Problem 32 Determine whether 4227 is divisi... [FREE SOLUTION] (2024)

Expert verified

Before we move forward, it's essential to know how to perform basic addition. When we talk about basic addition, we mean summing up digits. For example, to add the digits of 4227, we break it down:

• First, identify each digit: 4, 2, 2, and 7.
• Next, sum them one by one:
• Start by adding the first two digits: 4 + 2 = 6.
• Then, add the next digit to the previous result: 6 + 2 = 8.
• Finally, add the last digit: 8 + 7 = 15.

So, the sum of the digits in 4227 is 15. Basic addition is easy if you take it one step at a time.

The rule of divisibility by 3 states that a number is divisible by 3 if the sum of its digits is also divisible by 3. This rule helps us determine the divisibility without actually performing long division. After finding the sum of the digits (which is 15 in our case):

• We check if 15 is divisible by 3.
• To do this, simply divide 15 by 3:
• 15 ÷ 3 = 5.
• Since the result is 5, which is an integer with no remainder, 15 is divisible by 3.

Consequently, since 15 is divisible by 3, the original number 4227 is also divisible by 3. This method simplifies the divisibility checking process, utilizing only basic addition and a simple divisibility check.

Following the problem-solving steps makes the process smooth and structured. Let's recap the math steps to determine if 4227 is divisible by 3:

• First, understand the rule: A number is divisible by 3 if the sum of its digits is divisible by 3.
• Identify the digits: For 4227, the digits are 4, 2, 2, and 7.
• Calculate the sum of the digits: Add them step by step:
• 4 + 2 = 6,
• 6 + 2 = 8,
• 8 + 7 = 15.
• Check the sum for divisibility by 3: Since 15 ÷ 3 = 5 with no remainder, 15 is divisible by 3.

Thus, since the sum of the digits (15) is divisible by 3, the number 4227 is indeed divisible by 3. By following these clear and structured math steps, you can easily tackle similar problems in the future!