Numerical expressions are numerical groups calculated by mathematical operations (addition, subtraction, multiplication, division, etc.) that follow certain orders.
These sets of numbers are separated by graphic symbols—representations that determine the sequence in which the expressions should be made. The main signs are: curly brackets { }, parentheses () and brackets [ ].
Sequence of graphic symbols
Number expressions are usually written inside parentheses, curly brackets , or brackets. Therefore, it is essential to understand which graphic signs guide the procedures to be done.
Let’s see the order of preference:
• 1st: solve all operations within the parentheses.
• 2nd: solve all operations within brackets.
• 3rd: solve all operations within the keys.
The following example shows the correct sequence:
[(24) ÷ 8 + 5 . 3] ÷ 6 =
[24 ÷ 8 + 5 . 3] ÷ 6 =
[3 + 15] ÷ = 6
[18] ÷ 6 =
18 ÷ 6 = 3
Sequence of operations
As well as the graphic symbols, which are separated according to the degree of preference, there are also orders for the calculations of numerical expressions. Therefore, mathematical operations are carried out according to the following scheme:
Potentiation or rooting
The first step in solving numerical expressions is to find the values of the powers and roots. This rule only changes when the numbers are in parentheses, brackets or braces, that is, the sequence of graphic symbols becomes valid.
2². 3/ 2 = 4.3/ 2 = 12/2 = 6 or 2². 3/ 2 = 2². 1.5 = 4. 1.5 = 6
Between rooting and potentiation there are no priorities. Therefore, both can be carried out at the same time
Multiplication or division
If there is no composition of roots or powers, the orientation is to solve the multiplications and divisions. As there is also no preference between the two, it is calculated which appears first in the expression.
5.8 / 2 = 40/2 = 20 or 5.8/2 = 5. 4 = 50
Addition or subtraction
The last step is on account of addition and subtraction. As with the other operations, there are no priorities in the resolution. Then, develop them in the order that appears.
30 – 5 + 12 = 25 + 12 = 37 or 30 – 5 + 12 = 30 + 7 = 37
Activity
1) 2 + 8 – 3 – 5 + 15 =
2) 12 + [35 – (10 + 2) +2] =
3) [(18 + 3 · 2) ÷ 8 + 5 · 3] ÷ 6 =
4) 37 + [-25 – (-11 + 19 – 4)] =
5) 60 ÷ {2 · [-7 + 18 ÷ (-3 + 12)]} – [7 · (-3) – 18 ÷ (-2) + 1] =
6) -8 + {-5 + [(8 – 12) + (13 + 12)] – 10} =
Respostas