There are two parts to the following question. First, answer part A. Then, answer part B.

Question

Brianna and Gavin used partial quotients to show 552÷23
. See their work below.

Brianna's work Gavin's work
Step 1: Subtract (20×23)
from 552 to get 92. Step 1: Subtract (10×23)
from 552 to get 322.
Step 2: Subtract (4×23)
from 92 to get 0. Step 2: Subtract (10×23)
from 322 to get 92.
Step 3: Add partial quotients. Step 3: Subtract (2×23)
from 92 to get 46.
Step 4: Subtract (2×23)
from 46 to get 0.
Step 5: Add the partial quotients.




Part A
Which student(s) correctly calculated the quotient? Explain your answer.

(2 points)

Answer 1

To determine which student(s) correctly calculated the quotient for \( 552 \div 23 \), let's evaluate the work done by Brianna and Gavin.

Brianna's Work:

1. She subtracted \( 20 \times 23 = 460 \) from \( 552 \) to get \( 552 - 460 = 92 \).
2. Next, she subtracted \( 4 \times 23 = 92 \) from \( 92 \), resulting in \( 92 - 92 = 0 \).
3. Finally, her partial quotients were \( 20 + 4 = 24 \).

Gavin's Work:

1. He subtracted \( 10 \times 23 = 230 \) from \( 552 \) to get \( 552 - 230 = 322 \).
2. Then, he subtracted \( 10 \times 23 = 230 \) from \( 322 \), giving \( 322 - 230 = 92 \).
3. Next, he subtracted \( 2 \times 23 = 46 \) from \( 92 \), resulting in \( 92 - 46 = 46 \).
4. He subtracted \( 2 \times 23 = 46 \) from \( 46 \), yielding \( 46 - 46 = 0 \).
5. Adding his partial quotients, he has \( 10 + 10 + 2 + 2 = 24 \).

Conclusion: Both Brianna and Gavin calculated their partial quotients in different ways, but ultimately both arrived at the total quotient of \( 24 \). This means that both students correctly calculated the quotient of \( 552 \div 23 \) as \( 24 \).

So, both Brianna and Gavin correctly calculated the quotient.