indicates how many equal parts the whole is divided into.

Egyptian fractions refer to representations of fractions in the form of sums of distinct unit fractions, where a unit fraction is a fraction with a numerator of 1 and a positive integer as the denominator.

Cross-multiplication is a mathematical technique used primarily to solve equations involving fractions. It allows you to eliminate the fractions by multiplying each side of the equation by the denominators of the fractions involved. This is commonly used when dealing with proportions, which are equations that state two ratios are equal.

The term "decimal" typically refers to a base-10 numbering system, which is the standard system for representing numbers that most people use every day. In a decimal system, each position in a number represents a power of 10, and digits can range from 0 to 9.

Division by zero is an undefined operation in mathematics. To understand why, it's helpful to consider what division means. Division can be thought of as determining how many times one number (the divisor) fits into another number (the dividend). For example, if you divide 10 by 2, you are asking how many times 2 fits into 10, which is 5. However, when you try to divide any number by zero (e.g.

A dyadic rational is a type of number in the form of \(\frac{m}{2^n}\), where \(m\) is an integer and \(n\) is a non-negative integer. In other words, dyadic rationals are fractions where the denominator is a power of 2.

A Farey sequence, denoted as \( F_n \), is a sequence of completely reduced fractions between 0 and 1 that have denominators less than or equal to a given positive integer \( n \). The Farey sequence is arranged in increasing order. Each fraction in the sequence is expressed in simplest form, meaning that the numerator and denominator are coprime (they have no common factors other than 1).

A Ford circle is a geometric construct that is used in number theory to visually represent the fractions between 0 and 1. Specifically, for each positive fraction \( \frac{p}{q} \) (where \( p \) and \( q \) are coprime integers), the corresponding Ford circle is centered at \( \frac{p}{q} \) with a radius of \( \frac{1}{2q^2} \).

A fraction is a mathematical expression that represents the division of one quantity by another. It is composed of two parts: the numerator and the denominator. The numerator is the number above the line (or before the slash), which indicates how many parts we have. The denominator is the number below the line (or after the slash), representing the total number of equal parts that make up a whole.

The term "hundredth" generally refers to a position in a sequence or a fractional part. Here are some common contexts in which "hundredth" is used: 1. **Fractional/Decimal**: In terms of fractions, "hundredth" represents one part of a hundred, or \( \frac{1}{100} \). In decimal terms, it is expressed as 0.01.

An irreducible fraction, also known as a simplified or reduced fraction, is a fraction in which the numerator and denominator are coprime, meaning they have no common factors other than 1. In simpler terms, an irreducible fraction cannot be simplified any further.

Irregularity of distributions can refer to various concepts, depending on the context in which it is used. In general, it can denote a lack of regularity or uniformity in how a particular quantity is spread across a space or among a set of values.

The lowest common denominator (LCD) is the smallest multiple that two or more fractions share in their denominators. Finding the LCD is particularly useful when you're trying to add, subtract, or compare fractions, as it allows you to express all fractions with a common denominator. To determine the LCD: 1. **List the multiples:** Find multiples of each denominator. 2. **Identify the least common multiple (LCM):** Look for the smallest multiple that appears in each list.

In mathematics, particularly in the context of operations on sets and data, a "mediant" refers to a specific type of rational number derived from two fractions.

Midy's theorem is a result in number theory that pertains to the representation of numbers in a specific base. More specifically, it deals with the representation of numbers in base \( b \) and the relationship between a number and its "reverse".

"Millionth" refers to one part of a million total parts. It is a fraction that is expressed as \( \frac{1}{1,000,000} \). In contexts such as measurements, it can denote very small quantities, such as millionths of a meter (which is one micrometer) or millionths of a gram.

One half is a fraction represented as \( \frac{1}{2} \). It signifies a quantity that is divided into two equal parts, where one part is being considered. In decimal form, one half is equal to 0.5. In terms of percentage, it represents 50%. This concept is often used in various contexts, such as dividing objects, measuring ingredients in cooking, or calculating time.

"Per meg" is typically a shorthand reference in various contexts, but it often means "per megabit" when discussing data transfer rates or bandwidth. In the context of internet speed or network performance, "meg" is short for megabit (Mb), a unit of measurement representing 1 million bits.

A unit fraction is a fraction where the numerator is 1 and the denominator is a positive integer. In other words, it can be expressed in the form \( \frac{1}{n} \), where \( n \) is a positive integer. For example, \( \frac{1}{2} \), \( \frac{1}{3} \), and \( \frac{1}{4} \) are all unit fractions.