Multiples Of 6: Find Numbers Between 15 And 40

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Hey guys! Ever wondered how to figure out which numbers are multiples of something? Today, we're going to break down how to find the multiples of 6 that fall between 15 and 40. It's easier than you think, and by the end of this article, you'll be a pro at spotting these numbers. So, let's jump right in!

Understanding Multiples

Before we dive into the specific problem, let's make sure we all understand what multiples are. A multiple of a number is simply the result you get when you multiply that number by an integer (that's a whole number, like 1, 2, 3, and so on). For example, the multiples of 6 are: 6 (6 x 1), 12 (6 x 2), 18 (6 x 3), 24 (6 x 4), and so on. Think of it like the times table for that number.

Why is understanding multiples important? Well, multiples pop up everywhere in math! From simple arithmetic to more complex algebra and calculus, recognizing multiples can simplify problems and make calculations faster. Plus, it's a fundamental concept that builds the foundation for understanding factors, prime numbers, and many other mathematical ideas. Knowing your multiples helps you see patterns in numbers and solve problems more intuitively. So, understanding multiples isn't just about memorizing a list; it's about grasping a core concept that enhances your mathematical toolkit.

Identifying Multiples of 6

Now, let's focus on multiples of 6. To find them, you just keep adding 6 to the previous multiple. Start with 6 (6 x 1), then add 6 to get 12 (6 x 2), add another 6 to get 18 (6 x 3), and so on. You can also think of it as multiplying 6 by different whole numbers. For example:

  • 6 x 1 = 6
  • 6 x 2 = 12
  • 6 x 3 = 18
  • 6 x 4 = 24
  • 6 x 5 = 30
  • 6 x 6 = 36
  • 6 x 7 = 42

And so on! You could keep going forever, but for our problem, we only need to consider the multiples within a certain range.

Finding multiples of 6 is super useful in everyday situations too! Imagine you're splitting a batch of cookies evenly among 6 friends. Knowing the multiples of 6 helps you quickly figure out how many cookies each person gets if you have 12, 18, 24, or any other multiple of 6 cookies. Or, let's say you're planning a road trip and need to drive 300 miles. If you decide to stop every 60 miles for a break, you can easily calculate how many stops you'll make because 300 is a multiple of 60. So, understanding multiples of 6 isn't just an abstract math skill; it's a practical tool that simplifies calculations in various real-world scenarios.

Finding Multiples of 6 Between 15 and 40

Okay, here's where we get to the main question: How many multiples of 6 are between 15 and 40? This means we're looking for multiples of 6 that are greater than 15 but less than 40.

  1. First, let's list the multiples of 6 that we already know: 6, 12, 18, 24, 30, 36, 42, ...
  2. Now, let's eliminate the ones that are not between 15 and 40. We can get rid of 6 and 12 because they are less than 15. We can also get rid of 42 because it is greater than 40.
  3. That leaves us with: 18, 24, 30, 36.

So, the multiples of 6 between 15 and 40 are 18, 24, 30, and 36. If you count them, you'll see that there are four multiples of 6 in that range.

To make sure we're on the right track, let's verify our answer. We'll take each multiple and divide it by 6 to confirm that we get a whole number:

  • 18 / 6 = 3
  • 24 / 6 = 4
  • 30 / 6 = 5
  • 36 / 6 = 6

Since all these divisions result in whole numbers, we can be confident that 18, 24, 30, and 36 are indeed multiples of 6. And because they all fall between 15 and 40, our solution is correct. Understanding how to find multiples within a given range is a skill that can be applied to various mathematical problems, from simple arithmetic to more complex algebra. So, mastering this concept is definitely worth your time and effort!

Step-by-Step Method

If you want a more structured approach, here's a step-by-step method you can use:

  1. Find the first multiple: Start by finding the smallest multiple of 6 that is greater than 15. In this case, it's 18 (6 x 3).
  2. Find the last multiple: Next, find the largest multiple of 6 that is less than 40. In this case, it's 36 (6 x 6).
  3. List all multiples in the range: Write down all the multiples of 6 between 18 and 36. These are 18, 24, 30, and 36.
  4. Count the multiples: Finally, count how many multiples you have in your list. In this case, there are 4 multiples.

This method is great because it's systematic and helps you avoid missing any multiples. It's especially useful when dealing with larger ranges or when finding multiples of larger numbers. By following these steps, you can confidently identify and count multiples within any given interval. The key is to start by finding the boundaries (the first and last multiples within the range) and then systematically listing all the multiples in between. Remember, multiples are just the result of multiplying a number by an integer, so you're essentially finding the integers that, when multiplied by 6, fall within the specified range. Practice this method with different numbers and ranges, and you'll become a pro at identifying multiples in no time!

Why This Matters

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