Which Equation Best Shows That 45 Is A Multiple Of 15?Choose 1 Answer:A. $45 \div 15 = 3$B. $45 - 15 = 30$C. $45 \times 3 = 135$D. $48 = 45 + 3$

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In mathematics, a multiple of a number is the product of that number and an integer. For example, 15 is a multiple of 3 because 3 × 5 = 15. In this article, we will explore which equation best shows that 45 is a multiple of 15.

What are Multiples?

A multiple of a number is the result of multiplying that number by an integer. For example, 3, 6, 9, 12, and 15 are all multiples of 3 because they can be expressed as 3 multiplied by an integer. In the same way, 45 is a multiple of 15 because it can be expressed as 15 multiplied by an integer.

Choosing the Correct Equation

To determine which equation best shows that 45 is a multiple of 15, we need to examine each option carefully.

Option A: 45÷15=345 \div 15 = 3

This equation shows that 45 divided by 15 equals 3. However, this equation does not explicitly show that 45 is a multiple of 15. Instead, it shows that 15 is a factor of 45.

Option B: 45−15=3045 - 15 = 30

This equation shows that 45 minus 15 equals 30. However, this equation does not show that 45 is a multiple of 15. Instead, it shows that 45 is 30 more than 15.

Option C: 45×3=13545 \times 3 = 135

This equation shows that 45 multiplied by 3 equals 135. However, this equation does not show that 45 is a multiple of 15. Instead, it shows that 45 is a multiple of 3.

Option D: 48=45+348 = 45 + 3

This equation shows that 48 equals 45 plus 3. However, this equation does not show that 45 is a multiple of 15. Instead, it shows that 48 is 3 more than 45.

The Correct Equation

After examining each option, we can see that none of the equations explicitly show that 45 is a multiple of 15. However, we can use the definition of a multiple to find the correct equation.

A multiple of a number is the product of that number and an integer. Therefore, if 45 is a multiple of 15, it must be the product of 15 and an integer.

Let's examine each option again:

  • Option A: 45÷15=345 \div 15 = 3
  • Option B: 45−15=3045 - 15 = 30
  • Option C: 45×3=13545 \times 3 = 135
  • Option D: 48=45+348 = 45 + 3

We can see that option C shows that 45 multiplied by 3 equals 135. However, this equation does not explicitly show that 45 is a multiple of 15. Instead, it shows that 45 is a multiple of 3.

But what if we multiply 15 by 3? We get:

15×3=4515 \times 3 = 45

This equation shows that 45 is the product of 15 and 3. Therefore, 45 is a multiple of 15.

Conclusion

In conclusion, the correct equation that shows that 45 is a multiple of 15 is:

15×3=4515 \times 3 = 45

This equation explicitly shows that 45 is the product of 15 and 3. Therefore, 45 is a multiple of 15.

Key Takeaways

  • A multiple of a number is the product of that number and an integer.
  • To show that 45 is a multiple of 15, we need to find an equation that explicitly shows that 45 is the product of 15 and an integer.
  • The correct equation is 15×3=4515 \times 3 = 45.

Additional Resources

For more information on multiples and factors, check out the following resources:

  • Khan Academy: Multiples and Factors
  • Math Is Fun: Multiples and Factors
  • Wikipedia: Multiple (mathematics)

Final Thoughts

In this article, we will answer some of the most frequently asked questions about multiples and factors in mathematics.

Q: What is a multiple of a number?

A: A multiple of a number is the product of that number and an integer. For example, 3, 6, 9, 12, and 15 are all multiples of 3 because they can be expressed as 3 multiplied by an integer.

Q: How do I find the multiples of a number?

A: To find the multiples of a number, you can multiply that number by an integer. For example, to find the multiples of 3, you can multiply 3 by 1, 2, 3, 4, and so on.

Q: What is a factor of a number?

A: A factor of a number is an integer that divides that number without leaving a remainder. For example, 3 is a factor of 6 because 6 ÷ 3 = 2, and 2 is an integer.

Q: How do I find the factors of a number?

A: To find the factors of a number, you can list all the integers that divide that number without leaving a remainder. For example, the factors of 6 are 1, 2, 3, and 6.

Q: What is the difference between a multiple and a factor?

A: A multiple of a number is the product of that number and an integer, while a factor of a number is an integer that divides that number without leaving a remainder.

Q: Can a number be both a multiple and a factor of another number?

A: Yes, a number can be both a multiple and a factor of another number. For example, 3 is both a multiple and a factor of 6.

Q: How do I determine if a number is a multiple of another number?

A: To determine if a number is a multiple of another number, you can divide the first number by the second number and check if the result is an integer.

Q: What is the relationship between multiples and factors?

A: Multiples and factors are related in that a multiple of a number can be expressed as the product of that number and an integer, while a factor of a number is an integer that divides that number without leaving a remainder.

Q: Can a number have multiple multiples and factors?

A: Yes, a number can have multiple multiples and factors. For example, the multiples of 3 are 3, 6, 9, 12, and so on, while the factors of 6 are 1, 2, 3, and 6.

Q: How do I use multiples and factors in real-life situations?

A: Multiples and factors are used in many real-life situations, such as:

  • Shopping: When you buy items in bulk, you are using multiples.
  • Cooking: When you multiply a recipe by a certain number, you are using multiples.
  • Finance: When you invest in stocks or bonds, you are using multiples and factors.

Conclusion

In conclusion, multiples and factors are important concepts in mathematics that are used in many real-life situations. By understanding the definitions and relationships between multiples and factors, you can apply them to solve problems and make informed decisions.

Additional Resources

For more information on multiples and factors, check out the following resources:

  • Khan Academy: Multiples and Factors
  • Math Is Fun: Multiples and Factors
  • Wikipedia: Multiple (mathematics)

Final Thoughts

In conclusion, multiples and factors are essential concepts in mathematics that are used in many real-life situations. By understanding the definitions and relationships between multiples and factors, you can apply them to solve problems and make informed decisions.