Jorge thinks they should use a generic rectangle because there are two terms multiplied by two terms.
Cadel thinks the answer is 8 × 1010 but he cannot explain why.
Lauren thinks they should multiply the like parts. Her answer is 8 × 10021.
Who is correct? Explain why each student is correct or incorrect.
Online, “*” is used to indicate multiplication to avoid confusion with “x” as an unknown.
It would help if you would proofread your work before you post it.
Lacking data. Do you have typos? I don't see "two terms multiplied by two terms".
No
Jorge is correct in saying that using a generic rectangle is a good approach because there are indeed two terms multiplied by two terms. This means we can use the distributive property to break down the problem into simpler calculations.
Cadel's answer of 8 × 1010 is incorrect. It seems like Cadel might have mistakenly multiplied the first digit of 10021, which is 1, with 8, resulting in the answer 8. However, when multiplying two numbers, we need to multiply each digit of one number with each digit of the other number. Therefore, Cadel's answer does not correctly account for all the digits in 10021.
Lauren's answer of 8 × 10021 is also incorrect. While Lauren correctly identifies that the like parts should be multiplied, the answer she provides is not accurate. When multiplying two numbers with multiple digits, we need to consider place value and carry over when necessary. In this case, multiplying 8 with 1 does indeed give us 8, but when we multiply 8 by the remaining digits in 10021, we need to carry over any excess values to the next place value in order to get the correct result.
To find the correct answer, we can use the generic rectangle method by representing the multiplication as:
8 0 0 2 1
× 1 0 0 2 1
___________________________
8 0 0 2 1
+ 0 0 0 2 8
+ 0 0 0 2 8
Adding up all the products, we get 8021, which means the correct answer is 8 × 10021. Thus, Lauren's approach was correct, but she made an error in performing the calculation.