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Addition

From Simple English Wikipedia, the free encyclopedia
"Add" redirects here. For other articles with the same name, seeADD (disambiguation).
Not to be confused withbuilding extensions which are also called additions.
Addition

Inmathematics,addition, represented by the symbol+{\displaystyle +}, is an operation which combines two mathematical objects together into another mathematical object of the same type, called thesum.[1][2][3] Addition can occur with simple objects such asnumbers, and more complex objects and concepts such asvectors andmatrices.[4]

Addition has several important properties. It iscommutative, meaning that the order of theoperands does not matter, and it isassociative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (seeSummation). Repeated addition of1 is the same as counting. Addition of0 does not change a number. Addition also obeys predictable rules concerning related operations such assubtraction andmultiplication.

Arithmetic

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Inarithmetic, addition is the operation where two or morenumbers called "addends" are used to make a new number, which is the "sum" or total that is expressed with theequals sign. The symbol for addition, ininfix notation, is the plus sign "+" placed between the operands.

Two plus three is equal to five.
2shapes + 3 shapes = 5 shapes

Counting examples

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For example, there areobjects in two groups (as shown on the right). The objects are various shapes, where one group has 3 of them while the other has 2. When the two groups combine into one, the overall amount (sum) of the shapes become 5.

Vertical Addition

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The animation above demonstrates the addition of seven hundred eighty six and four hundred sixty seven. The problem's digits have been separated into units, tens and hundreds (seePlace value).

First, the units 6 and 7 are added together to make 13, so 1 ten and 3 units, with the 3 written below and the 1 ten carried to the tens column. Next, in the tens column, the 1, 8, and 6 are added together to make 15 tens, so 1 hundred and 5 tens, with the 5 written below and the 1 hundred carried to the hundreds column. Finally, in the hundreds column, 1, 7, and 4 are added together to make 12 hundreds, so 1 thousand and 2 hundreds, with the 2 written below and the 1 thousand carried to the thousand column. The final answer is thus one thousand two hundred fifty three.

A measurement example

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Tom wants to know the distance between his house and Sally's house. Bob's house is 300 m east of Tom's house. Sally's house is 120 m east of Bob's house:

Tom's house←{\displaystyle \leftarrow }300 m→{\displaystyle \rightarrow }Bob's house←{\displaystyle \leftarrow }120 m→{\displaystyle \rightarrow }Sally's house

The distance from Tom's house to Sally's house can be found by adding the distances already measured. The distance from Tom's house to Bob's house, added to the distance from Bob's house to Sally's house, is the same as the distance from Tom's house to Sally's house. That is, 300 m plus 120 m.

300+120=420{\displaystyle 300+120=420}

Hence Sally's house is 420 m to the east of Tom's house.

Properties

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Commutativity

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4+2=2+4{\displaystyle 4+2=2+4} with blocks

Addition iscommutative, meaning that one can change the order of the numbers in a sum, but still get the same result. For example:

4+5=9{\displaystyle 4+5=9} and5+4=9{\displaystyle 5+4=9}

Associativity

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2+(1+3)=(2+1)+3{\displaystyle 2+(1+3)=(2+1)+3} with parts of a cylinder

Addition is alsoassociative, which means that when three or more numbers are added together, theorder of operations does not change the result.

For any three numbersa{\displaystyle a},b{\displaystyle b}, andc{\displaystyle c}, it is true that1=(a+b)+c=a+(b+c){\displaystyle 1=(a+b)+c=a+(b+c)}. For example,1=(1+2)+3=3+3=6{\displaystyle 1=(1+2)+3=3+3=6} and1=1+(2+3)=1+5=6{\displaystyle 1=1+(2+3)=1+5=6}, which means that1=(1+2)+3=1+(2+3){\displaystyle 1=(1+2)+3=1+(2+3)}.

When addition is used together with other operations, the order of operations becomes important. In the standard order of operations, addition is to be computed later thanexponentiation,roots,multiplication anddivision, but has equal importance assubtraction.[5]

Addition table

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Addition table
Addition table of 1
1+0=1
1+1=2
1+2=3
1+3=4
1+4=5
1+5=6
1+6=7
1+7=8
1+8=9
1+9=10
1+10=11
Addition table of 2
2+0=2
2+1=3
2+2=4
2+3=5
2+4=6
2+5=7
2+6=8
2+7=9
2+8=10
2+9=11
2+10=12
Addition table of 3
3+0=3
3+1=4
3+2=5
3+3=6
3+4=7
3+5=8
3+6=9
3+7=10
3+8=11
3+9=12
3+10=13
Addition table of 4
4+0=4
4+1=5
4+2=6
4+3=7
4+4=8
4+5=9
4+6=10
4+7=11
4+8=12
4+9=13
4+10=14
Addition table of 5
5+0=5
5+1=6
5+2=7
5+3=8
5+4=9
5+5=10
5+6=11
5+7=12
5+8=13
5+9=14
5+10=15
Addition table of 6
6+0=6
6+1=7
6+2=8
6+3=9
6+4=10
6+5=11
6+6=12
6+7=13
6+8=14
6+9=15
6+10=16
Addition table of 7
7+0=7
7+1=8
7+2=9
7+3=10
7+4=11
7+5=12
7+6=13
7+7=14
7+8=15
7+9=16
7+10=17
Addition table of 8
8+0=8
8+1=9
8+2=10
8+3=11
8+4=12
8+5=13
8+6=14
8+7=15
8+8=16
8+9=17
8+10=18
Addition table of 9
9+0=9
9+1=10
9+2=11
9+3=12
9+4=13
9+5=14
9+6=15
9+7=16
9+8=17
9+9=18
9+10=19
Addition table of 10
10+0=10
10+1=11
10+2=12
10+3=13
10+4=14
10+5=15
10+6=16
10+7=17
10+8=18
10+9=19
10+10=20

Related pages

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References

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  1. ↑"List of Arithmetic and Common Math Symbols".Math Vault. 2020-03-17. Retrieved2020-08-26.
  2. ↑"Addition".www.mathisfun.com. Retrieved2020-08-26.
  3. ↑Weisstein, Eric W."Addition".mathworld.wolfram.com. Retrieved2020-08-26.
  4. ↑"Comprehensive List of Algebra Symbols".Math Vault. 2020-03-25. Retrieved2020-08-26.
  5. ↑Bronstein, Ilja Nikolaevič; Semendjajew, Konstantin Adolfovič (1987) [1945]. "2.4.1.1.". In Grosche, Günter; Ziegler, Viktor; Ziegler, Dorothea (eds.).Taschenbuch der Mathematik (in German). Vol. 1. Translated by Ziegler, Viktor. Weiß, Jürgen (23 ed.). Thun and Frankfurt am Main:Verlag Harri Deutsch (andB.G. Teubner Verlagsgesellschaft, Leipzig). pp. 115–120.ISBN 978-3-87144-492-0.

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