"The other operations are addition, subtraction, and multiplication."
The process of distributing a quantity into equal parts or groups.
Division of whole numbers: It involves dividing a larger number by a smaller number to find the quotient and remainder.
Division of fractions: Involves dividing one fraction by another by cross-multiplication to find the quotient.
Division of decimals: It involves dividing decimals using long division or short division methods.
Division of mixed numbers: Involves converting mixed numbers into improper fractions and then dividing them.
Division of positive and negative numbers: It involves dividing numbers with different signs, which results in a negative quotient.
Division by zero: It is not possible and results in an undefined answer.
Division word problems: It involves using division to solve real-life problems, such as dividing a pizza into equal slices.
Division with remainders: It involves dividing numbers where the quotient is not a whole number, resulting in a remainder.
Divisibility rules: These rules help in identifying if a number is divisible by another number.
The binary division algorithm: Used in computer programming to divide binary numbers. It is a simplified version of long division.
Long division: This is the most common method of division. It involves dividing a large number by a smaller number and writing out each step so that the answer is clear.
Short division: This is a quicker method of division that is used when the divisor is small enough that it can be easily divided into the dividend.
Partial quotient division: This is a method of long division where the quotient is written as a sum of partial quotients instead of a single quotient.
Synthetic division: This is a method of division that is used to divide polynomials. It involves using the coefficients of the polynomial and following a specific algorithm to find the quotient and remainder.
Decimal division: This is division where the divisor and dividend are expressed as decimal values. It involves placing the decimal in the correct position and then following the rules of long division.
Bus stop division: This is a method of short division where the dividend is written in a tabular form and the divisor is divided into each digit individually.
Chunking/Sharding division: This is a method of division where the divisor is not used directly. Instead, the dividend is broken down into smaller parts that can be divided more easily.
Lattice division: This is a method of division that uses a grid-like lattice to find the quotient and remainder.
Egyptian division: This is an ancient method of division where the dividend is repeatedly halved and the divisor is repeatedly doubled until the quotient is found.
Galley division: This is a method of division that is used in printing presses. It involves setting the divisor and dividend in a row and dividing them through several stages to produce the quotient.
"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...the process of calculating the number of times one number is contained within another."
"This number of times need not be an integer."
"...everyone receives 5 apples."
"The division with remainder or Euclidean division of two natural numbers provides an integer quotient..."
"...the number of times the second number is completely contained in the first number."
"...a remainder, which is the part of the first number that remains..."
"...everyone receives 5 apples again, and 1 apple remains."
"For division to always yield one number rather than an integer quotient plus a remainder, the natural numbers must be extended to rational numbers or real numbers."
"In these enlarged number systems, division is the inverse operation to multiplication."
"If b = 0, then this is a division by zero, which is not defined."
"In the 21-apples example, everyone would receive 5 apple and a quarter of an apple..."
"Those in which a Euclidean division (with remainder) is defined are called Euclidean domains..."
"...include polynomial rings in one indeterminate."
"Those in which a division (with a single result) by all nonzero elements is defined are called fields and division rings."
"In a ring, the elements by which division is always possible are called the units..."
"...for example, 1 and -1 in the ring of integers."
"Another generalization of division to algebraic structures is the quotient group, in which the result of "division" is a group rather than a number."