The combined operations they are mathematical operations that must be performed to determine a certain result. These are taught for the first time in elementary school, although they are usually used in later courses, being key to solving higher mathematical operations.
A mathematical expression with combined operations is an expression where different types of calculations must be carried out, following a certain order of hierarchy, until all the operations in question have been carried out.
In the previous image, you can see an expression where different types of basic mathematical operations appear, therefore, it is said that this expression contains combined operations. The basic operations that are carried out are the addition, subtraction, multiplication, division and / or enhancement of mainly whole numbers.
Article index
As already said before, an expression with combined operations is an expression where mathematical calculations such as addition, subtraction, product, division and / or the calculation of a power must be performed.
These operations may involve real numbers, but for ease of understanding, only whole numbers will be used in this article..
Two expressions with different combined operations are as follows:
5 + 7 × 8-3
(5 + 7) x (8-3).
The previous expressions contain the same numbers and the same operations. However, if the calculations are performed, the results will be different. This is due to the parentheses that the second expression has and the hierarchy with which the first must be resolved.
When there are grouping symbols such as parentheses (), square brackets [], or braces , what is inside each pair of symbols should always be resolved first.
In the case that there are no grouping symbols, the hierarchy is as follows:
- powers are resolved first (if any)
- then the products and / or divisions are resolved (if any)
- Lastly, the addition and / or subtraction are solved
Here are some examples where you have to solve expressions that contain combined operations.
Solve the two operations presented above: 5 + 7 × 8-3 and (5 + 7) x (8-3).
Solution
Since the first expression does not have grouping signs, the hierarchy described above must be followed, therefore, 5+ 7 × 8- 3 = 5 + 56-3 = 58.
On the other hand, the second expression has grouping signs, so that we must first solve what is inside said signs and therefore, (5 + 7) x (8-3) = (12) x (5) = 60.
As said before, the results are different.
Solve the following expression with combined operations: 3² - 2³x2 + 4 × 3-8.
Solution
In the given expression, you can see two powers, two products, an addition and a subtraction. Following the hierarchy, you must first solve the powers, then the products, and finally the addition and subtraction. Therefore, the calculations are as follows:
9 - 8 × 2 + 4 × 3 - 8
9 - 16 +12 - 8
-3.
Calculate the result of the following expression with combined operations: 14 ÷ 2 + 15 × 2 - 3³.
Solution
In the expression in this example, there is a power, a product, a division, an addition and a subtraction, and therefore the calculations proceed as follows:
14 ÷ 2 + 15 × 2 - 27
7 + 30 - 27
10
The result of the given expression is 10.
What is the result of the following expression with combined operations: 1 + 6 × 3 - 46 ÷ 2 + 4² ÷ 2 ?
Solution
The previous expression, as you can see, contains addition, subtraction, multiplication, division and empowerment. Therefore, it must be solved step by step, respecting the order of the hierarchy. The calculations are as follows:
1 + 6 × 3 - 46 ÷ 2 + 4² ÷ 2
1 + 6 × 3 - 46 ÷ 2 + 16 ÷ 2
1 + 18 - 23 + 8
3
In conclusion, the result is 3.
Yet No Comments