Brianna and Gavin used partial quotients to show 552 / 23 see their work below Brianna work step one subtract 20 * 23 from 552 to get 92 step 2 subtract 4 * 23 from 92 to get 0 step 3 add partial quotients Gavin work step one subtract 10 * 23 from 552 to get 322 step two subtract 10 * 23 from 322 to get 92 step 3 subtract 2 * 23 from 92 to get 46 step 4 subtract 2 * 23 from 46 to get zero step step 5 add the partial quotients

Answer 1

Let's review the work of both Brianna and Gavin to see how they applied the partial quotients method to solve \( 552 \div 23 \).

Brianna's Work:

1. Step 1: She subtracted \( 20 \times 23 = 460 \) from 552: \[ 552 - 460 = 92 \]
2. Step 2: Next, she subtracted \( 4 \times 23 = 92 \) from 92: \[ 92 - 92 = 0 \]
3. Partial Quotients: She added the partial quotients: \[ 20 + 4 = 24 \]

Gavin's Work:

1. Step 1: He subtracted \( 10 \times 23 = 230 \) from 552: \[ 552 - 230 = 322 \]
2. Step 2: Then he subtracted \( 10 \times 23 = 230 \) from 322: \[ 322 - 230 = 92 \]
3. Step 3: He subtracted \( 2 \times 23 = 46 \) from 92: \[ 92 - 46 = 46 \]
4. Step 4: Finally, he subtracted \( 2 \times 23 = 46 \) from 46: \[ 46 - 46 = 0 \]
5. Partial Quotients: He added the partial quotients: \[ 10 + 10 + 2 + 2 = 24 \]

Conclusion

Both Brianna and Gavin correctly calculated the quotient of \( 552 \div 23 \) using the partial quotients method, arriving at a final quotient of \( 24 \). Each provided a legitimate approach, demonstrating how partial quotients can vary while still yielding the same result.