Does the calculation \( 78,604-3514=74,090 \) have an error based on casting out nines? elect the correct choice below and fill in the answer box within your choice. A. The calculation checks using casting out nines. The remainder is 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 \( 78,604 - 3,514 = 74,090 \) using casting out nines, we follow these steps: 1. **Calculate the digital root (or remainder when divided by 9) of each number:** - For \( 78,604 \): - Sum of digits: \( 7 + 8 + 6 + 0 + 4 = 25 \) - Sum of digits of \( 25 \): \( 2 + 5 = 7 \) - Remainder: \( 7 \) - For \( 3,514 \): - Sum of digits: \( 3 + 5 + 1 + 4 = 13 \) - Sum of digits of \( 13 \): \( 1 + 3 = 4 \) - Remainder: \( 4 \) - For \( 74,090 \): - Sum of digits: \( 7 + 4 + 0 + 9 + 0 = 20 \) - Sum of digits of \( 20 \): \( 2 + 0 = 2 \) - Remainder: \( 2 \) 2. **Perform the subtraction and check the remainder:** - Calculate the expected remainder from the subtraction: - Remainder of \( 78,604 - 3,514 \) is \( 7 - 4 = 3 \). 3. **Compare the remainders:** - The calculated remainder from the subtraction is \( 3 \). - The remainder of the given answer \( 74,090 \) is \( 2 \). Since the remainders do not match, there is an error in the calculation. Now, let's fill in the answer based on the findings: B. Casting out nines shows there is an error. The given answer has a remainder of \( 2 \), but casting out nines gives a remainder of \( 3 \). The correct answer is \( 78,604 - 3,514 = 75,090 \) (since \( 78,604 - 3,514 = 75,090 \) gives a remainder of \( 3 \)).