Multiply.$5.5 \times (-0.2) = \square$

Introduction

Multiplication is a fundamental operation in mathematics that involves the repeated addition of a number. When it comes to multiplying negative numbers, it can be a bit tricky to understand the concept. In this article, we will delve into the world of negative numbers and explore the concept of multiplication with a focus on the problem $5.5 \times (-0.2) = \square$. We will also discuss the rules and properties of multiplication with negative numbers, and provide examples to illustrate the concept.

What are Negative Numbers?

Negative numbers are numbers that are less than zero. They are denoted by a minus sign (-) and are used to represent quantities that are opposite in direction or magnitude. For example, -5 is a negative number that represents a quantity that is 5 units less than zero.

The Concept of Multiplication

Multiplication is a mathematical operation that involves the repeated addition of a number. For example, 3 × 4 can be thought of as 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3, which equals 12. When it comes to multiplying negative numbers, the concept is similar, but with a twist.

Multiplication of Negative Numbers

When multiplying two negative numbers, the result is always positive. This is because the negative signs cancel each other out, leaving a positive result. For example, (-3) × (-4) = 12. On the other hand, when multiplying a negative number by a positive number, the result is always negative. For example, (-3) × 4 = -12.

The Rule for Multiplying Negative Numbers

The rule for multiplying negative numbers is as follows:

• When multiplying two negative numbers, the result is always positive.
• When multiplying a negative number by a positive number, the result is always negative.

Example 1: Multiplying Two Negative Numbers

Let's consider the problem $5.5 \times (-0.2) = \square$. To solve this problem, we need to multiply 5.5 by -0.2. Since both numbers are negative, the result will be positive.

$5.5 \times (-0.2) = -1.1$

Example 2: Multiplying a Negative Number by a Positive Number

Let's consider the problem $(-3) \times 4 = \square$. To solve this problem, we need to multiply -3 by 4. Since one number is negative and the other is positive, the result will be negative.

$(-3) \times 4 = -12$

Properties of Multiplication with Negative Numbers

There are several properties of multiplication with negative numbers that are worth noting:

• Commutative Property: The order of the numbers being multiplied does not change the result. For example, (-3) × 4 = 4 × (-3) = -12.
• Associative Property: The order in which the numbers are multiplied does not change the result. For example, (-3) × (4 × 5) = (-3) × 20 = -60.
• Distributive Property: The multiplication of a number by a sum can be distributed to each term in the sum. For example, (-3) × (4 + 5) = (-3) × 4 + (-3) × 5 = -12 - 15 = -27.

Conclusion

In conclusion, multiplication with negative numbers can be a bit tricky to understand, but with the right rules and properties, it can be a breeze. Remember, when multiplying two negative numbers, the result is always positive, and when multiplying a negative number by a positive number, the result is always negative. By following the rule and properties of multiplication with negative numbers, you can solve problems like $5.5 \times (-0.2) = \square$ with ease.

Frequently Asked Questions

• Q: What is the result of multiplying two negative numbers? A: The result of multiplying two negative numbers is always positive.
• Q: What is the result of multiplying a negative number by a positive number? A: The result of multiplying a negative number by a positive number is always negative.
• Q: What are the properties of multiplication with negative numbers? A: The properties of multiplication with negative numbers include the commutative property, associative property, and distributive property.

References

• [1] Khan Academy. (n.d.). Multiplication of Negative Numbers. Retrieved from https://www.khanacademy.org/math/algebra/x2f1f4c6/x2f1f4c7/x2f1f4c8
• [2] Math Open Reference. (n.d.). Multiplication of Negative Numbers. Retrieved from https://www.mathopenref.com/multiplicationnegatives.html

Glossary

• Negative Number: A number that is less than zero.
• Multiplication: A mathematical operation that involves the repeated addition of a number.
• Commutative Property: The order of the numbers being multiplied does not change the result.
• Associative Property: The order in which the numbers are multiplied does not change the result.
• Distributive Property: The multiplication of a number by a sum can be distributed to each term in the sum.
  Multiplication of Negative Numbers: A Comprehensive Guide ===========================================================

Q&A: Multiplication of Negative Numbers

Q: What is the result of multiplying two negative numbers?

A: The result of multiplying two negative numbers is always positive. For example, (-3) × (-4) = 12.

Q: What is the result of multiplying a negative number by a positive number?

A: The result of multiplying a negative number by a positive number is always negative. For example, (-3) × 4 = -12.

Q: Why do we get a positive result when multiplying two negative numbers?

A: When we multiply two negative numbers, the negative signs cancel each other out, leaving a positive result.

Q: Why do we get a negative result when multiplying a negative number by a positive number?

A: When we multiply a negative number by a positive number, the negative sign remains, resulting in a negative product.

Q: Can you give me an example of a problem that involves multiplying two negative numbers?

A: Yes, here's an example: $5.5 \times (-0.2) = \square$. To solve this problem, we need to multiply 5.5 by -0.2. Since both numbers are negative, the result will be positive.

$5.5 \times (-0.2) = -1.1$

Q: Can you give me an example of a problem that involves multiplying a negative number by a positive number?

A: Yes, here's an example: $(-3) \times 4 = \square$. To solve this problem, we need to multiply -3 by 4. Since one number is negative and the other is positive, the result will be negative.

$(-3) \times 4 = -12$

Q: What are the properties of multiplication with negative numbers?

A: The properties of multiplication with negative numbers include the commutative property, associative property, and distributive property.

Q: What is the commutative property of multiplication with negative numbers?

A: The commutative property of multiplication with negative numbers states that the order of the numbers being multiplied does not change the result. For example, (-3) × 4 = 4 × (-3) = -12.

Q: What is the associative property of multiplication with negative numbers?

A: The associative property of multiplication with negative numbers states that the order in which the numbers are multiplied does not change the result. For example, (-3) × (4 × 5) = (-3) × 20 = -60.

Q: What is the distributive property of multiplication with negative numbers?

A: The distributive property of multiplication with negative numbers states that the multiplication of a number by a sum can be distributed to each term in the sum. For example, (-3) × (4 + 5) = (-3) × 4 + (-3) × 5 = -12 - 15 = -27.

Q: How do I apply the rules of multiplication with negative numbers to solve problems?

A: To apply the rules of multiplication with negative numbers, you need to follow these steps:

1. Determine if the numbers being multiplied are both negative or if one is negative and the other is positive.
2. If both numbers are negative, the result will be positive.
3. If one number is negative and the other is positive, the result will be negative.
4. Use the commutative, associative, and distributive properties to simplify the problem if necessary.

Q: What are some common mistakes to avoid when multiplying negative numbers?

A: Some common mistakes to avoid when multiplying negative numbers include:

• Forgetting to change the sign of the product when multiplying a negative number by a positive number.
• Not using the commutative, associative, and distributive properties to simplify the problem.
• Not following the rules of multiplication with negative numbers.

Q: How can I practice multiplying negative numbers?

A: You can practice multiplying negative numbers by working on problems like $5.5 \times (-0.2) = \square$ or $(-3) \times 4 = \square$. You can also try using online resources or math apps to practice multiplying negative numbers.

Q: What are some real-world applications of multiplying negative numbers?

A: Multiplying negative numbers has many real-world applications, including:

• Calculating the cost of a product that is on sale.
• Determining the amount of money that will be lost or gained in a business transaction.
• Solving problems in physics and engineering that involve negative numbers.

Q: Can you give me some additional resources for learning about multiplying negative numbers?

A: Yes, here are some additional resources for learning about multiplying negative numbers:

• Khan Academy: Multiplication of Negative Numbers
• Math Open Reference: Multiplication of Negative Numbers
• IXL: Multiplication of Negative Numbers
• Mathway: Multiplication of Negative Numbers

Conclusion

In conclusion, multiplying negative numbers can be a bit tricky, but with the right rules and properties, it can be a breeze. Remember, when multiplying two negative numbers, the result is always positive, and when multiplying a negative number by a positive number, the result is always negative. By following the rule and properties of multiplication with negative numbers, you can solve problems like $5.5 \times (-0.2) = \square$ with ease.