Subtracting Negative Numbers Worksheet, Rules, and Examples

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Subtracting Negative Numbers the EASY way (How to Subtract Negative Numbers)

Key Points about Subtracting Negative Numbers

  • Subtracting a negative number is the same as adding a positive number.
  • Two negative signs next to each other cancel each other out, resulting in a positive number.
  • Mastering the rules and techniques involved in subtracting negative numbers is essential for success in mathematics.

How to Subtract Two Negative Numbers

Subtracting Negative Numbers is when you subtract integers that have a negative sign with another integer that can be positive or negative. Negative Numbers are less than zero and, therefor, negative. The way to subtract negative numbers depends on if you are subtracting two negative numbers from each other or if you are subtracting one negative number with one positive number.

Subtracting negative numbers is a fundamental skill in mathematics that is often taught in middle school. While it may seem daunting at first, mastering this skill is essential for success in more advanced math courses. When subtracting negative numbers, it is important to understand the rules and techniques involved to avoid making common mistakes.

When Subtracting Negative Numbers you find the absolute value of the numbers being subtracted. The absolute value of a number is the distance of that number from zero. Because the absolute value is distance, it will always be positive since distance cannot be negative. Once you have the absolute value of each number, you will just subtract the smaller number from the larger number. Then you will keep the sign of the larger number.

One of the key rules for subtracting negative numbers is that subtracting a negative number is the same as adding a positive number. This can be a confusing concept for some students, as it seems counterintuitive. However, understanding this rule is essential for performing accurate calculations. Additionally, it is important to remember that two negative signs next to each other cancel each other out, resulting in a positive number.

If the expression has two negatives next to each other, they will turn into a positive. Typically you will hear this referred to as “leave-change-change.” This means that you keep the sign of the first number the same, then change the subtraction sign to an addition sign, and change the sign of the last number.

By mastering the rules and techniques involved in subtracting negative numbers, students can build a strong foundation in mathematics that will serve them well in their academic and professional lives. With practice and patience, anyone can become proficient in this essential skill.

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

How to Subtract Negative Numbers

Subtracting negative numbers is a fundamental concept in mathematics that is essential to understanding more complex mathematical operations. It is important to understand the rules and techniques involved in subtracting negative numbers to solve problems accurately and efficiently.

To subtract a negative number, you can follow the rule of adding a positive number. This means that subtracting a negative number is the same as adding a positive number. For example, subtracting -3 from 5 can be rewritten as 5 + 3 = 8.

When subtracting a negative number, it is important to remember that two negative signs cancel each other out and become a positive sign. For example, subtracting -7 from -3 can be rewritten as -3 + 7 = 4.

To subtract two negative numbers, you can use the same rule of adding a positive number. For example, subtracting -5 from -2 can be rewritten as -2 + 5 = 3.

It is also important to understand the difference between negative numbers and negative integers. A negative integer is a whole number that is less than zero, while a negative number can be any real number that is less than zero. When subtracting negative integers, the result will always be a negative integer. However, when subtracting negative numbers, the result can be either a negative or positive number.

In summary, subtracting negative numbers involves adding a positive number and canceling out two negative signs to become a positive sign. Understanding these rules and techniques is crucial to solving mathematical problems accurately and efficiently.

 

Rules for Subtracting Negative Numbers

When it comes to subtracting negative numbers, there are two main approaches: the Number Line Approach and Adding the Opposite. Both methods are useful and can be used interchangeably depending on the situation.

The Number Line Approach

The Number Line Approach is a visual method that allows students to better understand the concept of negative numbers. In this approach, students use a number line to represent positive and negative numbers. To subtract a negative number, students move to the right on the number line.

For example, to solve the problem -5 – (-3), students start at -5 on the number line and move three units to the right to get to -2. This method is particularly helpful for students who struggle with abstract concepts.

Adding the Opposite

Adding the Opposite is a more algebraic method of subtracting negative numbers. In this approach, students change the subtraction problem into an addition problem by adding the opposite of the second number.

For example, to solve the problem -5 – (-3), students change the problem to -5 + 3. They then add the opposite of -3, which is 3. This gives them the answer of -2.

This method is useful when students are comfortable with algebraic concepts and can easily manipulate equations.

Regardless of the approach used, students should remember the following rules when subtracting negative numbers:

  • Subtracting a negative number is the same as adding a positive number. For example, -5 – (-3) is the same as -5 + 3.
  • When subtracting a negative number, remember that the two back-to-back minus signs cancel each other out, leaving you with a plus sign. For example, -5 – (-3) is the same as -5 + 3.
  • To subtract a negative number, add the opposite of the number. For example, -5 – (-3) is the same as -5 + 3.

By following these rules and using either the Number Line Approach or Adding the Opposite, students can become confident in their ability to subtract negative numbers.

 

Subtracting Negative Numbers Solution

Solve Subtracting Negative Numbers Examples in 2 Easy Steps

  1. If the two numbers have opposite signs, you subtract them then keep the sign of the larger number.
  2. If the expression has a subtraction sign next to a negative number, you must change the subtraction sign to an addition sign and the negative number into a positive number. This is called “leave-change-change.”

Subtracting negative numbers can be a tricky concept to understand, but with a few examples, it can become clearer.

Consider the following example:

-4 – (-10)

To solve this problem, one needs to remember that subtracting a negative number is the same as adding a positive number. Therefore, -4 – (-10) can be rewritten as -4 + 10.

-4 + 10 = 6

Thus, -4 – (-10) = 6.

Another example is:

-7 – (-2)

To solve this problem, one needs to rewrite the subtraction as addition and then simplify.

-7 – (-2) can be rewritten as -7 + 2.

-7 + 2 = -5

Therefore, -7 – (-2) = -5.

It is important to remember that when subtracting negative numbers, one must be careful with signs.

For example, consider the problem:

-8 – (-6)

To solve this problem, one can rewrite the subtraction as addition and then simplify.

-8 – (-6) can be rewritten as -8 + 6.

-8 + 6 = -2

Therefore, -8 – (-6) = -2.

In summary, to subtract negative numbers, one needs to remember that subtracting a negative number is the same as adding a positive number. Additionally, one must be careful with signs when simplifying the problem.

 

5 Quick Subtracting Negative Numbers Practice Problems

/5

Subtracting Negative Numbers

Click Start to begin the practice quiz!

1 / 5

Solve.

-4 - (-2)

2 / 5

Solve.

1 - (-5)

3 / 5

Solve.

-1 - (-8)

4 / 5

Solve.

3 - (-2)

5 / 5

Solve.

-9 - (-2)

Your score is

0%

 

Negative Minus Negative Equals: How to Solve

When subtracting negative numbers, it is important to understand that subtracting a negative number is the same as adding a positive number. In other words, “minus a negative” equals a positive. This concept can be a bit confusing, but with practice, it becomes easier to understand and apply.

To evaluate a subtraction problem with two negative numbers, the following steps can be taken:

  1. Identify the two negative numbers being subtracted.
  2. Change the subtraction sign to an addition sign.
  3. Change the second negative number to a positive number.
  4. Add the two numbers together.

For example, let’s evaluate the problem -3 – (-2):

  1. The two negative numbers being subtracted are -3 and -(-2).
  2. Change the subtraction sign to an addition sign: -3 + (-2).
  3. Change the second negative number to a positive number: -3 + 2.
  4. Add the two numbers together: -1.

Therefore, -3 – (-2) equals -1.

It is important to note that when subtracting negative numbers, the order of the numbers being subtracted does matter. For example, if you were to evaluate -2 – (-3), the steps would be as follows:

  1. Identify the two negative numbers being subtracted: -2 and -(-3).
  2. Change the subtraction sign to an addition sign: -2 + 3.
  3. Add the two numbers together: 1.

Therefore, -2 – (-3) equals 1.

In summary, when subtracting negative numbers, remember that “minus a negative” equals a positive. Follow the steps outlined above to evaluate a subtraction problem with two negative numbers.

 

FAQ about Subtracting Negative Numbers

What is the rule for subtracting negative numbers?

The rule for subtracting negative numbers is to add the opposite of the number. For example, to subtract -5 from 10, you add 5 to 10, which gives you 15.

How do you subtract negative and negative integers?

To subtract negative and negative integers, you add the opposite of the second number. For example, to subtract -3 from -7, you add 3 to -7, which gives you -10.

How do you subtract a positive minus a negative?

To subtract a positive minus a negative, you add the two numbers. For example, to subtract 5 – (-3), you add 5 and 3, which gives you 8.

What are the rules for subtracting and adding negative numbers?

The rules for subtracting and adding negative numbers are the same. When adding or subtracting negative numbers, you add the opposite of the number.

What happens when you subtract a negative number from a positive number?

When you subtract a negative number from a positive number, you add the two numbers. For example, to subtract -3 from 7, you add 3 to 7, which gives you 10.

Why is subtracting a negative number the same as adding a positive number?

Subtracting a negative number is the same as adding a positive number because the negative of a negative is a positive. For example, -(-3) is the same as 3.

What is an example of subtracting two negative numbers?

An example of subtracting two negative numbers is -5 – (-3). To solve this problem, you add 3 to -5, which gives you -2.

Is subtracting negative integers adding?

Subtracting negative integers is the same as adding positive integers. When you subtract a negative integer, you add the opposite of the number.

 

Subtracting Negative Numbers Worksheet Video Explanation

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

Watch the free Subtracting Negative Numbers video on YouTube here: Subtracting Negative Numbers Video

Video Transcript:
This video is about negative numbers problems. You can get the adding and subtracting negative numbers worksheets​ using this video for free by clicking on the link in the description below.

There are two different types of problems you may encounter when figuring out how to subtract negative numbers. In general, the rule is when you have two negatives next to each other, the negatives will cancel and they will become a positive. Sometimes this is referred to as leave, change, change. In other words, you leave the first one then you change both the second, this one right here and this sign right here. so these will both become positive. I like to think of it as instead of rewriting it as a plus and a plus as one big plus sign like this. When you have the two negatives next to each other they will cancel a make a positive.

In this first example on our add and subtract negative numbers worksheet is three minus negative one we have the two negatives next to each other and we already know that they have to make a positive. So, I’m going say leave, change, change or that this just becomes a big plus. Rewriting this gives us just three plus one which is obviously three plus one is just four. That’s easy. On the second example you have a very similar problem except this number in front is negative. This time it’s negative four minus a negative two. Again, we have two negatives next to each other, so they become a positive and when I rewrite it this time this will be negative four plus positive two.

If you remember anytime you have a negative plus a positive or when you have two numbers that are not alike when you’re adding two numbers with different signs you have to actually subtract them so we subtract four minus two and we get two so we know our answer has to be two and then in order to determine the sign of the answer you take the sign of the larger number in this case four is larger than two four is negative which means your answer also has to be negative, so the answer for this is negative two.

Jumping to our first problem on our worksheet about how to subtract negative numbers the first problem gives us one minus negative five. So again, you can use the rule leave, change, change and we leave this one and then we’re going to change the signs on the next, to this one, and this one. When we do that, we use the rule for positive minus negative and we’re going to make both of these into a plus, then we can rewrite our problem because we have to change both of these from negative to positive, into one plus five. So now it’s real easy just one plus five which we know one plus five is obviously six. Our answer is going to be six. This is the easiest way to learn subtracting positive and negative numbers.

The second problem on our negative number’s worksheet gives us negative one minus negative eight. This time we have a negative minus a negative. When you have a negative minus a negative, the same rule applies. You will do leave, change, change, so we leave this one as negative one then we change this sign, so this changes and also this changes. Leave, change, change, so this will become a positive and a positive or I’ve been writing as a big plus sign. You can do it either way but I’m going to rewrite it as a big plus sign. Now our problem is negative one plus eight.

Now when we add these together when you have a negative plus a positive you actually subtract those, so we’re going to do eight minus one and we will get seven. We know our answer has to be seven and then to determine what the sign is on this you take the sign of the larger number. Because one’s negative and ones positive you have to look at these and determine which ones larger. In this case eight is larger which means this seven is going to be positive. Our answer is just going to be positive seven or just seven.

Our last example gives us negative four minus negative two. Again this problem is a negative minus a negative and shows subtracting negative and positive numbers. Anytime you have a negative minus another negative you can use the rule leave, change, change. So we’re going to leave this one as negative four, then we’re going to change this one into a positive, and this one into a positive. I’ve been rewriting them as a big plus for leave, change, change. Now it’s negative four plus 2, so just plus 2. Now you have negative four plus two and you have two different signs.

To determine the answer to that you actually subtract them. Four minus two is two, so we know it’s going to be two. And then to determine what the sign is of your answer, you look at the two numbers that you subtracted. Negative four is larger or four is larger than two and because this is negative that means your answer also has to be negative. Our final answer for our subtracting negative numbers problem is negative two. You can try all the practice problems by downloading the free adding subtracting negative numbers worksheet above.

free Subtracting Negative Numbers worksheet download

Free Subtracting Negative Numbers Worksheet

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