Question

Brianna and Gavin used partial quotients to show 552 / 23 see their work below Brianna's work step one subtract 20 * 23 from 552 to get 92 step two subtract 4 * 43 from 92 to get zero step three 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 0 step 5 add the patial quotients which student correctly calculate the quotients explain your answer

Answer 1

To determine which student, Brianna or Gavin, correctly calculated the quotient of 552 divided by 23 using partial quotients, let's break down their calculations step by step.

**Brianna's Work:**
1. Step one: Subtract \(20 \times 23\) from 552.
- \(20 \times 23 = 460\)
- \(552 - 460 = 92\)

2. Step two: Subtract \(4 \times 23\) from 92.
- \(4 \times 23 = 92\)
- \(92 - 92 = 0\)

3. Add the partial quotients:
- Brianna's partial quotients: \(20 + 4 = 24\)

So, Brianna concludes that \(552 / 23 = 24\).

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**Gavin's Work:**
1. Step one: Subtract \(10 \times 23\) from 552.
- \(10 \times 23 = 230\)
- \(552 - 230 = 322\)

2. Step two: Subtract \(10 \times 23\) from 322.
- \(10 \times 23 = 230\)
- \(322 - 230 = 92\)

3. Step three: Subtract \(2 \times 23\) from 92.
- \(2 \times 23 = 46\)
- \(92 - 46 = 46\)

4. Step four: Subtract \(2 \times 23\) from 46.
- \(2 \times 23 = 46\)
- \(46 - 46 = 0\)

5. Add the partial quotients:
- Gavin's partial quotients: \(10 + 10 + 2 + 2 = 24\)

So, Gavin also concludes that \(552 / 23 = 24\).

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**Conclusion:**
Both Brianna and Gavin arrived at the same final quotient of 24, which is correct. Therefore, both students correctly calculated the quotient using the partial quotient method.

The answer to \(552 / 23\) is indeed **24**.