Without dividing, determine if 45,678 is divisible by 3 and explain how you know. Answer Attempt 2 out of 2 \( 45,678 \quad \) divisible by 3 Submit Answer

To determine if a number is divisible by 3, we can use the rule of divisibility for 3, which states that a number is divisible by 3 if the sum of its digits is divisible by 3. Let's apply this rule to the number \( 45,678 \): 1. **Extract the digits**: The digits of \( 45,678 \) are \( 4, 5, 6, 7, \) and \( 8 \). 2. **Calculate the sum of the digits**: \[ 4 + 5 + 6 + 7 + 8 \] 3. **Perform the addition step by step**: - First, add \( 4 + 5 = 9 \). - Next, add \( 9 + 6 = 15 \). - Then, add \( 15 + 7 = 22 \). - Finally, add \( 22 + 8 = 30 \). 4. **Sum of the digits**: The total sum is \( 30 \). 5. **Check if the sum is divisible by 3**: Now, we need to check if \( 30 \) is divisible by \( 3 \): - Calculate \( 30 \div 3 = 10 \), which is a whole number. Since \( 30 \) is divisible by \( 3 \), we conclude that the original number \( 45,678 \) is also divisible by \( 3 \). Thus, \( 45,678 \) is divisible by \( 3 \).