Wyatt and Allyson were asked to solve a percent problem using the number 13 and 38. Wyatt found 13% of 38 and allyson found 38% of 13. Explain why they both got the same answer. Would this work for other numbers as well? Why or why not?
To understand why both Wyatt and Allyson got the same answer, let's look at how percent problems work. When we find a certain percentage of a number, we multiply the number by the percentage and divide by 100.
Wyatt found 13% of 38:
13% of 38 = (13/100) x 38 = 4.94
Allyson found 38% of 13:
38% of 13 = (38/100) x 13 = 4.94
They both got the same answer of 4.94.
This happens because the process of finding a certain percentage of a number is commutative, meaning the order of the numbers does not affect the result. In mathematical terms, multiplication is commutative. So, multiplying the percentage by the number or multiplying the number by the percentage will give the same outcome.
To illustrate why this works, let’s take a simple example using different numbers.
Let's say we want to find 20% of 50:
20% of 50 = (20/100) x 50 = 10
Now, let's find 50% of 20:
50% of 20 = (50/100) x 20 = 10
As you can see, in both cases, we get the same answer of 10.
In conclusion, Wyatt and Allyson got the same answer because the process of finding a certain percentage of a number is commutative. It is not dependent on the specific numbers used, meaning this concept will work for any numbers.