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 total 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.
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 (binary adder). 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.
The animation above demonstrates the addition of seven hundred and eighty six and four hundred and sixty seven, the problems digits have been separated into units, tens and hundreds (place value). First the units 6 and 7 are added together to make 13, so 1 ten and 3 units, the 3 is written below and the 1 ten is 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, the 5 is written below and the 1 hundred is 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, the 2 is written below and the 1 thousand is carried to the thousand column. Giving the answer one thousand two hundred and fifty three.
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 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 (300) meters plus 120 meters.