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 divide 23. see their work below

Brianna's work                                                              Gavin's work 
Step 1: Subtract ( 20 x 23 )                                     Step 1: Subtract ( 10 x 23 ) 
from 552 to get 92.                                                  from 552 to get 322.
______________________                                  ________________________
Step 2: Subtract ( 4 x 23 )                                    Step 2: Subtract ( 10 x 23 )
from 92 to get 0.                                                   from 322 to get 92. 
______________________                               ____________________________
Step 3 : Add partial quotients                           Step 3: Subtract (2 x 23) from
                                                                          92 to get 46.
                                                                        
                                                                       ______________________________
                                                                           Step 4: Subtract ( 2 x 23 ) from 46 
                                                                           to get 0.

Bot GPT 4-o mini · Answer

### Part A Brianna and Gavin both used the partial quotients method to compute $552 \div 23$. Let’s summarize each of their steps and understand their calculations. **Brianna's Work:** 1. **Step 1:** She subtracted $20 \times 23$ from $552$: $$ 552 - 460 = 92 $$ 2. **Step 2:** She then subtracted $4 \times 23$ from $92$: $$ 92 - 92 = 0 $$ 3. **Step 3:** She adds her partial quotients: $$ 20 + 4 = 24 $$ **Conclusion:** According to Brianna’s calculation, $552 \div 23 = 24$. **Gavin's Work:** 1. **Step 1:** He subtracted $10 \times 23$ from $552$: $$ 552 - 230 = 322 $$ 2. **Step 2:** He then subtracted another $10 \times 23$ from $322$: $$ 322 - 230 = 92 $$ 3. **Step 3:** Next, he subtracted $2 \times 23$ from $92$: $$ 92 - 46 = 46 $$ 4. **Step 4:** Finally, he subtracted $2 \times 23$ from $46$: $$ 46 - 46 = 0 $$ 5. **Step 5:** He adds his partial quotients: $$ 10 + 10 + 2 + 2 = 24 $$ **Conclusion:** According to Gavin’s calculation, $552 \div 23 = 24$. Both Brianna and Gavin reach the same result of $24$. ### Part B Both methods correctly demonstrated that $552 \div 23 = 24$, although they used different partial quotients in their calculations. 1. **A key difference** in their methods is the choice of which multiples of $23$ to consider as they subtract from $552$. Brianna used bigger chunks (like $20 \times 23$), while Gavin used smaller chunks (like $10 \times 23$). 2. **The efficiency** of each method can vary based on how quickly the divisor is subtracted from the dividend. Brianna's method led to a more straightforward and quicker reduction in her second step since she dealt with a larger subtraction initially. In conclusion, both approaches yield the correct quotient of $24$, demonstrating the flexibility of the partial quotients method in division.