If 56*72is Divisible By 11 The Possible Digit Which Can Replace *is
Introduction
In mathematics, divisibility rules are essential tools for determining whether a number is divisible by a specific divisor. One of the most commonly used divisibility rules is the rule for divisibility by 11. This rule states that a number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or a multiple of 11. In this article, we will explore the concept of divisibility by 11 and use it to find the possible digit that can replace the asterisk () in the number 5672.
Divisibility by 11: A Brief Overview
Divisibility by 11 is a fundamental concept in mathematics that has numerous applications in various fields, including arithmetic, algebra, and number theory. The rule for divisibility by 11 is based on the concept of alternating sums of digits. To determine whether a number is divisible by 11, we need to calculate the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions.
For example, consider the number 123456. To determine whether this number is divisible by 11, we need to calculate the difference between the sum of the digits in the odd positions (1 + 3 + 5) and the sum of the digits in the even positions (2 + 4 + 6). If the difference is 0 or a multiple of 11, then the number is divisible by 11.
Applying the Divisibility Rule to 56*72
Now, let's apply the divisibility rule to the number 56*72. To determine whether this number is divisible by 11, we need to calculate the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions.
The sum of the digits in the odd positions is 5 + 7 + * = 12 + *. The sum of the digits in the even positions is 6 + 2 = 8.
Calculating the Difference
To determine whether 56*72 is divisible by 11, we need to calculate the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions.
The difference is (12 + *) - 8 = 4 + *.
Finding the Possible Digit
Since 56*72 is divisible by 11, the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions must be 0 or a multiple of 11. Therefore, we can set up the equation 4 + * = 0 or a multiple of 11.
Solving the Equation
To solve the equation 4 + * = 0 or a multiple of 11, we need to find the possible values of *. Since the difference is 4 + *, we can add 4 to both sides of the equation to get * = -4 or a multiple of 11 minus 4.
Finding the Possible Digit
Since the digit * must be a single digit, we can ignore the negative value -4. Therefore, we need to find the possible values of * that are multiples of 11 minus 4.
Possible Values of *
The possible values of * that are multiples of 11 minus 4 are 7, 18, and 29. However, since the digit * must be a single digit, we can ignore the values 18 and 29.
Conclusion
In conclusion, the possible digit that can replace the asterisk () in the number 5672 is 7.
Frequently Asked Questions
Q: What is the rule for divisibility by 11?
A: The rule for divisibility by 11 states that a number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or a multiple of 11.
Q: How do I determine whether a number is divisible by 11?
A: To determine whether a number is divisible by 11, you need to calculate the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions. If the difference is 0 or a multiple of 11, then the number is divisible by 11.
Q: What is the possible digit that can replace the asterisk () in the number 5672?
A: The possible digit that can replace the asterisk () in the number 5672 is 7.
Q: Why is the digit * a single digit?
A: The digit * is a single digit because it is a placeholder for a single digit in the number 56*72.
Q: What is the significance of the divisibility rule for 11?
A: The divisibility rule for 11 is a fundamental concept in mathematics that has numerous applications in various fields, including arithmetic, algebra, and number theory.
Q: How do I apply the divisibility rule to a number?
A: To apply the divisibility rule to a number, you need to calculate the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions. If the difference is 0 or a multiple of 11, then the number is divisible by 11.
Q: What are the possible values of * that are multiples of 11 minus 4?
A: The possible values of * that are multiples of 11 minus 4 are 7, 18, and 29. However, since the digit * must be a single digit, we can ignore the values 18 and 29.
Q: Why is the value 18 ignored?
A: The value 18 is ignored because it is not a single digit.
Q: Why is the value 29 ignored?
A: The value 29 is ignored because it is not a single digit.
Q: What is the conclusion of the article?
A: The conclusion of the article is that the possible digit that can replace the asterisk () in the number 5672 is 7.
Introduction
In our previous article, we explored the concept of divisibility by 11 and used it to find the possible digit that can replace the asterisk () in the number 5672. In this article, we will continue to answer more questions related to divisibility by 11.
Q&A
Q: What is the rule for divisibility by 11?
A: The rule for divisibility by 11 states that a number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or a multiple of 11.
Q: How do I determine whether a number is divisible by 11?
A: To determine whether a number is divisible by 11, you need to calculate the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions. If the difference is 0 or a multiple of 11, then the number is divisible by 11.
Q: What is the significance of the divisibility rule for 11?
A: The divisibility rule for 11 is a fundamental concept in mathematics that has numerous applications in various fields, including arithmetic, algebra, and number theory.
Q: How do I apply the divisibility rule to a number?
A: To apply the divisibility rule to a number, you need to calculate the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions. If the difference is 0 or a multiple of 11, then the number is divisible by 11.
Q: What are the possible values of * that are multiples of 11 minus 4?
A: The possible values of * that are multiples of 11 minus 4 are 7, 18, and 29. However, since the digit * must be a single digit, we can ignore the values 18 and 29.
Q: Why is the value 18 ignored?
A: The value 18 is ignored because it is not a single digit.
Q: Why is the value 29 ignored?
A: The value 29 is ignored because it is not a single digit.
Q: What is the conclusion of the article?
A: The conclusion of the article is that the possible digit that can replace the asterisk () in the number 5672 is 7.
Q: Can you provide more examples of numbers that are divisible by 11?
A: Yes, here are a few examples of numbers that are divisible by 11:
- 121: The sum of the digits in the odd positions is 1 + 1 = 2, and the sum of the digits in the even positions is 2. The difference is 2 - 2 = 0, which is a multiple of 11.
- 242: The sum of the digits in the odd positions is 2 + 2 = 4, and the sum of the digits in the even positions is 4. The difference is 4 - 4 = 0, which is a multiple of 11.
- 363: The sum of the digits in the odd positions is 3 + 3 = 6, and the sum of the digits in the even positions is 6. The difference is 6 - 6 = 0, which is a multiple of 11.
Q: Can you provide more examples of numbers that are not divisible by 11?
A: Yes, here are a few examples of numbers that are not divisible by 11:
- 123: The sum of the digits in the odd positions is 1 + 3 = 4, and the sum of the digits in the even positions is 2. The difference is 4 - 2 = 2, which is not a multiple of 11.
- 246: The sum of the digits in the odd positions is 2 + 6 = 8, and the sum of the digits in the even positions is 4. The difference is 8 - 4 = 4, which is not a multiple of 11.
- 369: The sum of the digits in the odd positions is 3 + 9 = 12, and the sum of the digits in the even positions is 6. The difference is 12 - 6 = 6, which is not a multiple of 11.
Q: Can you provide more information about the divisibility rule for 11?
A: Yes, the divisibility rule for 11 states that a number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or a multiple of 11. This rule can be applied to any number, regardless of its length or complexity.
Q: Can you provide more information about the significance of the divisibility rule for 11?
A: Yes, the divisibility rule for 11 is a fundamental concept in mathematics that has numerous applications in various fields, including arithmetic, algebra, and number theory. It is used to determine whether a number is divisible by 11, which is an important concept in mathematics.
Q: Can you provide more information about how to apply the divisibility rule to a number?
A: Yes, to apply the divisibility rule to a number, you need to calculate the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions. If the difference is 0 or a multiple of 11, then the number is divisible by 11.
Conclusion
In conclusion, the divisibility rule for 11 is a fundamental concept in mathematics that has numerous applications in various fields, including arithmetic, algebra, and number theory. It is used to determine whether a number is divisible by 11, which is an important concept in mathematics. We hope that this article has provided you with a better understanding of the divisibility rule for 11 and how to apply it to numbers.