Answer The Questions Below. Be Sure To Mark All Answers That Apply.$[ \begin{tabular}{|l|c|c|c|c|} \hline & & 982 & 877 & 282 \ \hline (a) Which Numbers Are Divisible By 9? & □ \square □ & □ \square □ & □ \square □ & □ \square □ \ \hline (b) Which

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Introduction

In mathematics, divisibility is a fundamental concept that deals with the relationship between numbers and their factors. One of the most interesting properties of numbers is their divisibility by 9. In this article, we will explore the concept of divisibility by 9 and answer the questions provided.

Divisibility by 9

What is Divisibility by 9?

Divisibility by 9 is a property of numbers that states a number is divisible by 9 if the sum of its digits is also divisible by 9. This means that if we take the individual digits of a number and add them together, the result should be a multiple of 9 for the original number to be divisible by 9.

Examples of Divisibility by 9

Let's consider some examples to illustrate this concept:

  • 18: 1 + 8 = 9 (divisible by 9)
  • 27: 2 + 7 = 9 (divisible by 9)
  • 36: 3 + 6 = 9 (divisible by 9)
  • 45: 4 + 5 = 9 (divisible by 9)

Answering the Questions

Now that we have a good understanding of divisibility by 9, let's answer the questions provided.

(a) Which numbers are divisible by 9?

To determine which numbers are divisible by 9, we need to check if the sum of their digits is also divisible by 9.

  • 982: 9 + 8 + 2 = 19 (not divisible by 9)
  • 877: 8 + 7 + 7 = 22 (not divisible by 9)
  • 282: 2 + 8 + 2 = 12 (not divisible by 9)

None of the numbers 982, 877, or 282 are divisible by 9.

Conclusion

In conclusion, divisibility by 9 is a property of numbers that states a number is divisible by 9 if the sum of its digits is also divisible by 9. We have explored this concept and answered the questions provided. None of the numbers 982, 877, or 282 are divisible by 9.

References

Discussion

  • What are some other properties of numbers that are similar to divisibility by 9?
  • Can you think of any real-world applications of divisibility by 9?
  • How can we use divisibility by 9 to solve problems in mathematics and other fields?
    Q&A: Divisibility by 9 ==========================

Introduction

In our previous article, we explored the concept of divisibility by 9 and answered the questions provided. In this article, we will continue to delve deeper into the world of divisibility by 9 and provide answers to some of the most frequently asked questions.

Q&A

Q: What is the rule for divisibility by 9?

A: The rule for divisibility by 9 states that a number is divisible by 9 if the sum of its digits is also divisible by 9.

Q: How do I determine if a number is divisible by 9?

A: To determine if a number is divisible by 9, you need to add up the individual digits of the number and check if the result is a multiple of 9.

Q: What are some examples of numbers that are divisible by 9?

A: Some examples of numbers that are divisible by 9 include:

  • 18: 1 + 8 = 9 (divisible by 9)
  • 27: 2 + 7 = 9 (divisible by 9)
  • 36: 3 + 6 = 9 (divisible by 9)
  • 45: 4 + 5 = 9 (divisible by 9)

Q: What are some examples of numbers that are not divisible by 9?

A: Some examples of numbers that are not divisible by 9 include:

  • 982: 9 + 8 + 2 = 19 (not divisible by 9)
  • 877: 8 + 7 + 7 = 22 (not divisible by 9)
  • 282: 2 + 8 + 2 = 12 (not divisible by 9)

Q: Can you give me a formula to determine if a number is divisible by 9?

A: Yes, the formula to determine if a number is divisible by 9 is:

(Σd) mod 9 = 0

where Σd is the sum of the digits of the number and mod is the modulo operator.

Q: How can I use divisibility by 9 to solve problems in mathematics and other fields?

A: Divisibility by 9 can be used to solve problems in mathematics and other fields in a variety of ways. For example, you can use it to:

  • Check if a number is a multiple of 9
  • Find the remainder when a number is divided by 9
  • Determine if a number is a perfect square or a perfect cube
  • Solve problems involving modular arithmetic

Conclusion

In conclusion, divisibility by 9 is a fundamental concept in mathematics that has many practical applications. We have provided answers to some of the most frequently asked questions about divisibility by 9 and hope that this article has been helpful in your understanding of this concept.

References

Discussion

  • What are some other properties of numbers that are similar to divisibility by 9?
  • Can you think of any real-world applications of divisibility by 9?
  • How can we use divisibility by 9 to solve problems in mathematics and other fields?

Additional Resources