THE addition is a mathematical operation that is associated with the idea of grouping elements of one or more sets. With this operation, we can solve several problems in our daily lives, but for this to be possible, first, it is necessary to understand how to carry out this operation and also understand some of its properties.
Read too: addition multiplication table
What is addition?
THE addition is a mathematical operation that is associated with the idea of grouping elements of a set. To indicate an addition, we use O symbol (+).
Imagine two friends are playing with their marbles. One of them has blue balls, and the other has green balls.
To determine the total amount of balls, we must match the blue balls with the green balls, that is, match the quantity of blue balls with the quantity of green balls.
Looking at the image above, we notice that the total of marbles is nine, so we can write the addition operation as follows:
3 + 6 = 9
Calculation of addition
To perform the addition operation, it is not necessary to resort to images, as imagine having to perform an addition between two relatively large numbers through drawings – having to draw them can be a not so much task easy. So, to perform an addition, we must follow the following step by step:
Example 1
1064 + 334 |
Step 1 – The first step is to “arm” the operation. To perform this first step, we must put the bigger number ondthe smallest number. Putting unit under unit, ten under ten, hundred under hundred and so on (If you don't remember what unity, tens and hundreds is, we recommend reading this text: Decimal numbering system.).
Step 2 – In the second step, we have to add the unit of the first number with the unit of the second number, ten of the first number with the ten of the second number and so on. Look:
4 +4 = 8 (unit)
6 + 3 = 9 (ten)
0 + 3 = 3 (hundreds)
1 + 0 = 1 (unit of a thousand)
The result of the operation is 1,398. We can find this result more directly by adding the numbers in the already-armed operation.
Example 2
2.543 + 1.538 |
As in the previous example, let's “arm” the operation.
Adding term to term of the operation, we have:
3 + 8 = 11
4 + 3 = 7
5 + 5 = 10
2 + 1 = 3
Note that, when adding the units, the result was a second-order number (order of tens) and the same occurred when we added the hundreds. In these cases, we must add the number of tens formed in the tens place.
As the number 11 has 1 ten and 1 unit, we must add 1 ten in casthe one of the tens. And since 10 is in the hundreds place, that is, 10 hundreds equals 1 unit of thousands (10 · 100 = 1,000), we must add 1 unit of thousands to the thousand units place.
3 + 8 = 11
4 + 3 = 7 +1
5 + 5 = 10
2 + 1 = 3 +1
Thus, 2,543 + 1,538 = 4,081.
To facilitate the addition process in these cases, we will “arm” the operation and, whenever the above fact occurs, we will “raise” the number that exceeds its order. Look:
Read too: Adding more than two numbers
Addition properties
The addition has some properties that help us in solving some problems.
Property 1: In the addition operation, the number zero It is known as neutral element, that is, when adding between any number and the number zero, the result will be the number itself. Look:
3 + 0 = 3
0 + 6 = 6
Property 2: addition is commutative, that is, we can change the order of the parcels and the result will still be the same. Look:
6 + 4 = 10
and
4 + 6 = 10
Note that the order of the parcels does not change the final result.
Property 3: The addition operation is also associative, which means that we can add the parts of an addition in different ways and the result does not change. Look:
(4 + 6) + 3
10 + 3
13
Now performing the addition in a different order, the result does not change.
4 + (6 + 3)
4 + 9
13
Therefore, (4 + 6) + 3 = 4 + (6 + 3) = 13.
Read too: Adding decimal numbers
solved exercises
question 1 – View the following scores, which show how many points each team has scored in a basketball match.
→ 1st half scoreboard:
→ 2nd half scoreboard:
What was the winning team and by what score?
Solution
The winning team is the one with the most points joining the points of the first and second half, that is, we must add up the amount of points scored by each team.
Team 1:49 + 55 = 104 points.
Team 2: 58 + 50 = 108 points.
Therefore, the winning team is 2, with 108 points.
