THE addition is one of the main mathematical operations, it is associated with the idea of join or group elements of sets. We can also, based on it, define the operations of subtraction and multiplication. In addition, the addition operation is widely used in our daily lives, for example, when we go to the supermarket, so it is very important to understand its idea and the method of how to carry it out.
Read too: Decimal numbering system - system using base 10
What is addition?
The idea of addition is linked to the concept of join elements of two or more sets. For example, consider the set formed by circles and the set formed by triangles.
Now imagine that our interest is to determine the total number of geometric figures, for that we will have to get together the circles with the triangles. When we carry out this process, we are adding the number of circles with the number of triangles, and we indicate this sum with the symbol +.
Joining the elements of the two sets we have:
Note the number of elements in each of the sets, we have 4 (four) circles and 2 (two) triangles. See also that, by joining these elements, we obtained a total of 6 (six) geometric figures, we can synthesize all this reasoning in a mathematical expression, see:
4 + 2 = 6
How to make an addition?
Note that the process of graphing each addition element becomes complicated when we place larger numbers. For example, to determine the sum of 1500 and 1432, we would have to draw 1500 units and then 1432 units, in order to count the total amount of them. Next, we will see a method that facilitates this process.
Example 1
Find the sum between 1500 and 1432.
To determine the sum between the numbers, we must first "arm" the operation. This process consists of placing one number under another so that the units of the first number are under the units of the second, as well as the tens of the first number must be under the tens of the second, and so successively. Look:
Now, to determine the value of the addition, just add, term by term, the values from the previous table, that is, add unit to unit, ten to ten, and so on.
0 + 2 = 2 → Unit
0 + 3 = 3 → Ten
5 + 4 = 9 → Hundred
1 +1 = 2 → Unit of Thousand
So we can say that 1500 + 1432 = 2932. We can simplify the writing of the addition process by deleting the table and writing the orders, see:
See too: Ordinal numbers - numbers that represent order or position
Example 2
Find the sum between the numbers 5854 and 4217.
Again the first step is to set up the operation between the two numbers.
Then adding term to term we have:
4 + 7 = 11 → Units
5 + 1 = 6 → Tens
8 + 2 = 10 → Hundreds
5 + 4 = 9 → Unit of Thousand
When adding term by term, note that the sum of the units exceeds its capacity, as well as the sum of the hundreds, when this occurs, we must add what was exceeded to the end of the next order.
So we must add 1 ten to the tens place, taking it out of the units, and add 1 unit of thousands to the thousands place, taking it out of the hundreds place, see:
4 + 7 = 11 – 10→ Units
5 + 1 = 6 + 1 → Tens
8 + 2 = 10– 10→ Hundreds
5 + 4 = 9 + 1→ Thousand Unit
Logo: 5854 + 4217 = 10,071.
There is also a simplified way to perform this procedure, just raise the number which passes in each square to the square of the next order, see:
Example 3
Arm and add between numbers 6432 and 9993.
See that each apparition of the number 1 above the numbers 4 and 6 represents, respectively, the hundred and the thousand unit that were surpassed.
Also access: Roman numbers - numbering system represented by letters
Exercises
question 1 – Arm the following additions and determine their results.
a) 54 + 99
b) 1,544 + 199
c) 77 + 83
d) 1,432,765 + 65,876
e) 87 + 34 + 876
f) 543 + 423 + 54
g) 76 + 43 + 1,677
Resolution
a) 153
b) 1743
c) 160
d) 1,498,641
e) 997
f) 1020
g) 1796
question 2 – Fill in each of the blanks with the correct value.
a) 54 + ____ = 67
b) 99 + ____ = 209
c) ____ + 150 = 300
d) ____ + 34 = 100
Resolution
a) 13
b) 110
c) 150
d) 66
