Use the commutative property

Oct 13, 2025 by miodeya.com 11 views

Introduction

Multiplication is a fundamental operation in mathematics that involves the repeated addition of a number. In this article, we will explore the concept of multiplication and how it can be used to solve equations. Specifically, we will examine the equation $-6 \times \square = -60$ and determine the integer that makes this equation true.

Understanding the Equation

The equation $-6 \times \square = -60$ involves the multiplication of the integer $-6$ by an unknown integer, denoted by the symbol $\square$ . The goal is to find the value of the unknown integer that makes the equation true.

To begin, let's consider the properties of multiplication. When we multiply two integers, the result is always an integer. In this case, the product of $-6$ and the unknown integer must be equal to $-60$ .

Properties of Multiplication

Multiplication is a commutative operation, meaning that the order of the factors does not change the result. In other words, $a \times b = b \times a$ . However, in this case, we are dealing with a negative integer, which affects the result of the multiplication.

When we multiply a negative integer by a positive integer, the result is always negative. Conversely, when we multiply a negative integer by a negative integer, the result is always positive.

Solving the Equation

To solve the equation $-6 \times \square = -60$ , we need to find the value of the unknown integer that makes the equation true. Let's start by isolating the unknown integer.

We can do this by dividing both sides of the equation by $-6$ . This gives us:

\square = \frac{-60}{-6}

Simplifying the Expression

Now, let's simplify the expression on the right-hand side of the equation.

\square = \frac{-60}{-6} = 10

Conclusion

Therefore, the integer that makes the equation $-6 \times \square = -60$ true is $\boxed{10}$ .

Why is this the Correct Answer?

The correct answer is 10 because when we multiply $-6$ by 10, the result is $-60$ . This is due to the properties of multiplication, specifically the commutative property and the effect of negative integers on the result.

Real-World Applications

Understanding the concept of multiplication and how to solve equations involving integers is crucial in various real-world applications, such as:

Finance: When calculating interest rates or investment returns, multiplication is used to determine the total amount of money earned or lost.
Science: In physics, multiplication is used to calculate the force or energy required to perform a task.
Engineering: In engineering, multiplication is used to calculate the stress or strain on materials.

Tips and Tricks

Here are some tips and tricks to help you solve equations involving integers:

Use the commutative property: When multiplying two integers, the order of the factors does not change the result.
Understand the effect of negative integers: When multiplying a negative integer by a positive integer, the result is always negative. Conversely, when multiplying a negative integer by a negative integer, the result is always positive.
Simplify expressions: When simplifying expressions, look for common factors or use the distributive property to expand the expression.

Conclusion

In conclusion, the integer that makes the equation $-6 \times \square = -60$ true is $\boxed{10}$ . Understanding the concept of multiplication and how to solve equations involving integers is crucial in various real-world applications. By following the tips and tricks outlined in this article, you can improve your skills in solving equations involving integers and become more confident in your math abilities.

Introduction

In our previous article, we explored the concept of multiplication and how it can be used to solve equations. Specifically, we examined the equation $-6 \times \square = -60$ and determined the integer that makes this equation true. In this article, we will answer some frequently asked questions related to this topic.

Q&A

Q: What is the value of the unknown integer in the equation $-6 \times \square = -60$ ?

A: The value of the unknown integer is 10.

Q: Why is the value of the unknown integer 10?

A: The value of the unknown integer is 10 because when we multiply $-6$ by 10, the result is $-60$ . This is due to the properties of multiplication, specifically the commutative property and the effect of negative integers on the result.

Q: What is the commutative property of multiplication?

A: The commutative property of multiplication states that the order of the factors does not change the result. In other words, $a \times b = b \times a$ .

Q: What is the effect of negative integers on the result of multiplication?

A: When we multiply a negative integer by a positive integer, the result is always negative. Conversely, when we multiply a negative integer by a negative integer, the result is always positive.

Q: How can I simplify expressions involving integers?

A: To simplify expressions involving integers, look for common factors or use the distributive property to expand the expression.

Q: What are some real-world applications of multiplication and solving equations involving integers?

A: Understanding the concept of multiplication and how to solve equations involving integers is crucial in various real-world applications, such as finance, science, and engineering.

Q: What are some tips and tricks for solving equations involving integers?

A: Here are some tips and tricks to help you solve equations involving integers:

Use the commutative property: When multiplying two integers, the order of the factors does not change the result.
Understand the effect of negative integers: When multiplying a negative integer by a positive integer, the result is always negative. Conversely, when multiplying a negative integer by a negative integer, the result is always positive.
Simplify expressions: When simplifying expressions, look for common factors or use the distributive property to expand the expression.

Conclusion

Additional Resources

If you want to learn more about multiplication and solving equations involving integers, here are some additional resources:

Math textbooks: Check out math textbooks for more information on multiplication and solving equations involving integers.
Online resources: Websites such as Khan Academy, Mathway, and Wolfram Alpha offer interactive lessons and exercises on multiplication and solving equations involving integers.
Practice problems: Try solving practice problems to improve your skills in solving equations involving integers.

Final Thoughts

Solving equations involving integers is an essential skill in mathematics that has numerous real-world applications. By understanding the concept of multiplication and how to solve equations involving integers, you can become more confident in your math abilities and tackle complex problems with ease.