Subtraction isFour arithmetic operationsOne that subtracts one number from anotheroperationIt's called subtraction;Two knownAddendThe sum of and one of the addends, and the operation of finding the other addend is called subtraction.The sign for subtraction is "-", read asminus sign。
Subtraction is a mathematical operation that represents the operation of removing objects from a collection.Its sign is a minus sign (−).For example, in the picture on the right, there are 5 − 2 apples, 5 apples, and 2 apples are taken away, leaving 3 apples.So 5 − 2=3.Subtraction means removing or reducing physical and abstract quantities with different objects (including negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices).
Subtraction follows several important patterns.It is anti commutative, meaning that changing the order changes the sign of the answer.It is not associative, that is, when a subtraction exceeds two numbers, the order of subtraction is important.Subtracting 0 does not change a number.Subtraction also follows predictable rules related to addition and multiplication.All of these rules can be proved, starting with the subtraction of integers and generalizing through real numbers and other things.Continue the general binary operations of these patterns and learn in abstract algebra.[1]
Symbols and terms
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When subtraction is used, there is a minus sign "−" between two items, and the result is represented by an equal sign.For example,
All these terms are derived from Latin."Subtraction" is an English word derived from the Latin verb subtrahere. It is a compound word of "from under" and "to pull", so it should be extracted from below.The result of using gerun diving suffix - nd in "subtrahend", "subtracted things".Similarly, from the minute "reduce or decrease", one gets "small" and "things decrease".
Integers and Real Numbers
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integer
Suppose there is a line segment with a length of b, marked a at the left end and c at the right end, starting from a and moving right to c.
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Then a+b=c.
Start from c, walk left and return to a. The left movement is modeled by subtraction:
c-b=a。
Natural number
Subtraction of natural numbers is not closed.It can be closed unless the minuend is greater than the minuend.For example, 26 cannot be subtracted by 11.In this case, one of two methods is used:
(1) Say 26 cannot be subtracted from 11;
(2) Take the answer as an integer to represent a negative number, so subtracting 26 from 11 yields - 15.
real number
Subtraction of real numbers is defined by adding signed numbers.Specifically, a number is subtracted by adding a negative number of another number.Then there is 3 − π=3+(− π).This helps keep real numbers "simple" by avoiding the introduction of "new" operators such as subtraction.
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Anti exchange rate
Subtraction is anti commutative.If a and b are any two numbers, then
Anti associative law
Subtraction is anti associative. It appears when you try to redefine subtraction.Should express
Definition means a-b-c or a − (b − c)?These two possibilities give different answers.To solve this problem, an operation sequence must be established, and different commands give different results.[2]
Unit of measure
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When two numbers are subtracted in units such as kilograms or pounds, they must have the same unit.In most cases, the difference is the same as the original number.
percentage
The percentage change can be reflected in at least two forms, percentage change and percentage change.The percentage change represents the relative change percentage between two quantities, while the percentage change is the figure obtained by subtracting two percentages.
For example, suppose that 30% of the parts produced by the factory are defective.Six months later, 20% of the small parts were defective.The percentage change is - 33/3%, while the percentage change is - 10 percentage points.
calculation
Place filling is used to subtract one number from another. You need to borrow one.This method is widely used in mechanical calculators and still has applications in modern computers.
Subtract a binary number y (the subtract end) from a number x (the minuend), add the complement of y to x, and add one to sum.The leading number "1" of the result is then discarded.
Complementary methods are particularly useful in binary (radix 2) because their complements can be easily obtained through the inverse ratio of each point (change "0" to "1", and vice versa).Two complements can be obtained by analog carry to the least important bit.For example:
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Became and
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Subtraction in Abstract Algebra
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Vector addition and subtraction:
In linear algebra, vector space is an algebraic structure that allows the addition of any two vectors and scaling vectors.A familiar vector space is a collection of all ordered real number pairs;Ordered pair (a, b) is interpreted as a pair fromEuclidean planeThe vector from the origin in to the point (a, b) in the plane.The difference between the two vectors is obtained by adding their respective coordinates:
This subtraction is at the heart of classical mechanics, where vectors are interpreted as forces.
Matrix subtraction:
Define matrix subtraction for two matrices of the same size.The difference between two m × n matrices A and B represented by A+B (pronounced "m times n") is a matrix calculated by subtracting elements, for example:
