(d) Does the calculation \( 394 \times 582=229,408 \) have an error based on casting out nines? Select the correct choice below and fill in the answer box within your choice. A. The calculation checks using casting out nines. The remainder is \( \square \). B. Casting out nines shows there is an error. The given answer has a remainder of \( \square \), but casting out nines gives a remainder of \( \square \). The correct answer is

To check the calculation using casting out nines, first, sum the digits of the numbers involved. For \(394\), the digits sum to \(3 + 9 + 4 = 16\) which further simplifies to \(1 + 6 = 7\). For \(582\), the digits sum to \(5 + 8 + 2 = 15\) which simplifies to \(1 + 5 = 6\). Now, calculate the product’s digit sum \(229,408\): \(2 + 2 + 9 + 4 + 0 + 8 = 25\) which simplifies to \(2 + 5 = 7\). The combined remainder for the operands is \(7 \times 6 = 42\) which simplifies to \(4 + 2 = 6\). Now we see that \(7\) (from \(394\)) and \(6\) (from \(582\)) gives a product remainder of \(6\) but the computed answer gives \(7\), indicating an error in the calculation. So, the final options would appear like this: B. Casting out nines shows there is an error. The given answer has a remainder of \(7\), but casting out nines gives a remainder of \(6\). The correct answer is \(229,200\) (the correct product of \(394 \times 582\)).