Multiplying Negative and Positive Numbers

Oct 13, 2025 by recoveryshake.com 124 views

Introduction

Multiplication is a fundamental operation in mathematics that helps us find the product of two or more numbers. In this article, we will focus on solving the multiplication problem $-10 \times 8$ . We will break down the solution into simple steps, making it easy to understand and follow.

Understanding the Problem

The problem $-10 \times 8$ involves multiplying a negative number, $-10$ , by a positive number, $8$ . To solve this problem, we need to understand the concept of multiplying negative and positive numbers.

Multiplying Negative and Positive Numbers

When we multiply a negative number by a positive number, the result is always negative. This is because the negative sign is "carried over" to the product. In this case, we have $-10 \times 8$ , which means we are multiplying a negative number by a positive number.

Step 1: Multiply the Numbers

To solve the problem, we need to multiply the numbers $-10$ and $8$ . We can do this by multiplying the absolute values of the numbers and then applying the negative sign.

Step 2: Apply the Negative Sign

Since we are multiplying a negative number by a positive number, the result will be negative. We can apply the negative sign to the product by placing a negative sign in front of it.

Step 3: Simplify the Expression

Now that we have multiplied the numbers and applied the negative sign, we can simplify the expression. In this case, the product of $-10$ and $8$ is $-80$ .

Conclusion

In this article, we solved the multiplication problem $-10 \times 8$ by breaking it down into simple steps. We understood the concept of multiplying negative and positive numbers, multiplied the numbers, applied the negative sign, and simplified the expression. The final answer is $-80$ .

Tips and Tricks

When multiplying a negative number by a positive number, the result is always negative.
To solve a multiplication problem involving negative numbers, multiply the absolute values of the numbers and then apply the negative sign.
Simplify the expression by combining like terms.

Practice Problems

Try solving the following multiplication problems:

$-5 \times 3$
$-2 \times 9$
$-8 \times 6$

Answer Key

$-5 \times 3 = -15$
$-2 \times 9 = -18$
$-8 \times 6 = -48$

Real-World Applications

Multiplication is used in many real-world applications, such as:

Calculating the cost of items
Finding the area of a room
Determining the volume of a container

Conclusion

Introduction

Multiplication of negative numbers can be a challenging concept for many students. In this article, we will address some of the most frequently asked questions about multiplying negative numbers.

Q: What is the rule for multiplying negative numbers?

A: The rule for multiplying negative numbers is that the product of two negative numbers is positive, and the product of a negative number and a positive number is negative.

Q: Why is the product of two negative numbers positive?

A: The product of two negative numbers is positive because the negative signs "cancel out" each other. When you multiply two negative numbers, you are essentially multiplying two positive numbers, which results in a positive product.

Q: Why is the product of a negative number and a positive number negative?

A: The product of a negative number and a positive number is negative because the negative sign is "carried over" to the product. When you multiply a negative number by a positive number, you are essentially multiplying a positive number by a negative number, which results in a negative product.

Q: How do I remember the rules for multiplying negative numbers?

A: One way to remember the rules for multiplying negative numbers is to use the acronym "NINE":

N: Negative number
I: Inverse (i.e., the product of two negative numbers is positive)
N: Negative sign (i.e., the product of a negative number and a positive number is negative)
E: Even (i.e., the product of two negative numbers is even)

Q: Can you give me an example of multiplying two negative numbers?

A: Yes, here is an example of multiplying two negative numbers:

$-3 \times -4 = 12$

In this example, the product of two negative numbers is positive.

Q: Can you give me an example of multiplying a negative number and a positive number?

A: Yes, here is an example of multiplying a negative number and a positive number:

$-5 \times 3 = -15$

In this example, the product of a negative number and a positive number is negative.

Q: How do I apply the rules for multiplying negative numbers to real-world problems?

A: The rules for multiplying negative numbers can be applied to many real-world problems, such as:

Calculating the cost of items
Finding the area of a room
Determining the volume of a container

For example, if you are calculating the cost of a product that is on sale, you may need to multiply a negative number (the discount) by a positive number (the original price).

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 apply the negative sign to the product
Confusing the product of two negative numbers with the product of a negative number and a positive number
Not simplifying the expression by combining like terms

Conclusion

In conclusion, multiplying negative numbers can be a challenging concept, but with practice and understanding of the rules, it can become easier. By remembering the acronym "NINE" and applying the rules to real-world problems, you can become more confident in your ability to multiply negative numbers.