# Multiplying Negative Numbers Worksheet, Rules, and Examples

Get the free Multiplying Negative Numbers worksheet and other resources for teaching & understanding how to Multiply Negative Numbers

### Key Points

- Multiplying two negative numbers always results in a positive number, while multiplying a negative number by a positive number or vice versa results in a negative number.
- To multiply negative numbers, it is crucial to understand the rules for multiplying positive numbers and keep them in mind.
- By understanding examples of multiplying negative numbers, students can solve more complex math problems with ease.

## Multiply Negative Numbers Introduction

Multiplying Negative Numbers is about expressions that have a negative number being multiplied. You may have to multiply negative numbers by a positive number or multiply a negative number by another negative number. When Multiplying Negative Numbers you can follow a simple pattern to get the answer. A negative times a positive makes a negative number. A negative times a negative makes a positive number. You can also count the number of negative numbers in an expression. If the total number of negative numbers is even, then your answer will be positive. If the total number of negative numbers is odd, then your answer will be negative.

Multiplying negative numbers is a fundamental concept in mathematics that can be confusing for many students. It is essential to understand the rules for multiplying negative numbers to solve complex math problems. When multiplying a negative number by another negative number, the result is always a positive number. However, when multiplying a negative number by a positive number or vice versa, the result is always negative.

To multiply negative numbers, one must first understand the rules for multiplying positive numbers. Multiplying two positive numbers always results in a positive number, and the same applies when multiplying two negative numbers. However, when multiplying a positive number by a negative number or vice versa, the result is always negative. It is essential to keep these rules in mind when multiplying negative numbers.

There are several examples of how to multiply negative numbers, and it is crucial to understand each one to solve more complex problems. One example is multiplying -3 by -4, which results in 12. Another example is multiplying -2 by 5, which results in -10. By understanding these examples and the rules for multiplying negative numbers, students can solve more complex math problems with ease.

**Common Core Standard: **7.NS.1**Related Topics: **Adding Negative Numbers, Subtracting Negative Numbers, Dividing Negative Numbers, Order of Operations**Return To: **Home, 7th Grade

## How to Multiply Negative Numbers in 3 Easy Steps

Multiplying negative numbers is an essential concept in mathematics that is often used in various fields of study. It is important to understand the rules of multiplying negative numbers to avoid errors in calculations. Here are the steps to follow when multiplying negative numbers:

- Multiply the absolute values of the numbers: The first step is to ignore the signs of the numbers and multiply their absolute values. For example, if you want to multiply -2 and -3, you will first multiply 2 and 3, which gives you 6.
- Determine the sign of the product: The sign of the product depends on the signs of the numbers being multiplied. If both numbers have the same sign, the product is positive. If they have different signs, the product is negative. For example, when you multiply -2 and -3, both numbers have a negative sign, so the product is positive.
- Add the sign to the product: Finally, you add the sign to the product. For example, if the product is positive, you will add a positive sign to it. If the product is negative, you will add a negative sign to it. Therefore, the product of -2 and -3 is 6, and since both numbers have a negative sign, the final answer is -6.

It is important to note that when you multiply more than two negative numbers, the same rules apply. You will first multiply the absolute values of the numbers, determine the sign of the product, and add the sign to the product.

In conclusion, multiplying negative numbers is a straightforward process that requires you to follow a few simple rules. By understanding these rules, you can avoid mistakes and accurately solve problems that involve negative numbers.

## Rules for Multiplying Negative Numbers

When it comes to multiplying negative numbers, there are a few rules that one must follow to get the correct answer. In this section, we will discuss these rules and how they apply to both positive and negative numbers.

### Multiplying Positive Numbers

When you multiply two positive numbers, the answer is always positive. For example, 2 x 3 = 6. This is because both numbers have the same sign, and when you multiply them, the result will also have the same sign.

### Multiplying Negative Numbers

When you multiply two negative numbers, the answer is also positive. For example, (-2) x (-3) = 6. This may seem counterintuitive at first, but it follows the same logic as multiplying two positive numbers. Both numbers have the same sign, so the result will also have the same sign, which is positive.

However, when you multiply a positive number and a negative number, the answer is always negative. For example, (-2) x 3 = -6. This is because the two numbers have different signs, and when you multiply them, the result will have the opposite sign.

To summarize:

Multiplying | Same Signs | Different Signs |
---|---|---|

Positive x Positive | Positive | Positive |

Negative x Negative | Positive | Positive |

Positive x Negative | Negative | Negative |

It is important to remember these rules when multiplying negative numbers to ensure that you get the correct answer. With practice, these rules will become second nature, and you will be able to multiply negative numbers with ease.

## Dividing and Multiplying Negative Numbers Examples

When dividing and multiplying negative numbers, there are some simple rules to follow.

- When you multiply a negative times a positive, the answer will equal a negative number.
- When you multiply a negative times a negative, the answer will equal a positive number.

Here are some examples:

### Example 1: Multiplying two negative numbers

When multiplying two negative numbers, the result is always a positive number. For example:

- (-2) x (-3) = 6
- (-5) x (-1) = 5

### Example 2: Multiplying a negative and a positive number

When multiplying a negative and a positive number, the result is always a negative number. For example:

- (-2) x 3 = -6
- (-5) x 2 = -10

### Example 3: Dividing a negative number by a positive number

When dividing a negative number by a positive number, the result is always a negative number. For example:

- (-6) / 2 = -3
- (-12) / 4 = -3

### Example 4: Dividing a positive number by a negative number

When dividing a positive number by a negative number, the result is always a negative number. For example:

- 12 / (-4) = -3
- 20 / (-5) = -4

It’s important to remember these rules when working with negative numbers. By following these simple rules, you can easily multiply and divide negative numbers without making mistakes.

## 5 Quick Multiplying Negative Numbers Practice Problems

## How to Solve a Negative Multiplied by a Positive

When multiplying a negative number by a positive number, the resulting product is negative. This is because when you multiply a negative number by a positive number, you are essentially subtracting the positive number from zero.

For example, -4 multiplied by 3 equals -12. To solve this problem, you can use the following steps:

- Multiply the absolute values of the two numbers. In this case, you would multiply 4 and 3 to get 12.
- Determine the sign of the product. Since one of the numbers is negative, the product will be negative.
- Write the product with the correct sign. In this case, the product is -12.

It’s important to note that the order in which you multiply the two numbers does not matter. For example, 3 multiplied by -4 would also result in -12.

When solving more complex problems involving negative numbers, it may be helpful to use a number line or a table to keep track of the signs and values of the numbers.

Overall, solving a negative multiplied by a positive is a straightforward process that can be easily mastered with practice.

## FAQ about Multiplying Negative Numbers

### What happens when you multiply two negative numbers?

When two negative numbers are multiplied, the result is always a positive number. This is because when we multiply two negative numbers, we are essentially multiplying two numbers that are in opposite directions, and the product of two opposite directions is always positive.

### How do you multiply a negative number by a positive number?

When multiplying a negative number by a positive number, the product is always negative. For example, -3 multiplied by 4 is equal to -12. This is because when we multiply a positive number by a negative number, the product is always negative.

### What is the product of a negative number and a positive number?

The product of a negative number and a positive number is always negative. For example, -4 multiplied by 2 is equal to -8.

### What is the result of multiplying two positive numbers?

When two positive numbers are multiplied, the result is always a positive number. For example, 3 multiplied by 4 is equal to 12.

### What is the product of negative two and negative two?

The product of negative two and negative two is positive four. This follows the rule that when we multiply two negative numbers, the result is always positive.

### What is the rule for multiplying negative numbers?

The rule for multiplying negative numbers is that when we multiply two negative numbers, the result is always a positive number. When we multiply a negative number by a positive number, the product is always negative.

### Does multiplication cancel out negatives?

No, multiplication does not cancel out negatives. In fact, multiplying two negative numbers results in a positive number.

### Why does multiplying 2 negatives make a positive?

Multiplying two negatives makes a positive because when we multiply two numbers that are in opposite directions, the product is always positive. In the case of multiplying two negative numbers, both numbers are in the negative direction, but when they are multiplied together, the result is in the positive direction.

### How do you multiply two negatives?

When multiplying two negative numbers, the product is always positive. For example, -3 multiplied by -4 is equal to 12.

## Multiplying Negative Numbers Worksheet Video Explanation

Watch our free video on how to **Multiply Negative Numbers**. This video shows how to solve problems that are on our free Multiplying Negative Numbers worksheet that you can get by submitting your email above.

**Watch the free Multiplying Negative Numbers video on YouTube here: How to Multiple Negative Numbers Video**

**Video Transcript:**

This video is about multiplying negative numbers. You can get the multiplying negatives worksheet used in this video for free by clicking on the link in the description below.

There are two important rules to remember when figuring out how to multiply negative numbers. The first rule is if you are multiplying two numbers together that have the same sign your answer will be a positive number. If you’re doing a positive times a positive, and they have the same sign, both have two positives that’s going to equal a positive number.

If you’re doing a negative times another negative, so they have the same sign, that’s also going to be a positive number. If you are multiplying two numbers together that have opposite signs, your answer will be a negative number. For example, you do a negative times a positive that will be a negative number and if you do a positive times a negative that will also equal a negative number. This is why is a negative times a negative a positive.

Just to give you a couple quick examples, if we did negative 2 times negative 3 both of these are negative numbers. So, this is a negative times negative because they have the same sign because they’re both negative so that means our answer has to be a positive number. In this case negative 2 times negative 3 or just 2 times 3 is 6, and then we know a negative times a negative makes a positive, because they have the same sign.

So the answer to this would just be positive 6. A quick example for opposite signs if we did positive 5 times a negative 4, that means they have opposite signs, so they’re different. This is a positive and this is a negative and that means that our answer has to be negative. When we multiply these together, we just multiply the numbers 5 times 4 and that gives us 20, but because they’re opposite signs, a positive number times a negative number, that gives us a negative as our final solution. This would be negative 20.

Here we are the first problem on our multiply negative numbers worksheet. You can see this problem gives us negative one times negative five. Now the first thing you may notice is that this is a negative number, and this five is also a negative number. We already know that two negatives, negative times a negative, is going to equal a positive. This is because they have the same sign and are negative times negative.

So, all you have to do is multiply one times five, and one times five is obviously five, and then we know that our answer has to be positive because a negative times a negative makes a positive. Our final solution is going to be positive five, or just five.

Jumping down to number two on the worksheet for how to multiply negative numbers we have 1 times negative 8. Now this time we have opposite signs, this is a positive and this 8 is negative. We already know that a positive times a negative are opposite, which means that our answer has to be negative. If they have different signs, that means your answer will be negative. It doesn’t matter if it’s positive times negative or negative times positive.

In this case when you multiply 1 times 8 that gives you 8 but then it’s a positive times a negative so your answer has to be a negative. Your answer for this will be negative 8.

Number three on our worksheet gives us negative 4 times negative 2. Again this is a negative number times another negative number, and we know that negative times a negative is going to equal positive. So you just multiply 4 times 2 and 4 times 2 is 8, and then you know the negative times the negative is going to be a positive, so we know our answer is going to be positive 8, or just 8.

The last example for this video is number 4. This gives us 3 times negative 1. We have a positive 3 right here times a negative number, which is negative 1. In this case they are not like signs, which means that our answer is going to be negative. When we multiply 3 times 1, we just do 3 times 1, and that gives us 3. Then this is a positive and this as a negative, so this negative 1 makes our final solution negative. Our answer has to be negative 3.

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