In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression.
These rules are formalized with a ranking of the operations. The rank of an operation is called its precedence, and an operation with a higher precedence is performed before operations with lower precedence. Calculators generally perform operations with the same precedence from left to right,[1] but some programming languages and calculators adopt different conventions.
For example, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation.[2][3] Thus, in the expression 1 + 2 × 3, the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9. When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication and placed as a superscript to the right of their base.[2] Thus 3 + 52 = 28 and 3 × 52 = 75.
These conventions exist to avoid notational ambiguity while allowing notation to remain brief.[4] Where it is desired to override the precedence conventions, or even simply to emphasize them, parentheses ( ) can be used. For example, (2 + 3) × 4 = 20 forces addition to precede multiplication, while (3 + 5)2 = 64 forces addition to precede exponentiation. If multiple pairs of parentheses are required in a mathematical expression (such as in the case of nested parentheses), the parentheses may be replaced by brackets or braces to avoid confusion, as in [2 × (3 + 4)] − 5 = 9.
These rules are meaningful only when the usual notation (called infix notation) is used. When functional or Polish notation are used for all operations, the order of operations results from the notation itself.
^Cite error: The named reference Microsoft was invoked but never defined (see the help page).
^ abCite error: The named reference BS was invoked but never defined (see the help page).
^Cite error: The named reference Peterson was invoked but never defined (see the help page).
^Cite error: The named reference Swokowski was invoked but never defined (see the help page).
and 27 Related for: Order of operations information
programming, the orderofoperations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given...
An OperationOrder, often abbreviated to OPORD, is a plan format meant to assist subordinate units with the conduct of military operations. An OPORD describes...
This is the orderof battle for Operation Barbarossa, the German invasion of the Soviet Union during World War II. It was fought between the German-led...
certain precedence rules determine the orderofoperations. Tree traversal: Infix (In-order) is also a tree traversal order. It is described in a more detailed...
operations due to their longer instruction pipelines and other architectural design choices, bitwise operations do commonly use less power because of...
operation, a "train order" is an order issued by or through a proper railway official to govern the movement of trains". Train orderoperation was widely used...
Operation Husky orderof battle is a listing of the significant military and air force units that were involved in the campaign for Sicily, July 10 –...
the orderofoperation in accordance with rules set by convention. If the reader evaluates an expression but does not follow the correct orderof operation...
Operation Law and Order was an Israeli military operation against a Hezbollah base in the village of Maydoun. On April 26, 1988, a Hezbollah infiltration...
This is the Operation Telic orderof battle, which lists the British forces that took part in Operation Telic, including the 2003 Invasion of Iraq, subsequent...
This is the Operation Herrick ground orderof battle, which lists any British ground forces that have taken part in the duration ofOperation Herrick between...
of Britain in 1940 during World War II was code-named Operation Sea Lion (Unternehmen Seelöwe in German). This is the orderof battle for Operation Sea...
Operation Nordwind was launched by German ground forces on 31 December 1944 against U.S. and French ground forces in the Rhineland-Palatinate and the...
out sequences of arithmetic or logical operations (computation). Modern digital electronic computers can perform generic sets ofoperations known as programs...
on One (disambiguation) Out ofOrder (disambiguation) Alturas Municipal Airport, former FAA LID O00 Orderofoperations, in evaluating mathematical expressions...
is the orderof battle for Operation Granby, the name given to the British Armed Forces deployment to the Middle East after the Iraqi invasion of Kuwait...
Operation Diadem orderof battle is a listing of the significant formations that were involved in the fighting on the Winter Line and at the Anzio bridgehead...
ordering generated by a CPU during runtime. In modern microprocessors, memory ordering characterizes the CPU's ability to reorder memory operations –...
This is the orderof battle for Operation Badr, an Egyptian military operation that initiated the Yom Kippur War against Israel along the Suez Canal in...
This is the orderof battle for the Operation Perch, a World War II operation between British and German forces in Normandy, France between June 6 and...
If the order in time between certain operations is not determined by the system, then a partial order is used. Examples of such operations are requesting...
the orderof a single FIFO queue. In sequential consistency, there is no notion of time or most recent write operations. There are some operations interleaving...
allied expeditionary force composed of British, French, and Free Polish formations. The following list formed the orderof battle for this campaign. On 1 March...
The Japanese and Manchukuoan orderof battle for Operation Nekka was: Kwantung Army Jehol Operation Force - Field Marshal Baron Nobuyoshi Muto, 6th Division...
leadership during active operations", with all ranks being eligible. It is a level 2A decoration (order) in the British system of military decorations. Instituted...
Operation Jubilee was the Allied code name for the raid at Dieppe on the French coast on August 19, 1942. The following orderof battle lists the significant...
Global Information