Addition

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In arithmetic, addition is a method for finding out how many things there are if the things are already partly counted. Addition is also a method for measuring things that are already partly measured. The word "addition" slso means to make something bigger.

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[edit] Arithmetic

In arithmetic, addition is an action that is done with two or more numbers. The arithmetic symbol for addition is "+". The name for the symbol "+" is "plus".

The simplest type of addition is the addition of two numbers. Adding two numbers produces another number. For example, if the two numbers to be added are 2 and 3, adding them is written two plus three, or in symbols "2+3". The result of adding 2+3 is another number. By the rules for addition, this other number is five, so two plus three is five. In symbols:

2 + 3 = 5

[edit] Counting examples

For example, there are objects in two groups. The objects are small circles: "o". One group has five of these objects. The other group has 3 of these objects. To find the number of objects in both groups, the objects can be counted. Another way to find the number of objects in both groups is to add the numbers in each group.

[edit] Counting

Group A has five objects: " o o o o o "
Group B has three objects: " o o o "

Group A has already been counted and found to have five objects. Group B has already been counted and found to have three objects:

Group A: " o o o o o "
Counting the objects in Group A: " 1 2 3 4 5 "

Each object is given a number. The first object gets the number one. The next object gets the second number, the number two. The next object gets the third number, the number three. The next object gets the fourth number, the number four. The last object gets the number five. There are no more objects, and so counting shows that there are five objects in group A.

In the same way, group B can be counted:

Group B: " o o o "
Counting the objects in Group B: " 1 2 3 "

How many objects are in group A and group B? One method is to count all the objects in group A and B:

Group A, Group B " o o o o o "," o o o "
Counting the objects in Group A and B together:" 1 2 3 4 5 6 7 8"

[edit] Adding

Another method is to add the numbers of objects in group A and group B, since they are already counted. In symbols:

5 + 3 

There are rules for adding numbers that people learn. There are also rules for adding numbers that are built into machines. The rule says that:

 5+3=8

In another counting example, Sally and Bill have 2 children. Sally and Bill get 3 more children. Sally and Bill have added three children to their two children and now have five children.

[edit] A measurement example

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

Tom's house<------------300 meters-------------->Bob's house<-----120 meters----->Sally's house

The distance from Tom's house to Sally's house can be found by measuring, or 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, three hundred meters plus 120 meters. In symbols:

300 + 120 = 420

[edit] Addition as increase

Addition can also mean to increase or make bigger.

[edit] Example of addition as increase

  • For example, Tom has a house. Tom puts a new room on the house. This new room is called an addition.
  • John is making food. To make the food taste better, John puts salt in the food. That is, John adds salt to the food. The salt is an addition to the food.

[edit] Less Simple

Addition is the arithmetic operation for finding the total, or sum, of two or more numbers. If you are adding three or more terms together, mathematicians call those numbers summands; if you are only adding two numbers they are called the augend and the addend. Augend + addend = sum; summand + summand + summand = sum. The addition expression 3 + 8 = 11 is spoken as "three plus eight equals eleven."

Adding two numbers together is a dyadic operation. Addition of summands is calculated by putting dyadic additions together.

40 + 20 + 3 = (40 + 20) + 3 = 60 + 3 = 63

Dyadic addition can be done by adding 1 again and again, the most basic mathematical operation.

For all x, successor(x)=x+1

For all x, predeccessor(x)=x-1

How dyadic addition is adding 1 again an again:

a+b=successor(a+predecessor(b))

How this is done for 5+5:

5 + 5 = s(5 + p5) = ss(5 + pp5) = sss(5 + ppp5) = ssss(5 + pppp5) = sssss(5 + ppppp5) = sssss(5 + pppp4) = sssss(5 + ppp3) = sssss(5 + pp2) = sssss(5 + p1) = sssss(5) = ssss(6) = sss(7) = ss(8) = s(9) = 10 Putting additions together is the same as a multiplication. Putting multiplications together is the same as exponentiation, or powers. Putting powers together makes tetration. This never ends.

[edit] Notes


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