Question

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 step 2 subtract 4 * 23 from 92 to get 0 step 3 add partial quotients Gavin work step 1 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 5 add the partial quotients which student correctly calculated the quotation explain your answer

Answer 1

To evaluate Brianna's and Gavin's work using partial quotients, let's break down their steps and see who calculated the correct quotient for \(552 \div 23\).

**Brianna's Work:**
1. Step 1: Subtract \(20 \times 23\) from \(552\):
\[
552 - 460 = 92
\]
(Here, she correctly recognizes that \(20 \times 23 = 460\).)

2. Step 2: Subtract \(4 \times 23\) from \(92\):
\[
92 - 92 = 0
\]
(She correctly identifies that \(4 \times 23 = 92\).)

3. Partial Quotients: \(20 + 4 = 24\)

**Gavin's Work:**
1. Step 1: Subtract \(10 \times 23\) from \(552\):
\[
552 - 230 = 322
\]
(He correctly calculates \(10 \times 23 = 230\).)

2. Step 2: Subtract \(10 \times 23\) from \(322\):
\[
322 - 230 = 92
\]
(Again, he correctly identifies that \(10 \times 23 = 230\).)

3. Step 3: Subtract \(2 \times 23\) from \(92\):
\[
92 - 46 = 46
\]
(He correctly identifies that \(2 \times 23 = 46\).)

4. Step 4: Subtract \(2 \times 23\) from \(46\):
\[
46 - 46 = 0
\]
(He correctly identifies that \(2 \times 23 = 46\).)

5. Partial Quotients: \(10 + 10 + 2 + 2 = 34\)

### Comparison of Quotients
- Brianna found a quotient of \(24\).
- Gavin found a quotient of \(34\).

### Calculation Check
Now let's calculate \(552 \div 23\) directly to verify:

\[
552 \div 23 = 24
\]

### Conclusion
**Brianna's calculations are correct, and Gavin's calculations are incorrect.** The final quotient is \(24\), which Brianna reached correctly through the partial quotients method.