Understanding Multiples of 7

Oct 13, 2025 by miodeya.com 134 views

Introduction

When dealing with probability, it's essential to understand the concept of chance and the likelihood of an event occurring. In this case, we're asked to find the probability that a randomly chosen two-digit number is a multiple of 7. To approach this problem, we need to consider the total number of two-digit numbers and the number of multiples of 7 within that range.

Understanding Multiples of 7

Multiples of 7 are numbers that can be divided by 7 without leaving a remainder. For example, 14, 21, 28, and 35 are all multiples of 7. To find the number of multiples of 7 within a given range, we can use the formula:

Number of multiples = (Upper limit - Lower limit) / 7 + 1

Finding the Number of Multiples of 7 in the Two-Digit Range

The two-digit range includes numbers from 10 to 99. To find the number of multiples of 7 within this range, we can use the formula:

Number of multiples = (99 - 14) / 7 + 1 = 85 / 7 + 1 = 12 + 1 = 13

However, we need to consider that the first multiple of 7 in the two-digit range is 14, not 0. Therefore, we need to subtract 1 from the result:

Number of multiples = 13 - 1 = 12

Calculating the Probability

To calculate the probability, we need to divide the number of multiples of 7 by the total number of two-digit numbers. There are 90 two-digit numbers in total (from 10 to 99).

Probability = Number of multiples / Total number of two-digit numbers = 12 / 90 = 2 / 15

Conclusion

The probability that a randomly chosen two-digit number is a multiple of 7 is 2/15. This means that out of every 15 two-digit numbers, 2 will be multiples of 7.

Comparison with the Given Options

Let's compare our result with the given options:

A. 13/90 B. 12/90 C. 11/90 D. 1/9

Our result is 2/15, which is equivalent to 12/90. Therefore, the correct answer is:

B. 12/90

Final Thoughts

Probability is a fundamental concept in mathematics, and understanding it is crucial for making informed decisions in various aspects of life. By applying the concept of probability to real-world scenarios, we can make more accurate predictions and take calculated risks. In this case, we used the formula for finding the number of multiples of 7 and calculated the probability to arrive at the correct answer.

Introduction

In our previous article, we explored the concept of probability and how it applies to the scenario of choosing a two-digit number at random. We calculated the probability that the chosen number is a multiple of 7 and arrived at the answer 2/15. However, we received several questions from readers who wanted to know more about the topic. In this article, we'll address some of the most frequently asked questions and provide additional insights into the concept of probability.

Q&A

Q: What is the formula for finding the number of multiples of a number within a given range?

A: The formula for finding the number of multiples of a number within a given range is:

Number of multiples = (Upper limit - Lower limit) / Number + 1

For example, to find the number of multiples of 7 within the range 10 to 99, we would use the formula:

Number of multiples = (99 - 14) / 7 + 1 = 85 / 7 + 1 = 12 + 1 = 13

However, we need to consider that the first multiple of 7 in the two-digit range is 14, not 0. Therefore, we need to subtract 1 from the result:

Number of multiples = 13 - 1 = 12

Q: Why do we need to subtract 1 from the result when finding the number of multiples of 7?

A: We need to subtract 1 from the result because the first multiple of 7 in the two-digit range is 14, not 0. By subtracting 1, we ensure that we're only counting the multiples of 7 within the two-digit range.

Q: What is the difference between the probability of an event and the probability of a number being a multiple of another number?

A: The probability of an event is the likelihood of that event occurring, whereas the probability of a number being a multiple of another number is a specific type of probability that deals with the number of multiples of a number within a given range.

Q: Can you provide more examples of finding the number of multiples of a number within a given range?

A: Here are a few examples:

To find the number of multiples of 5 within the range 10 to 100, we would use the formula: Number of multiples = (100 - 10) / 5 + 1 = 90 / 5 + 1 = 18 + 1 = 19
To find the number of multiples of 3 within the range 10 to 99, we would use the formula: Number of multiples = (99 - 12) / 3 + 1 = 87 / 3 + 1 = 29 + 1 = 30

Q: How do we calculate the probability of a number being a multiple of another number?

A: To calculate the probability of a number being a multiple of another number, we need to divide the number of multiples of that number by the total number of numbers within the given range.

Probability = Number of multiples / Total number of numbers = 12 / 90 = 2 / 15

Conclusion

In this article, we addressed some of the most frequently asked questions about the concept of probability and how it applies to the scenario of choosing a two-digit number at random. We provided additional insights into the formula for finding the number of multiples of a number within a given range and calculated the probability of a number being a multiple of another number. We hope that this article has been helpful in clarifying any doubts you may have had about the topic.