Question

in your journal you explain associative and commutative properties of multiplication to a friend. you told them they would get the same answer everytime they multiplied the numbers in the problem. imagine your neighbor us scrolling social media. your cousin is considering making an in app purchase. your neighbor shows you advertisements.

Answer 1

In my journal, I wanted to explain the associative and commutative properties of multiplication, so I thought I'd use some relatable examples for my friend to understand these concepts better.

Commutative Property of Multiplication: The commutative property states that the order in which you multiply numbers does not affect the product. This means that even if you change the order of the numbers, the result will always be the same. For instance:

• If you multiply 3 and 4, you get 12 (3 × 4 = 12).
• If you switch the numbers and multiply 4 and 3, you still get 12 (4 × 3 = 12).

So, no matter how you arrange the numbers, you will always arrive at the same answer.

Associative Property of Multiplication: Now, the associative property refers to how numbers are grouped when multiplying. It tells us that the way we group numbers in a multiplication expression does not change the product. For example:

• If you have (2 × 3) × 4, you can first multiply 2 and 3 to get 6, and then multiply that by 4 to get 24.
• If you regroup the numbers and calculate 2 × (3 × 4), you would first multiply 3 and 4 to get 12, and then multiply that by 2 to also get 24.

In both cases, regardless of how we group the numbers, we end up with the same product: 24.

Now, let’s tie this into our everyday experiences. Imagine my neighbor scrolling through social media and seeing various advertisements. Just like the commutative property, the ads might come in different orders or placements on their feed, yet they still convey the same message: them trying to advertise products or promote content.

On the other hand, my cousin considering making an in-app purchase could relate to the associative property. Perhaps they have different items they want to buy, but regardless of how they bundle or group their purchases – buying one item first or grouping two items together for a discount – as long as the total remains consistent, the outcome (total price) won’t change.

So, just as multiplication is unaffected by the order or grouping of numbers, our daily decisions, like browsing ads or making purchases, can have underlying rules that ensure consistency despite a changing order or arrangement. Understanding these mathematical properties not only helps in math but can also shed light on patterns and predictability in our daily lives!