Annabelle and Navene are multiplying (4275)(4372).
Annabelle's Work
(4275)(4372) = 4^2 + 375 + 2 = 4577
Navene's Work:
(4275)(4372) = 42â‹…375â‹…2 = 46710
Is either of them correct? Explain your reasoning.
none are correct
Neither Annabelle nor Navene is correct.
To calculate the product of two numbers, you need to multiply each digit of the first number by each digit of the second number and then sum up the results. Let's go through the correct steps:
Annabelle's Work:
(4275)(4372) = 4 * 4 + 2 * 3 + 7 * 7 + 5 * 2 = 16 + 6 + 49 + 10 = 81
Navene's Work:
(4275)(4372) = 42 * 37 * 52 = 61992
Comparing the correct solutions, we can see that neither Annabelle nor Navene has the correct answer. The correct answer is 61992.
To determine which calculation is correct, let's break down the steps taken by Annabelle and Navene:
Annabelle's Work:
(4275)(4372) = 4^2 + 375 + 2 = 4577
Annabelle seems to have made an error in her calculation. She squared the first digit (4) and then added 375 and 2, resulting in 4577. This method is incorrect because multiplying two numbers together requires multiplying each digit of one number with each digit of the other number, and then adding up the products.
Navene's Work:
(4275)(4372) = 42⋅375⋅2 = 46710
Navene's method is also incorrect. It appears that Navene multiplied the tens digits (42), the ones digit (2), and the thousands digit (375) separately. However, valid multiplication involves multiplying each digit of one number by every digit of the other number and then summing up those products.
To correctly multiply (4275)(4372), we need to use the standard multiplication method like this:
4275
× 4372
---------
12825 (5 times 4272)
+ 34100 (7 times 4272, shifted one place to the left)
+ 21360 (3 times 4272, shifted two places to the left)
+ 17080 (4 times 4272, shifted three places to the left)
-----------
= 18683400
Therefore, the correct answer to (4275)(4372) is 18,683,400. Neither Annabelle's nor Navene's calculation is correct.
What are you doing ????
(4275)(4372) = 18,690,300