In addition to the distributive nature already described earlier, in mathematics there is also called commutative nature. Do you know what is the nature of commutative mathematics? if you do not already know, Here Basic Mathematical Formulas will explain it for you guys. In simple terms, commutative nature can be interpreted as the nature of exchange in mathematical operations, consider the calculation in the figure below:
So it can be concluded that the commutative nature in mathematics satisfies the formula a + b = b + a where a and b are integers. This property not only applies to addition operations but also applies to multiplication operations (a x b = b x a). Thus, in the commutative nature of mathematics we are allowed to exchange numbers in addition and multiplication with the same fixed result.
Understanding Commutative Properties of Mathematics, Sample Problem and Discussion
The commutative nature of the sum arithmetic operation
Now let's learn more about the concept of commutative nature in the sum arithmetic operation below:
Sample Problem 1
Calculate the result from 26.983 + 99.281 = ...
Answer:
Results from 26.983 + 99.281 = 126.264
If both numbers are exchanged, will the result be the same?
99.281 + 26.983 = 126.264
It turns out the result remains the same, ie 126.264. This means that commutative law applies to the sum arithmetic operation.
The commutative nature of the countdown operation
Now let's try in countdown operation.
99.281 - 26.983 = 72.298
Should the position of the numbers be exchanged is the result the same?
26.983 - 99.281 = - 72.298
It appears that the result is different, if the position of the number is exchanged then the result will be negative. That is, commutative properties do not apply to countdown operations (a - b ≠ b - a)
The commutative nature of multiplication counting operations
Next, let's look at the use of these properties in counting operations in multiplication form. Observe the example below:
Sample Problem 2
What is the result of 25 x 45 = ...
Answer:
Results of 25 x 45 = 1125
To test commutative nature, let's swap its position:
45 x 25 = 1125
It turns out the result remains the same, meaning that in the operation of the multiplication form, the commutative nature of mathematics can apply.
The commutative nature of the division counting operation
Now let's see if these properties can apply to division counting operations. Let's take the following example:
80: 20 = 4
If exchanged will the results be the same?
20: 80 = 0.25
It turns out after the position is exchanged the results obtained differently. Then it can be concluded that commutative nature can not apply in division counting operations (a: b ≠ b: a)
How? do you already understand the material explanation about Understanding Commutative Properties of Mathematics, Examples of Problems and Complete Discussions that have been described above? If not, try to read it again carefully, surely you will be able to understand it if paying close attention to the examples of calculations given.