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Rihanna 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

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To calculate \( 552 \div 23 \) using partial quotients, let's break down both Rihanna's and Gavin's work to see how each arrived at their results and verify the calculations.

Rihanna's Work:

  1. Step 1: She subtracts \( 20 \times 23 \) from \( 552 \): \[ 552 - (20 \times 23) = 552 - 460 = 92 \] (This part is correct.)

  2. Step 2: She then subtracts \( 4 \times 23 \) from \( 92 \): \[ 92 - (4 \times 23) = 92 - 92 = 0 \] (This part is also correct, and she reaches zero.)

  3. Step 3: Now, we add the partial quotients: \[ 20 + 4 = 24 \] Thus, Rihanna's quotient is 24.

Gavin's Work:

  1. Step 1: He subtracts \( 10 \times 23 \) from \( 552 \): \[ 552 - (10 \times 23) = 552 - 230 = 322 \] (This is correct.)

  2. Step 2: He subtracts \( 10 \times 23 \) from \( 322 \): \[ 322 - (10 \times 23) = 322 - 230 = 92 \] (This is also correct.)

  3. Step 3: He subtracts \( 2 \times 23 \) from \( 92 \): \[ 92 - (2 \times 23) = 92 - 46 = 46 \] (This part is correct.)

  4. Step 4: Subtracts \( 2 \times 23 \) from \( 46 \): \[ 46 - (2 \times 23) = 46 - 46 = 0 \] (This part is also correct.)

  5. Step 5: Now, let's sum the partial quotients: \[ 10 + 10 + 2 + 2 = 24 \] Thus, Gavin's quotient is also 24.

Conclusion:

Both Rihanna and Gavin correctly calculated the quotient of \( 552 \div 23 \) to be 24.

The work done by both is valid, as they each used subtraction to progressively find how many times \( 23 \) can be subtracted from \( 552 \) until reaching zero, hence confirming the correctness of the division. The method of partial quotients allows for flexible division, and both students executed it successfully.