Commutative and Associative properties are quite interesting to learn about. You wouldn’t have noticed but the commutative property is used in our daily life as well. Let’s explore more about it with an example: Neha and Riya are very close to each other and whenever they get a reward from their maths teacher, they keep them together as a remark of joint preparation they do in scoring well.
Since the two gifts were similar they kept them in a “P + Q” manner. One day, a housemaid was cleaning the bookshelf and she kept those gift items in a “Q + P” manner. Quite doubtful to determine which gift was of Neha and which of Riya.
The next day, both sisters came to know that their gifts are rearranged still, they both seem to be the same. Both the sisters were happy to see that their gifts are the same (irrespective of knowing the price) that whatever sequence the gift is kept in, their hard work and rewards will remain in the same sequence and in unity.
Here, let us assume that a gift “P” was of Rs. 150 (as “P” was the teacher’s favorite student), while “Q” was of Rs. 80. Both the gifts were similar and if we do “P + Q” (the previous sequence), we get 150 + 80 = Rs. 230 which the teacher spent on gifting their students. In the new sequence of the gift, i.e., Q + P = 80 + 150 = Rs. 230, it was still the same.
So, we infer from our above text that P + Q = Q + P. When this situation comes, this is called the Commutative Property in Mathematics. Also, we call it a property of addition in maths.
Therefore, we studied that the sum of two quantities even after exchanging their positions still gives the same result as it was earlier like Q + P gives the same result as P + Q.
Now, we have another scenario of the multiplication of two quantities.
Example of Commutative Property with Multiplication
In ABC International school the rooms are very compact-sized as the school is on road. In the month of March, the school started the admissions process for Class V students and their target for admission was 120 students. People in GK society, and GS In-housing society were very eager to enroll their kids in that school. Luckily, the school got around 144 admissions in a week period.
Since a class can accommodate around 24-30 students, what class teachers did was, adjust 24 students in six sections, so it made it to five sections of Class 5 to accommodate 144 students. Now, we see that the arrangement is 24 * 6.
On 24 March, the school conducted a science olympiad for Class 4 and 5 students. So, in six rows, they made an arrangement in such a way that the first end of each row 12 students of Class 4, and the other end of the row has 12 students of Class 5, which made it to 24 in one row. So, in total, 6 rows had 6 * 24 students.
Now, we see that the arrangement again has 6 * 24 students, i.e., 144 students.
We see that 24 * 6 = 6 * 24 = 144. This is the property of multiplication or the commutative property in Mathematics.
Example of Cadbury Gems having Associative Property
So if you have enjoyed learning about communicative property in story form, let’s jump to another interesting property associative property in a similar manner. You can also learn it in a more fun way by visiting cuemath.com A blue, green, and red Cadbury gems were playing a game. The name of a Blue gem was Riya, Green as Rima, and Red as Rina.
Tina was preparing a cupcake for her kids and asked Riya, Rima, and Rina to spread the cake to make it more delicious.
However, Riya, Rima, and Rina like to get mixed with each other and build a delicious impact on the cake.
So, what they did was, Riya took out 20 grams of its part, Rina took out 10 grams of its part, and Rina about 5 gms of its part (as it was very small and cute in size). They mixed themselves as 20 * 10 * 5.
Tina was in a hurry as her kids started shouting for a cake, so she took an order of 5 * 10 * 20 parts of gems. Now, what she observed was the cake was very delicious.
So, whatever the order is, 20 * 10 * 5 or 5 * 10 * 20, Tina got 1000 gems of gems in her cake and that was delicious too. Thefeore, we understand that (P * Q) * R = P * (Q * R) i.e., (20 * 10) * 5 = 20 * (10 * 5) = 1000. This is called the assocative property in Mathematics.
