## Podcast Beta

## Questions and Answers

What is the rule to determine if a number is divisible by 3?

In what cases would a number be divisible by 3 but not have a sum of digits divisible by 3?

Which of the following numbers is an exception to the rule of divisibility by 3?

What practical application does divisibility by 3 have in account balances?

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If a person spends $17 on a purchase and has $28 left, what is the total amount spent on the purchase?

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If a person spends $22 on a purchase and has $31 left, what is the total amount spent on the purchase?

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## Study Notes

## Divisibility by 3

Understanding divisibility by 3 is crucial in the field of number theory. It allows us to determine whether a number is divisible by 3 simply by examining its digits.

### The Rule

A number is divisible by 3 if the sum of its digits is divisible by 3. For example, let's consider the number 123. The sum of the digits is 1 + 2 + 3 = 6. Since 6 is divisible by 3, 123 is also divisible by 3.

### Exceptions

However, there is a special case when a number is divisible by 3 but its sum of digits is not. This occurs when the number has the form 3k + 2, where k is an integer. For example, the number 4 is divisible by 3, but the sum of its digits is not.

### Real-World Applications

Divisibility by 3 has practical applications in various fields, such as in the verification of account balances in a check register. If the total of the deposits and withdrawals does not end in the digit 0, 3, 6, or 9, an error has occurred.

### Practice Problem

To practice testing divisibility by 3, try the following problem:

If a person spends $13 on a purchase and has $29 left, what is the total amount of money spent on the purchase?

The person spends $13, leaving $29. The sum of these numbers is $42, which is divisible by 3. Therefore, the total amount of money spent on the purchase is $42.

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## Description

Learn the rule for determining divisibility by 3, where the sum of the digits of a number must be divisible by 3 for the number itself to be divisible by 3. Explore practical applications of this rule, such as in account balance verification, and solve a practice problem to test your understanding.