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Questions and Answers
What is the rule to determine if a number is divisible by 3?
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?
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?
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?
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?
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?
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.
