additionmathematics
Main
Aspects of this topic are discussed in the following places at Britannica.
Assorted References
-
major reference
( in arithmetic: Addition and multiplication )
...objects. The number c is called the sum of a and b; and each of the latter is called a summand. The operation of forming the sum is called addition, the symbol + being read as “plus.” This is the simplest binary operation, where binary refers to the process of combining two objects.
-
fractions in Chinese mathematics
( in mathematics, East Asian: Arithmetic of fractions )
...of 2; this gives rise to the mixed quantity 3 + 2/5. The fractional parts are thus always less than one, and their arithmetic is described through the use of division. For instance, to get the sum of a set of fractions, one is instructed to
multiply the numerators by the denominators that do not correspond to them, add to get the dividend. Multiply the denominators all together...
-
rational numbers
( in combinatorics: BIB (balanced incomplete block) designs. )
A finite field is a finite set of marks with two operations, addition and multiplication, subject to the usual nine laws of addition and multiplication obeyed by rational numbers. In particular the marks may be taken to be the set X of non-negative integers less than a prime p. If this is so, then addition and multiplication are defined by modified addition and multiplication laws...
-
vectors ( in vector
)
Two vectors can be added or subtracted. For example, to add or subtract vectors v and w graphically (see the diagram), move each to the origin and complete the parallelogram formed by the two vectors; v + w is then one diagonal vector...
in mechanics: Vectors )If vector A is added to vector B, the result is another vector, C, written A + B = C. The operation is performed by displacing B so that it begins where A ends, as shown in Figure 1A. C is then the vector that starts where A...
in physical science, principles of: Fields )...the strength of the force, and the direction of the arrow shows the direction of the force. If a number of particles are acting simultaneously on the one considered, the resultant force is found by vector addition; the vectors representing each separate force are joined head to tail, and the resultant is given by the line joining the first tail to the last head.
Citations
Link to this article and share the full text with the readers of your Web site or blog-post.
If you think a reference to this article on "addition" will enhance your Web site,
blog-post, or any other web-content, then feel free to link to this article,
and your readers will gain full access to the full article, even if they do not subscribe to our service.
You may want to use the HTML code fragment provided below.
-
major reference arithmetic
...objects. The number c is called the sum of a and b; and each of the latter is called a summand. The operation of forming the sum is called addition, the symbol + being read as “plus.” This is the simplest binary operation, where binary refers to the process of combining two objects.
-
fractions in Chinese mathematics mathematics, East Asian
...of 2; this gives rise to the mixed quantity 3 + 2/5. The fractional parts are thus always less than one, and their arithmetic is described through the use of division. For instance, to get the sum of a set of fractions, one is instructed to
multiply the numerators by the denominators that do not correspond to them, add to get the dividend. Multiply the denominators all together...
-
rational numbers combinatorics
A finite field is a finite set of marks with two operations, addition and multiplication, subject to the usual nine laws of addition and multiplication obeyed by rational numbers. In particular the marks may be taken to be the set X of non-negative integers less than a prime p. If this is so, then addition and multiplication are defined by modified addition and multiplication laws...
-
vectors ( in vector
)
Two vectors can be added or subtracted. For example, to add or subtract vectors v and w graphically (see the diagram), move each to the origin and complete the parallelogram formed by the two vectors; v + w is then one diagonal vector...
in mechanics: Vectors )If vector A is added to vector B, the result is another vector, C, written A + B = C. The operation is performed by displacing B so that it begins where A ends, as shown in Figure 1A. C is then the vector that starts where A...
in physical science, principles of: Fields )...the strength of the force, and the direction of the arrow...
-
work of Peirce logic, history of
Peirce developed this symbolism extensively for relations. His earlier work was based on versions of multiplication and addition for relations—called relative multiplication and addition—so that Boolean laws still held. Both Peirce’s conception of the purposes of logic and the details of his symbolism and logical rules were enormously complicated by highly developed and unusual...
any of a class of chemical reactions in which an atom or group of atoms is added to a molecule.
Addition reactions are typical of unsaturated organic compounds—i.e., alkenes, which contain a carbon-to-carbon double bond, and alkynes, which have a carbon-to-carbon triple bond—and aldehydes and ketones, which have a carbon-to-oxygen double bond. An addition reaction may be visualized as a process by which the double or triple bonds are fully or partially broken in order to accommodate additional atoms or groups of atoms in the molecule. Addition reactions to alkenes and alkynes are sometimes called saturation reactions because the reaction causes the carbon atoms to become saturated with the maximum number of attached groups.
A typical addition reaction may be illustrated by the hydrochlorination of propene (an alkene), for which the equation is
CH3CH = CH2 + HCl →
CH3C+HCH3+Cl−→ CH3CHClCH3.
The reaction proceeds in two stages: first, the hydrogen ion, H+, of hydrogen chloride (the positively charged component) adds to one of the pair of carbon atoms joined by double bonds—in this case, the less alkylated carbon atom—followed by addition of the chloride ion, Cl− (the negatively charged component), to the other carbon atom.
In addition reactions to aldehydes and ketones, the sequence of events is reversed; i.e., the initial step is addition of the negatively charged component of the reagent to the carbon atom, followed by addition of the positively charged component to the oxygen atom. Thus, the reaction of a methyl ketone (CH3(C = O)R, where R is an alkyl group) with hydrogen cyanide proceeds as follows:
O
‖
H3CCR + HCN→
O− OH
||
H3CCCN + H+ → H3CCCN
||
RR
The hydrochlorination of propene or, in...
-
properties industrial polymers, major
...rings coupled by imide linkages—that is, linkages in which two carbonyl (CO) groups are attached to the same nitrogen (N) atom. There are two categories of these polymers, condensation and addition. The former are made by step-growth polymerization and are linear in structure; the latter are synthesized by heat-activated addition polymerization of diimides and have a network...
-
surface coatings surface coating
Step-growth polymers include polyesters, epoxies, polyurethanes, polyamides, melamine, and phenolic resins. They are formed most often by reactions between two dissimilar monomers—acids and alcohols in the case of polyesters. This general class of polymers is used widely in the field of organic coatings. Chain-growth polymers are built up by the opening of carbon-carbon double (or...
We welcome your comments. Any revisions or updates suggested for this article will be reviewed by our editorial staff. Contact us here.
Regular users of Britannica may notice that this comments feature is less robust than in the past. This is only temporary, while we make the transition to a dramatically new and richer site. The functionality of the system will be restored soon.