Multiplication (often denoted by the cross symbol "×", by the dot "⋅", by juxtaposition, or, on computers, by an asterisk "*") is one of the four elementary mathematical operations of arithmetic, with the others being addition, subtraction and division.
The multiplication of whole numbers may be thought as a repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the value of the other one, the multiplier. The multiplier can be written first and multiplicand second (though the custom can vary by culture); both can be called factors.
￼For example, 4 multiplied by 3 (often written as ￼ and spoken as "3 times 4") can be calculated by adding 3 copies of 4 together: Here 3 and 4 are the factors and 12 is the product.
One of the main properties of multiplication is the commutative property: adding 3 copies of 4 gives the same result as adding 4 copies of 3:
￼Thus the designation of multiplier and multiplicand does not affect the result of the multiplication.
The multiplication of integers (including negative numbers), rational numbers (fractions) and real numbers is defined by a systematic generalization of this basic definition.
Multiplication can also be visualized as counting objects arranged in a rectangle (for whole numbers) or as finding the area of a rectangle whose sides have given lengths. The area of a rectangle does not depend on which side is measured first, which illustrates the commutative property. The product of two measurements is a new type of measurement, for instance multiplying the lengths of the two sides of a rectangle gives its area, this is the subject of dimensional analysis.
The inverse operation of multiplication is division. For example, since 4 multiplied by 3 equals 12, then 12 divided by 3 equals 4. Multiplication by 3, followed by division by 3, yields the original number (since the division of a number other than 0 by itself equals 1).
Multiplication is also defined for other types of numbers, such as complex numbers, and more abstract constructs, like matrices. For some of these more abstract constructs, the order in which the operands are multiplied together matters. A listing of the many different kinds of products that are used in mathematics is given in the product (mathematics) page.
Plastic is material consisting of any of a wide range of synthetic or semi-synthetic organic compounds that are malleable and so can be molded into solid objects.
Plasticity is the general property of all materials which can deform irreversibly without breaking but, in the class of moldable polymers, this occurs to such a degree that their actual name derives from this specific ability.
Plastics are typically organic polymers of high molecular mass and often contain other substances. They are usually synthetic, most commonly derived from petrochemicals, however, an array of variants are made from renewable materials such as polylactic acid from corn or cellulosics from cotton linters.
Due to their low cost, ease of manufacture, versatility, and imperviousness to water, plastics are used in a multitude of products of different scale, including paper clips and spacecraft. They have prevailed over traditional materials, such as wood, stone, horn and bone, leather, metal, glass, and ceramic, in some products previously left to natural materials.
In developed economies, about a third of plastic is used in packaging and roughly the same in buildings in applications such as piping, plumbing or vinyl siding. Other uses include automobiles (up to 20% plastic), furniture, and toys. In the developing world, the applications of plastic may differ—42% of India's consumption is used in packaging. Worldwide, about 50 kg of plastic is produced annually per person, with production doubling every ten years.
Plastics have many uses in the medical field as well, with the introduction of polymer implants and other medical devices derived at least partially from plastic. The field of plastic surgery is not named for use of plastic materials, but rather the meaning of the word plasticity, with regard to the reshaping of flesh.
The world's first fully synthetic plastic was bakelite, invented in New York in 1907, by Leo Baekeland who coined the term 'plastics'. Many chemists have contributed to the materials science of plastics, including Nobel laureate Hermann Staudinger who has been called "the father of polymer chemistry" and Herman Mark, known as "the father of polymer physics".
The success and dominance of plastics starting in the early 20th century led to environmental concerns regarding its slow decomposition rate after being discarded as trash due to its composition of large molecules. Toward the end of the century, one approach to this problem was met with wide efforts toward recycling.
Packaging is the science, art and technology of enclosing or protecting products for distribution, storage, sale, and use. Packaging also refers to the process of designing, evaluating, and producing packages. Packaging can be described as a coordinated system of preparing goods for transport, warehousing, logistics, sale, and end use. Packaging contains, protects, preserves, transports, informs, and sells. In many countries it is fully integrated into government, business, institutional, industrial, and personal use.
Mincing is a food preparation technique in which food ingredients are finely divided into uniform pieces. Minced food is in smaller pieces than diced or chopped foods, and is often prepared with a chef's knife or food processor, or in the case of meat by a specialised meat grinder.
For a true mince, the effect is to create a closely bonded mixture of ingredients and a soft or pasty texture. However, in many recipes, the intention is for firmer foods such as onions and other root vegetables to remain in individual chunks when minced.
Flavoring ingredients such as garlic, ginger, and fresh herbs may be minced in this way to distribute flavor more evenly in a mixture. Additionally bruising of the tissue can release juices and oils to deliver flavors uniformly in a sauce. Mincemeat tarts/mince pies and pâtés employ mincing in the preparation of mouldable paste. Meat is also minced and this cooking technique is used in Greek cuisine.
Meat is animal flesh that is eaten as food. Humans have hunted and killed animals for meat since prehistoric times. The advent of civilization allowed the domestication of animals such as chickens, sheep, rabbits, pigs and cattle. This eventually led to their use in meat production on an industrial scale with the aid of slaughterhouses.
Meat is mainly composed of water, protein, and fat. It is edible raw, but is normally eaten after it has been cooked and seasoned or processed in a variety of ways. Unprocessed meat will spoil or rot within hours or days as a result of infection with and decomposition by bacteria and fungi.
Meat is important in economy and culture, even though its mass production and consumption has been determined to pose risks for human health and the environment. Many religions have rules about which meat may or may not be eaten. Vegetarians and vegans may abstain from eating meat because of concerns about the ethics of eating meat, environmental effects of meat production or nutritional effects of consumption.