Dividing Negative Numbers Worksheet, Rules, and Practice

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3 EASY Rules for Dividing Negative Numbers (How to Divide Negative Numbers)

Key Points about Dividing Negative Numbers

  • Dividing negative numbers can be confusing, but following a few simple rules can make it much easier.
  • When you divide a positive number by a negative number, the result is always negative. When you divide a negative number by a positive number, the result is also negative. However, when you divide two negative numbers, the result is positive.
  • Understanding how to divide negative numbers is an important skill that can be used in many different areas of math and science.

Division of Negative Numbers

Dividing negative numbers is an important concept in mathematics that is often taught in middle or high school. Negative numbers can be confusing, but once you understand the rules for dividing them, it becomes much easier. Dividing negative numbers is a basic arithmetic operation that can be used to solve a variety of problems.

To divide negative numbers, you need to follow a few simple rules. First, when you divide a positive number by a negative number, the result is always negative. Similarly, when you divide a negative number by a positive number, the result is always negative. However, when you divide two negative numbers, the result is positive. These rules may seem counterintuitive at first, but with practice, they become second nature.

Dividing Negative Numbers is about expressions that have a negative number being divided. You may have to divide negative numbers by a positive number or divide a negative number by another negative number. When Dividing Negative Numbers you can follow a simple pattern to get the answer. A negative divided by a positive makes a negative number. A negative divided by 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.

Learning how to divide negative numbers is an important skill that can be used in many different areas of math and science. Whether you are solving equations, graphing functions, or working with complex numbers, understanding the rules for dividing negative numbers is essential. By mastering this concept, you can gain a deeper understanding of mathematics and become a more confident problem solver.

Common Core Standard: 7.NS.1
Related Topics: Adding Negative Numbers, Subtracting Negative Numbers, Multiplying Negative Numbers, Order of Operations
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Dividing Negative Numbers

How to Divide Negative Numbers

Dividing negative numbers can be confusing, but it’s actually quite simple once you understand the rules. In general, when dividing two numbers with different signs, the result will be negative. However, if both numbers are negative, the result will be positive.

To divide a positive number by a negative number, divide the absolute values of the numbers and then add a negative sign to the result. For example, to divide 10 by -2, divide the absolute values of 10 and 2, which are 10 and 2, respectively. Then, add a negative sign to the result, giving you -5.

Conversely, to divide a negative number by a positive number, divide the absolute values of the numbers and then add a negative sign to the result. For example, to divide -12 by 3, divide the absolute values of 12 and 3, which are 12 and 3, respectively. Then, add a negative sign to the result, giving you -4.

When dividing two negative numbers, the result will be positive. For example, to divide -8 by -2, divide the absolute values of 8 and 2, which are 8 and 2, respectively. Then, the result will be positive 4.

It’s important to remember that when working with negative numbers, you can use a number line to help you visualize the problem. Simply draw a number line and place the numbers on it, with negative numbers to the left of zero and positive numbers to the right. Then, move left or right on the number line to find the result of the division.

In summary, to divide negative numbers, remember to divide the absolute values of the numbers and then apply the rules for the signs. Use a number line to help you visualize the problem, and remember that when dividing two negative numbers, the result will be positive.

 

Rules for Dividing Negative Numbers

When it comes to dividing negative numbers, there are a few rules to keep in mind. These rules are essential to ensure that the answer is correct and that you don’t make any mistakes. Here are the rules for dividing negative numbers:

Same Signs

When dividing two numbers with the same sign, the answer is always positive. For example, if you divide -6 by -2, you get a positive answer of 3. This is because two negative signs cancel each other out, resulting in a positive answer.

Different Signs

When dividing two numbers with different signs, the answer is always negative. For example, if you divide -6 by 2, you get a negative answer of -3. This is because a negative number divided by a positive number always results in a negative answer.

Undefined

It’s important to note that dividing by 0 is undefined. This means that if you try to divide any number, positive or negative, by 0, you will get an error. It’s essential to avoid dividing by 0 as it can lead to incorrect answers and errors.

Recap

To recap, when dividing two numbers with the same sign, the answer is always positive. When dividing two numbers with different signs, the answer is always negative. And, dividing by 0 is undefined. By following these rules, you can ensure that you get the correct answer when dividing negative numbers.

 

Dividing Negative Numbers Solution

2 Easy Rules to solve Dividing Negative Numbers Examples

When dividing negative numbers, it is essential to remember that two negatives make a positive.

  1. A negative divided by a negative equals a positive.
  2. A negative divided by a positive equals a negative.

Here are a few examples to illustrate this concept:

Example 1:

Divide -24 by -6.

The answer is 4 because two negatives make a positive. So, -24 ÷ -6 = 4.

Example 2:

Divide -36 by 9.

The answer is -4 because two negatives make a positive. So, -36 ÷ 9 = -4.

Example 3:

Divide 18 by -6.

The answer is -3 because a positive number divided by a negative number is always negative. So, 18 ÷ -6 = -3.

Example 4:

Divide -30 by 5.

The answer is -6 because two negatives make a positive. So, -30 ÷ 5 = -6.

Remember that dividing a negative number by a positive number always results in a negative number. Conversely, dividing a positive number by a negative number always results in a negative number.

It is important to keep these concepts in mind when working with negative numbers. Practice these examples and similar problems to become more comfortable with dividing negative numbers.

 

5 Quick Division of Negative Numbers Practice Problems

/5

Dividing Negative Numbers Quiz

Click Start to begin the practice quiz!

1 / 5

Divide the negative numbers.

-40 / (-2)

2 / 5

Divide the negative numbers.

-8 / (-2)

3 / 5

Divide the negative numbers.

-10 / (-5)

4 / 5

Divide the negative numbers.

16 / (-8)

5 / 5

Divide the negative numbers.

3 / (-1)

Your score is

0%

 

Multiplying and Dividing Negative Numbers

When it comes to multiplying and dividing negative numbers, there are a few rules to keep in mind. First, when you multiply two negative numbers, the product is always positive. For example, -2 x -3 = 6. On the other hand, when you multiply a negative number and a positive number, the product is always negative. For example, -2 x 3 = -6.

When it comes to dividing negative numbers, the rules are a bit different. If you divide a positive number by a negative number, the quotient is always negative. For example, 10 ÷ -2 = -5. Conversely, if you divide a negative number by a positive number, the quotient is always negative. For example, -10 ÷ 2 = -5.

It’s important to note that when you divide two negative numbers, the quotient is always positive. For example, -6 ÷ -3 = 2. This is because when you divide a negative number by a negative number, the negative sign “cancels out,” leaving you with a positive quotient.

To summarize, when multiplying and dividing negative numbers:

  • When you multiply two negative numbers, the product is always positive.
  • When you multiply a negative number and a positive number, the product is always negative.
  • When you divide a positive number by a negative number, the quotient is always negative.
  • When you divide a negative number by a positive number, the quotient is always negative.
  • When you divide two negative numbers, the quotient is always positive.

Remember, these rules only apply to negative numbers. When you’re dealing with positive numbers, the rules are the same as usual.

 

Dividing Positive and Negative Numbers

Dividing positive and negative numbers can be a bit tricky, but it is important to understand the rules to avoid mistakes. This section will cover the rules for dividing positive and negative numbers, including addition and subtraction, multiplication and division.

Addition and Subtraction

When adding or subtracting positive and negative numbers, the rule is to keep the sign of the larger number and subtract the smaller number. For example, if you have -5 + 3, you would keep the negative sign and subtract 3 from 5 to get -2.

Multiplication and Division

When multiplying or dividing positive and negative numbers, the rule is to remember that a negative times a positive is always negative, and a negative times a negative is always positive. Similarly, a positive divided by a negative is always negative, and a negative divided by a positive is always negative.

For example, if you have -3 * 2, you would get -6 because a negative times a positive is always negative. If you have -6 / 2, you would get -3 because a negative divided by a positive is always negative.

It is important to remember these rules when dividing positive and negative numbers to avoid mistakes. By keeping track of the signs and following the rules, you can ensure that your calculations are accurate.

 

FAQ about Dividing Negative Numbers

What is the rule for dividing negative numbers?

The rule for dividing negative numbers is the same as dividing positive numbers. The only difference is that the sign of the quotient is determined by the signs of the dividend and divisor. If both numbers have the same sign, the quotient is positive. If the numbers have different signs, the quotient is negative.

Why is neg divided by neg a positive?

When you divide a negative number by another negative number, the result is a positive number. This is because dividing a negative number by another negative number is the same as multiplying a positive number by another positive number.

How do you divide negative numbers using long division?

To divide negative numbers using long division, follow the same steps as you would for dividing positive numbers. The only difference is that you need to pay attention to the signs of the numbers. If both numbers have the same sign, the quotient is positive. If the numbers have different signs, the quotient is negative.

What happens when you divide a positive and a negative number?

When you divide a positive number by a negative number, the result is always negative. This is because dividing a positive number by a negative number is the same as multiplying a positive number by a negative number.

Can you divide a positive number by a negative number?

Yes, you can divide a positive number by a negative number. The result will always be negative.

What is the product of two negative numbers?

The product of two negative numbers is always a positive number. This is because multiplying two negative numbers is the same as multiplying a positive number by another positive number.

 

Dividing Negative Numbers Worksheet Video Explanation

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

Watch the free Dividing Negative Numbers video on YouTube here: How to Divide Negative Numbers Video

Video Transcript:

This video is about dividing by negative numbers​. You can get the worksheet using this video for free by clicking on the link in the description below.

Before we get started, I want to talk about two important rules that are important to remember in determining how to divide negative numbers. The first rule is that if the two numbers you are dividing have the same sign then your answer will be a positive number. This means if you have a positive number divided by another positive number your answer will be positive.

Or if you are dividing two negative numbers, so they have the same sign, your answer will also be positive, they have the same sign. Positive divided by positive, it’s positive or negative divided by negative, it’s also positive. When you’re dividing negative and positive numbers your answer will be negative. It doesn’t matter if you divide a positive divided by a negative, that will give you a negative as your answer. Or if you did a negative number divided by a positive number. That is still going to give you a negative as an answer.

Let’s do two real quick examples of dividing positive and negative numbers before we go to our practice worksheet. This first example gives us negative 10 divided by negative 2. Now these both have the same sign. This is a negative and this is also a negative.

We know that our answer automatically has to be a positive number because this is a negative divided by a negative because they both have the same sign. In this case negative all you have to do is actually divide the two numbers, 10 divided by 2 is 5 and then we know that because a negative divided by a negative is a positive. We know that it’s going to have to be positive 5 or just 5. Second example we’re going to do real fast is 9 divided by negative 3.

This time this 9 is positive and this 3 is negative and because they have opposite signs, positive divided by a negative, we automatically now that our answer has to be negative. To get the number answer you just do nine divided by three, and that’s going to be three, and then it has to be negative because a positive divided by a negative makes a negative. Our answer is going to be negative three.

Jumping to number one in our dividing negative numbers worksheet we have negative 10 divided by negative five. This problem gives us a negative number, this is a negative divided by another negative number. A negative divided by a negative, they have the same sign which means that our answer has to automatically be a positive number. What we’re going to do is when we divide we divide 10 divided by five, we divide the actual numbers 10 and five and that gives us two.

Then we automatically know that a negative divided by negative makes a positive. This has to be positive two or just two. Jumping down to number two it gives us sixteen divided by negative eight. Now this time we have a positive number, 16 is positive divided by a negative number, eight is negative. We already know that they have different signs and when they have different signs your answer will be a negative.

Positive divided by negative makes a negative. In this case 16 divided by eight is going to be two, and then we know positive divided by a negative has to be a negative number. Our answer is going to be negative two.

Here’s our third problem showing you how to divide negative numbers, and this time we have negative forty divided by negative two. In this case a negative divided by a negative, they have the same sign. We know our answer is going to have to be positive. What we do is we take our two numbers, in this case forty and two and we divide them.

40 divided by two is twenty, and then we know that a negative divided by a negative has to make a positive. We know this is going to be positive twenty, or just 20. The last example that we’re going to go we’re on our dividing negative numbers worksheet is number 4. In this case we have 3 divided by negative 1. We know that 3 is a positive number and it’s being divided by a negative number.

They have opposite signs and a rule for figuring out how to divide negative numbers is that a positive divided by a negative is going to equal a negative number, because they have opposite signs. We just take our numbers 3 & 1 and we divide them. 3 divided by 1 is 3, and then we know that it has to be negative because a positive divided by a negative makes a negative number. Our final answer for this one is going to be negative 3.

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Free Dividing Negative Numbers Worksheet

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