Brianna and Gavin use partial quotients to show 552 / 23 see their work below Brianna work step one subtract 20 * 23 from 552 to get 92 except to subtract 4 * 23 from 92° 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 922 step 3 subtract 2 * 23 from 92 to get 46 step 4 subtract two times 23 from 46 to get zero step five at the partial quotients which students correctly calculated the quotient explain your work

Answer 1

To determine who correctly calculated the quotient of 552 divided by 23 using partial quotients, let’s analyze both Brianna's and Gavin's work.

Brianna's Work:

1. Step 1: 552 - (20 * 23)
   • 20 * 23 = 460
   • 552 - 460 = 92
2. Step 2: 92 - (4 * 23)
   • 4 * 23 = 92
   • 92 - 92 = 0

Total Partial Quotients:

• 20 + 4 = 24

Gavin's Work:

1. Step 1: 552 - (10 * 23)
   • 10 * 23 = 230
   • 552 - 230 = 322
2. Step 2: 322 - (10 * 23)
   • 10 * 23 = 230
   • 322 - 230 = 92
3. Step 3: 92 - (2 * 23)
   • 2 * 23 = 46
   • 92 - 46 = 46
4. Step 4: 46 - (2 * 23)
   • 2 * 23 = 46
   • 46 - 46 = 0

Total Partial Quotients:

• 10 + 10 + 2 + 2 = 24

Conclusion:

Both students arrived at a total of 24 when adding their partial quotients:

• Brianna's partial quotients: 20 + 4 = 24
• Gavin's partial quotients: 10 + 10 + 2 + 2 = 24

Thus, both methods validly led to the conclusion that \( 552 \div 23 = 24 \).

Therefore, both students correctly calculated the quotient.