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
552
÷
23
. See their work below.

Brianna's work Gavin's work
Step 1: Subtract (20×23)
(
20
×
23
)
from 552 to get 92. Step 1: Subtract (10×23)
(
10
×
23
)
from 552 to get 322.
Step 2: Subtract (4×23)
(
4
×
23
)
from 92 to get 0. Step 2: Subtract (10×23)
(
10
×
23
)
from 322 to get 92.
Step 3: Add partial quotients. Step 3: Subtract (2×23)
(
2
×
23
)
from 92 to get 46.
Step 4: Subtract (2×23)
(
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 analyze Brianna's and Gavin's work, let's review the steps they each took to calculate \( 552 \div 23 \) using partial quotients.

Brianna's Work:

1. Step 1: She subtracted \( 20 \times 23 = 460 \) from 552, which results in \( 552 - 460 = 92 \).
2. Step 2: She subtracted \( 4 \times 23 = 92 \) from 92, which results in \( 92 - 92 = 0 \).
3. Step 3: She adds the partial quotients: \( 20 + 4 = 24 \).

Gavin's Work:

1. Step 1: He subtracted \( 10 \times 23 = 230 \) from 552, which results in \( 552 - 230 = 322 \).
2. Step 2: He again subtracts \( 10 \times 23 = 230 \) from 322, giving \( 322 - 230 = 92 \).
3. Step 3: He then subtracts \( 2 \times 23 = 46 \) from 92, resulting in \( 92 - 46 = 46 \).
4. Step 4: He subtracts \( 2 \times 23 = 46 \) again from 46, which gives \( 46 - 46 = 0 \).
5. Step 5: He adds the partial quotients: \( 10 + 10 + 2 + 2 = 24 \).

Conclusion:

Both Brianna and Gavin calculated the final result as \( 24 \), which is the correct quotient for \( 552 \div 23 \).

Answer: Both Brianna and Gavin correctly calculated the quotient, which is 24. They both arrived at the same final answer using different approaches.