Wyatt and Allyson were asked to solve a percent problem using the numbers 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?
really?
Did you write out the calculations and notice something?
hint:
what is 13x38 and 38x13 ?
Inverse property of multiplication...
Wyatt found 13% of 38, which means he calculated 13% of the whole quantity of 38. This can be done by multiplying 38 by 0.13.
Allyson, on the other hand, found 38% of 13, which means she calculated 38% of the whole quantity of 13. This can be done by multiplying 13 by 0.38.
If we calculate both of these expressions, we will see that the result is the same:
Wyatt: 38 * 0.13 = 4.94
Allyson: 13 * 0.38 = 4.94
The reason why they both got the same answer is that percent calculations can be commutative. This means that when you calculate a percentage of a number, it gives you the same result whether you find the percentage first and then multiply, or multiply first and then find the percentage.
In this case, 13% of 38 is the same as 38% of 13 because multiplying 38 by 0.13 gives the same result as multiplying 13 by 0.38.
This concept works for other numbers as well. As long as you have two numbers and you calculate a percentage of one number or the other, you will get the same result regardless of the order in which the multiplication and percentage calculations are performed.