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Arithmetic Involving Negatives Practice Questions

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These negative numbers worksheets will have your kids working with positive and negative integers in no time! Starting with adding and subtracting negative numbers, and gradully work up to multiplying and dividing negative numbers, multiplying multi-digit negative numbers and long division for negative numbers.

Adding and Subtracting Negative Numbers

36 negative numbers worksheets.

Worksheets for adding negative numbers and subtracting negative numbers.

Multiplying and Dividing Small Negative Numbers

16 negative numbers worksheets.

The worksheets in this section introduce negative numbers integers in multiplication and division math problems. All problems deal with smaller integers that can be solved without multi-digit multiplication or long division.

Multiple-Digit Multiplication with Negative Numbers

If you have mastered basic multiplication with negative integers, these worksheets for multiple digit multiplication will give your negative number skills a more thorough test.

Long Division with Negative Numbers

Ready to keep your signs straight? These long division worksheets have negative divisors and negative quotients (or both!). Some negative division problems include remainders.

Solving Math Problems with Negative Numbers

Negative numbers is a math topic that typically comes into play around 6th grade, and it's introduced as part of the Common Core standard at that grade level.

Negative numbers appear in a variety of situations in applied math. Often you'll see negative numbers directly in measurements, for example measuring altitude above or below sea level, temperature above or below freezing or in financial applications with positive and negative amounts of money. A more frequent, but also more abstract, application of negative numbers is dealing with rates of change. You will also encounter negative values in geometry when graphing in various quadrants on a coordinate plane. And of course, as you make your way into algebra and more advanced geometry, negative numbers play an increasingly important role.

Kids in the late primary grades should be capable of reasoning about negative integers on the number line, and this is usually a good place to start exploring the basic math operations with negative numbers. This is also a good way to start visualizing how the rules for signed numbers work. The two critical ones to learn are that a subtracting a negative number is the same as addition, and that multiplying two negative numbers yields a positive product. Most of the other behaviors of negative numbers with the conventional math operations seem to be straightforward and intuitive, but memorizing those two rules will give your grade schoolers a solid start. For more on the rules for managing signs with negative numbers for the various operations, see the respective worksheet pages for a complete discussion and tips.

The worksheets on this page introduce adding and subtracting negative numbers, as well as multiplying and dividing negative numbers. The initial sets deal with small integers before moving on to multi-digit multiplication and long division with negatives. Regardless of where you're at in your process of learning negative numbers, these worksheets will give your students plenty of practice when they need to master this often negative topic!

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Adding and Subtracting Negative Numbers

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Graded Adding and Subtracting Negative Numbers Worksheets

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There are some interesting problems to solve which will help develop the skill of adding and subtracting with negative numbers.

• Add and Subtract Negative Numbers Sheet 1
• PDF version
• Add and Subtract Negative Numbers Sheet 2
• Add and Subtract Negative Numbers Sheet 3

Other Recommended Resources

Here are some of our other related resources you might want to look at.

What are Negative Numbers?

• What are Negative Numbers

Online Negative Number Practice

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• Add Subtract Negative Numbers Online Practice
• Multiplying Negative Numbers Online Practice
• Divide Negative Numbers Online Practice

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• Adding Positive and Negative Numbers (randomly generated)
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• Multiply and Divide Negative Numbers (randomly generated)

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How to Add and Subtract Negatives

Last Updated: March 23, 2023 Fact Checked

This article was reviewed by Joseph Meyer . Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University. There are 7 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 71,683 times.

Problems with negative numbers may look difficult, but there's still only one right answer and with practice you can learn to find it quickly. There are at least two ways you can think your way through these problems. Most people start by learning on a number line.

Using a Number Line

• Here's another way to think of it: adding a negative number is the same as subtracting a positive number. 5 + (-2) = 5 - 2.

• Subtracting a negative number is the same as adding a positive number. 5 - (-2) = 5 + 2.

• Don't get confused by where you start on the number line. The first number only tells you where to begin on the number line. You'll always move right or left based on the type of problem and the second number.

• Here's a memory aid: it takes two lines to draw the two negative signs. It also takes two lines to draw a plus sign, so - - is the same as +, moving to the right.

Without a Number Line

• The absolute value of 6 is 6.
• The absolute value of -6 is also 6.
• 9 has a greater absolute value than 7.
• -8 has a greater absolute value than 5. It doesn't matter that one is negative.

• Rearrange it so you're subtracting the smaller absolute value from the larger one. Ignore the negative sign for now. For our example, write 4 - 2 instead.
• Solve that problem: 4 - 2 = 2. This isn't the answer yet!
• Look at the original problem and check the sign (+ or -) of the number with the largest absolute value number. 4 has a higher value than 2, so we look at that in the problem 2 + (-4). There's a negative sign in front of the 4, so our final answer will also have a negative sign. The answer is -2 .

• 3 - (-1) = 3 + 1 = 4
• (-2) - (-5) = (-2) + 5 = 5 - 2 = 3
• (-4) - (-3) = (-4) + 3 = 3 - 4 = -1

• (-7) - (-3) - 2 + 1
• = (-7) + 3 - 2 + 1
• = 3 - 7 - 2 + 1
• = (-4) - 2 + 1

Community Q&A

• The parentheses around negative numbers just make them easier to spot. You don't need to include them in our own work. Thanks Helpful 12 Not Helpful 0
• You can think of a negative number as debt, although this won't make sense for every problem. For instance, think of 40 + (-30) as having 40 dollars, and owing a debt of 30 dollars. After paying that debt, you end up with 40 + (-30) = 10. The same idea works if you have a debt of 40 dollars and get one more of 30 dollars: your total debt is -40 + (-30) = -70. Thanks Helpful 12 Not Helpful 5

You Might Also Like

• ↑ https://edu.gcfglobal.org/en/algebra-topics/negative-numbers/1/#
• ↑ https://www.chilimath.com/lessons/introductory-algebra/add-and-subtract-numbers-using-the-number-line/
• ↑ https://www.mathsisfun.com/positive-negative-integers.html
• ↑ https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-sub-neg-intro/a/subtracting-negative-numbers-review
• ↑ https://www.mathsisfun.com/numbers/absolute-value.html
• ↑ https://virtualnerd.com/middle-math/integers-coordinate-plane/add-integers/negative-number-addition
• ↑ https://edu.gcfglobal.org/en/algebra-topics/negative-numbers/1/

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Add & subtract neg. nos.

Adding and subtracting negative numbers

Here is everything you need to know about adding and subtracting negative numbers including adding and subtracting positive and negative numbers.

Students will first learn about adding and subtracting negative numbers as part of the number system in 7 th grade.

What is adding and subtracting negative numbers?

Adding and subtracting negative numbers is operating with non-positive numbers. Negative integers are numbers that have a value less than zero, like - \; 5 and - \; 21.

To do this, you can use the number line. If you are adding, move to the right of the number line. If you are subtracting, move the opposite direction, to the left, of the number line.

For example,

To solve - \; 5+6 on a number line, start at - \; 5 and move 6 to the right.

To solve - \; 1-3, start at - \; 1 on the number line and move left 3.

- \; 1-3=- \; 4

Using the number line in this way can help you solve each type of problem, except when adding or subtracting a negative number . For this, a step needs to be added.

There are a few ways to think about how to solve this:

• Think about the - symbol as the opposite \rightarrow so - \; ( - \; 2) means “the opposite of - \; 2 ” which is + \; 2.
• Consider negatives to be cold and positives to be warm. That means - \; ( - \; 2) is like taking away cold. When you take away cold, it gets warmer. So 2 warmer than - \; 5.

All three ways show that - \; 5-( - \; 2)=- \; 3. From this you can establish the rule that subtracting a negative is the same as adding a positive.

The grid below can help to work out whether to add or subtract with a positive or negative number.

If you have two signs next to each other, change them to a single sign.

• If the signs are the same, add.
• If the signs are different, subtract.

Common Core State Standards

How does this relate to 7 th grade math?

• Grade 7 – The Numbers System (7.NS.A.1d) Apply properties of operations as strategies to add and subtract rational numbers.

[FREE] Addition and Subtraction Worksheet (Grade 2, 3, 4 and 7)

Use this quiz to check your grade 2, 3, 4 and 7 students’ understanding of addition and subtraction. 15+ questions with answers covering a range of 2nd, 3rd, 4th and 7th grade addition and subtraction topics to identify areas of strength and support!

How to add and subtract negative numbers

In order to add and subtract negative numbers:

Change two adjacent signs to a single sign.

Circle the first number on the number line.

Use the number line to add or subtract.

Write your final answer.

Adding and subtracting negative numbers examples

Example 1: adding a positive number.

Solve - \; 4+7.

In this case you do not have two signs next to each other so no signs change.

2 Circle the first number on the number line.

The first number in the question is - \; 4.

3 Use the number line to add or subtract.

As you are calculating + \; 7, move 7 spaces right from - \; 4 on the number line:

4 Write your final answer.

Example 2: adding a negative number

Solve - \; 2+- \; 3.

In this case you have the two symbols +- next to each other. As the signs are different, subtract 3 from - \; 2.

- \; 2+- \; 3=- \; 2-3

The first number in the question is - \; 2.

In this case, you are subtracting 3 , so move 3 spaces left from - \; 2 on the number line:

Example 3: subtracting a positive number

Solve - \; 5-2.

In this case, you do not have two signs next to each other, so no signs change.

The first number in the question is - \; 5.

In this case, you are calculating - \; 2 so move 2 spaces left from - \; 5 on the number line:

Example 4: subtracting a negative number

Solve: - \; 8-- \; 10.

In this case, you have a minus and a minus next to each other (--).

Since the signs are the same, replace them with an addition.

- \; 8-- \; 10=- \; 8+10

The first number in the question is - \; 8.

In this case you are calculating + \; 10, so move 10 spaces right from - \; 8 on the number line:

Example 5: mixed operations

Answer the calculation below:

The - \; 5 has been placed in brackets to highlight that the number is negative. Removing or inserting the brackets here does not change the calculation. You can therefore write the same calculation as 7-8-- \; 5.

Since the signs are the same, these two signs are replaced with an addition.

7-8-- \; 5=7-8+5

Note: no other signs change.

The first number in the question is 7.

In this case, you are calculating - \; 8 , so move 8 spaces left from 7 on the number line:

Nex,t you are calculating + \; 5 , so move 5 spaces right from - \; 1 on the number line:

Example 6: word problem

Alina had \$ 12 in her bank account. She purchased a t-shirt for \$ 20. By how much did she overdraw her account?

To answer this question, first write an equation that expresses the question.

In this case, you do not have two signs next to each other so no signs need to change.

The first number in the question is 12.

In this case you are calculating - \; 20.

Instead of subtracting 1 each time, each jump is subtracting 2 so we can subtract 20 in 10 jumps.

She is overdrawn by \$ 8.

Teaching tips for adding and subtracting negative numbers

• Use visuals, such as number lines or counters, to illustrate the concept of adding and subtracting negative numbers.
• When teaching rules, such as when you add two negative numbers you get a positive, make sure to provide an explanation why it works and provide a visual if needed.
• When providing students with practice worksheets, make sure to begin with simple problems and progress to more challenging problems as students become confident with the concept.
• For students that are struggling with mastering the concept, consider the use of student math tutors. This is a strategy where students are in charge of the tutorials for other students. Sometimes allowing other students to use student language allows for deeper understanding.

Easy mistakes to make

• Greater negative does mean a larger number Students sometimes assume that the larger a negative number the greater it is. For example, students might incorrectly assume - \; 3 is greater than 2 because 3 is a larger number.
• Using the rules for two signs when the signs are not together For example, thinking that - \; 5+7 would change to 5-7 (since there is a \; + and a \; - ). Changing the signs only applies when the signs are together. So in the case of - \; 5+7, nothing would change and you would start at - \; 5 on the number line and move 7 spaces to the right. If the calculation was 5-+7 and the signs were together, you would then change it to 5-7.

Related addition and subtraction lessons

• Adding and subtracting integers
• Adding and subtracting rational numbers
• Add and subtract within 100
• Standard algorithm addition
• Order of operations
• Absolute value

Practice adding and subtracting negative numbers questions

1. Solve: – \; 6 + 10

Start at – \; 6 on the number line and move to the right 10 numbers.

2. Solve: – \; 4 +- \; 8.

There is a positive (+) and negative sign (-) together so change them to a subtraction (-) only.

Start at – \; 4 on the number line and move to the left 8 numbers. As each jump is – \; 2, this is 4 jumps.

3. Solve: – \; 9-12.

Start at – \; 9 on the number line and move to the left 12 numbers.

4. Solve: – \; 15- ( – \; 6).

There are two negatives (-) together, so change the signs to an addition (+) sign only.

Start at – \; 15 on the number line and move to the right 6 numbers.

5. Solve: – \; 7+ ( – \; 8)-5+2.

There is a positive (+) and a negative (-) together, so change the signs to a subtraction (-) sign only.

Start at – \; 7 and move 8 places to the left, then move another 5 places to the left, then move 2 places to the right.

6. At 5 am in the morning, the temperature in Fargo, North Dakota was – \; 9^{\circ} \mathrm{F}. By 10 am the temperature had risen by 11^{\circ} \mathrm{F}. What was the new temperature?

The equation you need to solve is – \; 9+11.

Start at – \; 9 on the number line and because it is an addition problem, move to the right 11 numbers.

At 10 am, it was 2^{\circ} \mathrm{F} in Fargo, North Dakota.

Adding and subtracting negative numbers FAQs

The additive inverse when you add any number to its opposite and the sum will always be zero. For example, 4+( - \; 4)=0.

Adding and subtracting negative numbers is similar to adding and subtracting whole numbers in a few ways. For one, you can represent both on a number line to support the visualization of adding and subtracting. In both, addition and subtraction are inverse operations of one another. Adding a negative value is equivalent to subtracting its absolute value, and subtracting a negative value is like adding its absolute value.

The next lessons are

• Multiplication and division
• Types of numbers
• Rounding numbers
• Adding and subtracting fractions
• Multiplying and dividing negative numbers

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What are Negative Numbers?

A guide for negative numbers and their real-world applications

Author Tess Loucka

Published November 7, 2023

Published Nov 1, 2023

Published Nov 7, 2023

• Key takeaways
• A negative number is any number smaller than zero.
• Two negative signs next to each other can be replaced by one positive sign (+). 
• When multiplying or dividing two numbers with the same sign, the result is positive. If the numbers have different signs, the result is negative.

Table of contents

• What are negative numbers?
• Properties of negative numbers

Practice problems

Have you ever woken up in the morning to see frost covering your window and snow piled high on the ground outside? Or maybe you’ve peeked into your freezer to see icicles hanging from the ceiling, and ice covering bags of frozen peas. In these instances, you may have looked at a thermometer wondering just how cold it is. Sometimes it’s so cold the number on the thermometer is less than 0 and the numbers turn into negatives. But what is a negative number anyways? 

We see numbers every day when reading the forecast, making purchases, or getting a score on a quiz, and they’re not always positive ! In our daily life, and in math problems, we come across negative numbers all the time. 

So, let’s go over what negative numbers are and how they’re used. 

Negative numbers are any numbers smaller than zero. They are represented with a minus sign (-) followed by a digit, such as -3, -2, -1, etc. 

The highlighted side of the number line above is the negative numbers side. They are to the left of the 0 because they have a smaller value than 0. Those to the right of the 0 are positive numbers. They have a greater value than 0. 

Properties of Negative Numbers

As stated above, a negative number is any number smaller than zero. However, there are a few more properties of negative numbers that you should know. 

• A negative number does not have to be a round number. Unlike integers which must be round numbers, negative numbers can be decimals or fractions, too.
• Negative numbers are real numbers. Real numbers in math include both rational and irrational numbers.
• Negative numbers are not natural numbers. Natural numbers only refer to positive integers, not including 0.
• Negative numbers are not whole numbers. Whole numbers only include positive integers and 0.

Examples of Negative Numbers in Real Life

We already mentioned that negative numbers appear on thermometers to show us that the temperature is “below zero”, but that’s not the only real-life example of negative numbers. 

Negative numbers are all around us! When we make purchases, the money or credit due is a negative number. Negative numbers also appear on elevation maps to indicate places that are “below sea level”. 

Negative numbers can be used as penalties in games, quizzes, and tests. When you get an answer wrong, you may get -5 points, meaning 5 points are being taken away from your total score. 

In sports, too, negative numbers can be used to denote the scores of teams. One great example is golf. The golfer with the lowest score, which represents the least amount of strokes, wins!

As you can see, there are many real-world applications of negative numbers. They may not be as common as positive numbers, but they’re just as important. 

Now, let’s go over the rules for working with negative numbers. 

Adding and Subtracting Negative Numbers

When working with negative numbers in addition and subtraction problems, there are certain laws that you will find to always be true. Remember these laws to make solving problems with negative numbers in the future easy!

One tip for adding and subtracting negative numbers involves the number signs beside each digit (+ or -):

• If the signs are the same, you can replace them with a plus sign (+). 
• If the signs are different, you can replace them with a minus sign ( -).

Adding Negative Numbers

When adding negative numbers , if the signs of the two numbers you are adding are the same, add the numbers together and keep the sign the same. 

-6 + -2 = -8 

Since + and – are next to each other in this problem, you can replace them with one negative sign (-). So, this problem can also be written as -6 – 2 = -8

If the signs of the two numbers are different, keep the sign of the greater absolute value. 

6 + -2 = 4 

Again, you can replace the + and – with one – sign. So, this problem can also be written as 6 – 2 = 4.

Subtracting Negative Numbers

When subtracting negative numbers , if the signs of the numbers are both negative, switch the two adjacent negative signs to a positive. 

-6 – (-2) = -4 can also be written as -6 + 2 = -4

If the signs of the numbers are different, switch the subtraction sign to an addition sign, and switch the sign of the second number. 

-6 – 2 = -8 becomes -6 + -2 = -8

-2 – 6 = -8 becomes -2 + -6 = -8

Multiplying and Dividing Negative Numbers

The laws to remember when multiplying and dividing negative numbers are actually more straightforward than those for adding and subtracting them. 

All you need to know is that when multiplying or dividing numbers with the same sign, the result will be positive. If the signs are different, the result will be negative.

Multiplying Negative Numbers

When multiplying two negative numbers together, the result will be a positive number. 

-6 x -2 = 12 

When multiplying a positive number with a negative number, the result will be a negative number. 

6 x -2 = -12 

Dividing Negative Numbers

When dividing two negative numbers together, the result is a positive number. 

-6 ÷ -2 = 3

When dividing a positive number and a negative number, the result is a negative number.

6 ÷ -2 = -3 

The more examples of negative number equations you go over, the more comfortable you will be with working with negative numbers. A good math app can provide you with as many examples as you need, as well as detailed solutions and explanations that make learning math easy and fun.

Click on the boxes below to see the answers!

When subtracting negative numbers , remember that two negatives equal a positive. Change the two negative signs into a positive. -10 – (-4) becomes -10 + 4. You can use mental math or a number line to get -6 as your answer. 

Multiplying any two numbers with different signs results in a negative number. So, -4 x 5 is -20. 

 To add two negative numbers, add the digits together and keep the sign the same. So, -9 + -3 becomes -12 . You can also rewrite this as -9 – 3.

FAQs about Negative Numbers

Yes, negative numbers are real numbers.

Negative round numbers are integers, but any fractions or decimals are not.

No, negative numbers are not whole numbers. Whole numbers are only positive round numbers, including 0.

Most negative numbers are rational numbers. If a number can be written as a fraction, that means it is a rational number.

Related Posts

What are Positive Numbers?

What are Number Lines?

Even & Odd Numbers

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Tess Loucka discovered her passion for writing in high school and has not stopped writing since. Combined with her love of numbers, she became a math and English tutor, focusing on middle- and high-school-level topics. Since graduating from Hunter College, her goal has been to use her writing to spread knowledge and the joy of learning to readers of all ages.

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Algebra Topics  - Negative Numbers

Algebra topics  -, negative numbers, algebra topics negative numbers.

Algebra Topics: Negative Numbers

Lesson 3: negative numbers.

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What are negative numbers?

A negative number is any number that is less than zero. For instance, -7 is a number that is seven less than 0.

It might seem a little odd to say that a number is less than 0. After all, we often think of zero as meaning nothing . For instance, if you have 0 pieces of chocolate left in your candy bowl, you have no candy. There's nothing left. It's difficult to imagine having less than nothing in this case.

However, there are instances in real life where you use numbers that are less than zero. For example, have you ever been outside on a really cold winter day when the temperature was below zero? Any temperature below zero is a negative number. For instance, the temperature on this thermometer is -20 , or twenty degrees below zero.

You can also use negative numbers for more abstract ideas. For instance, in finances negative numbers can be used to show debt . If I overdraw my account (take out more money than I actually have), my new bank balance will be a negative number . Not only will I have no money in the bank—I'll actually have less than none because I owe the bank money .

Watch the video below to learn more about negative numbers.

Any number without a minus sign in front of it is considered to be a positive number, meaning a number that's greater than zero. So while -7 is negative seven , 7 is positive seven , or simply seven .

Understanding negative numbers

As you might have noticed, you write negative numbers with the same symbol you use in subtraction: the minus sign ( - ). The minus sign doesn't mean you should think of a number like -4 as subtract four . After all, how would you subtract this?

You couldn't—because there's nothing to subtract it from. We can write -4 on its own precisely because it doesn't mean subtract 4 . It means the opposite of four.

Take a look at 4 and -4 on the number line:

You can think of a number line as having three parts: a positive direction, a negative direction, and zero . Everything to the right of zero is positive and everything to the left of zero is negative . We think of positive and negative numbers as being opposites because they are on opposite sides of the number line.

Another important thing to know about negative numbers is that they get smaller the farther they get from 0. On this number line, the farther left a number is, the smaller it is. So 1 is smaller than 3 . -2 is smaller than 1 , and -7 is smaller than -2 .

Understanding absolute value

When we talk about the absolute value of a number, we are talking about that number's distance from 0 on the number line. Remember how we said 4 and -4 were the same distance from 0? That means 4 and -4 have the same absolute value. We represent taking the absolute value of a number with two straight vertical lines | | . For example, |-3| = 3 . This is read "the absolute value of negative three is three."

Something important to remember: even though negative numbers get smaller as they get further from 0, their absolute value gets bigger . For example, -10 is smaller than -6. However, |-10| is bigger than |-6| because -10 has a greater distance from 0 than -6.

Calculating with negative numbers

Using negative numbers in arithmetic is fairly simple. There are just a few special rules to keep in mind.

Adding and subtracting negative numbers

When you're adding and subtracting negative numbers, it helps to think about a number line, at least at first. Let's take a look at this problem: 6 - 7 . Even though 7 is larger than 6, you can subtract it in the exact same way as any other number, as long as you understand there are numbers smaller than 0.

While the number line makes it easy to picture this problem, there's also a trick you could have used to solve it.

First, ignore the negative signs for a moment. Just find the difference between the two numbers. In this case, it means solving for 7 - 6 , which is 1 . Next, look at your original problem. Which number has the highest absolute value ? In this case, it's -7 . Because -7 is a negative number, our answer will be one too: -1 . Because the absolute value of -7 is greater than the distance between 6 and 0 , our answer ends up being less than 0 .

Adding negative numbers

How would you solve this problem?

Believe it or not, this is the exact same problem we just solved!

This is because the plus sign simply lets you know you're combining two numbers. When you combine a negative number with a positive one, the sum will be less than the original number—so you might as well be subtracting . So 6 + -7 is the same thing as 6 - 7 , and they both equal -1 .

6 + -7 = -1

Whenever you see a positive and negative sign next to each other, you should read it as a negative . Just like 6 + -7 is the same as 6 - 7:

• 10 + -11 is equal to 10 - 11 .
• 3 + -2 is equal to 3 - 2 .
• 50 + -100 is equal to 50 -100 .

This is true whenever you're adding a negative number. Adding a negative number is always the same as subtracting that number's absolute value.

Subtracting negative numbers

If adding a negative number is actually equal to subtracting, how do you subtract a negative number? For example, how do you solve this problem?

If you guessed that you add them, you're right. Here's why: Remember how we said a negative number was the opposite of a positive one? We compared them to you and your mirror image. Your mirror image is your opposite, which means your mirror image's opposite is you . In other words, the opposite of your opposite is you .

In the same way, you can simplify these two minus signs by reading them as two negatives. The first minus sign negates —or makes negative—the second. Because the negative—or opposite—of a negative is a positive, you can replace both minus signs with a plus sign. This means you'd solve for this:

This is a lot easier, to solve, right? If it seems confusing, you can just remember this simple trick: When you see two minus signs back to back , replace them with a plus sign .

So 6 minus negative 3 is equal to 6 plus 3 . That's equal to 9 . In other words, 6 - -3 is 9 .

Remembering all of the rules for adding and subtracting numbers can be overwhelming. Watch the video below for a trick to help you.

Multiplying and dividing negative numbers

There are two rules for multiplying and dividing numbers:

• If you're multiplying or dividing two numbers that are either both positive or both negative, your result will be positive .

• If you're multiplying or dividing a positive number and a negative number, your result will be negative .

That's it! You multiply or divide as normal, then use these rules to determine whether the answer is positive or negative. For instance, take this problem, -3 ⋅ -4 . 3 ⋅ 4 is 12 . Because both numbers we multiplied were negative, the answer is positive : 12 .

-3 ⋅ -4 = 12

On the other hand, if we were to multiply 3 ⋅ -4 , we'd get a different answer:

3 ⋅ -4 = -12

Again, 3 ⋅ 4 is 12 . But because one of our multiples is negative and the other is positive , our answer must also be negative : -12 .

It works the same way for division. -40 / -10 is 4 because - 40 and -10 are both negatives . However, -40 / 10 is -4 because one number is negative and the other is positive .

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Introduction to Negative Numbers

Intro Adding & Subtracting Multiplying & Dividing Exponents

Where did negative numbers come from? Who invented them?

Negative numbers have a long and sometimes contentious history. Mathematicians on the Indian subcontinent had been using negative numbers for a thousand years before Europeans got around to accepting the idea.

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Comparing Integers

If you go back far enough , you'll find that some Europeans didn't even necessarily think that 1 was a number.

(We owe our current so-called "Arabic" number system, including the number zero, to Indian mathematicians, too. Previously, Europeans had previously been stuck using Roman numerals for everything. There was a period in Europe during which using zero, or the " cipher ", as they called it then, could get you imprisoned or even executed.)

Chinese mathematicians beat the Europeans by two millennia in using negative numbers. (Humorous note: When the Indians were writing, they used the "plus" sign, "+", to indicate negative numbers.)

Were Europeans the only ones who didn't "get" negative numbers?

Europeans were not alone in being ignorant of, or dismissive of, or even morally opposed to, negative numbers. Egyptians, nearly two thousand years ago, regarded negative numbers as being ridiculous. Europeans, like the Egyptians, used a system of mathematics that was based purely on geometrical concepts such as area, which is always positive.

This retarded their mathematical progress, because they were thinking of numbers in an unhelpful way. However, when European scholars started translating Arabic texts obtained from North Africa, they were finally exposed to new ways of thinking, and Europe started catching up to the Indians, Chinese, and North-African Arabs.

The point of this history lesson is to explain that many generations of very intelligent people were unable to accept, let alone understand, negative numbers. ( Source [PDF] ) So if you're having difficulty with the concept, you're in good company. But you, like those eighteenth-century Europeans, can finally "get it", too!

What are negative numbers?

Negative numbers are the numbers that are less than zero. On the number line, the negative numbers are the ones to the left of zero.

How do you recognize negative numbers?

Negative numbers are designated by the "minus" sign in front of them; for instance, "negative five" is written as −5 . If you're plotting points on the number line, negative numbers are the ones to the left of zero.

When you first learned your numbers, way back in elementary school, you started with the counting numbers: 1, 2, 3, 4, 5, 6, and so on. Your number line looked something like this:

Later on, you learned about zero, fractions, decimals, square roots, and other types of numbers, so your number line started looking something like this:

Addition, multiplication, and division always made sense — as long as you didn't try to divide by zero — but sometimes subtraction didn't work. If you had " 9 − 5 ", you got 4 :

...but what if you had " 5 −"9 "? You just couldn't do this subtraction, because there wasn't enough "space" on the number line to go back nine units:

You can solve this "space" problem by using negative numbers. The "whole" numbers start at zero and count off to the right; these are the positive integers. The negative integers start at zero and count off to the left:

Note the arrowhead on the far right end of the number line above. That arrow tells you the direction in which the numbers are getting bigger. In particular, that arrow also tells you that the negatives are getting smaller as they move off to the left. For example, −5 is smaller than −4 .

How does the expanded number line help us do subtraction?

For starters, by using the number line that has been expanded to the left into negative numbers, we can now do the subtraction " 5 − 9 ". From zero, we go five units to the right, and then we subtract nine units to the left, as shown below:

We end up four units to the left of zero, so we now know that 5 − 9 = −4 .

Negative numbers might seem a bit weird at first, but that's okay; negatives take some getting used to. Let's look at a few inequalities, to practice your understanding. Refer to the number line below, as necessary.

• Complete the following inequality: 3 _____ 6

Look at the number line above. Since 6 is to the right of 3 , then 6 is larger, so the correct inequality is:

3    <    6

• Complete the following inequality: −3 _____ 6

Look at (or think of) the number line again. Every positive number is to the right of every negative number, so the correct inequality is:

−3    <    6

• Complete the following inequality: −3 _____ −6

Think of the number line again. Since −6 is to the left of −3 , then −3 , being further to the right, is actually the larger number. So the correct inequality is:

−3    >    −6

Complete the following inequality: 0 _____ 1

Zero is less than any positive number, so:

0     <     1

• Complete the following inequality: 0 _____ −1

Zero is greater than any negative number, so:

0    >    −1

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How to Add and Subtract Positive and Negative Numbers

Numbers can be positive or negative.

This is the Number Line :

No Sign Means Positive

If a number has no sign it usually means that it is a positive number.

Example: 5 is really +5

Play with it!

On the Number Line positive goes to the right and negative to the left.

Try the sliders below and see what happens:

Balloons and Weights

Let us think about numbers as balloons (positive) and weights (negative):

This basket has balloons and weights tied to it:

• The balloons pull up ( positive )
• And the weights drag down ( negative )

Adding a Positive Number

Adding positive numbers is just simple addition.

We can add balloons (we are adding positive value)

the basket gets pulled upwards (positive)

Example: 2 + 3 = 5

is really saying

"Positive 2 plus Positive 3 equals Positive 5"

We could write it as (+2) + (+3) = (+5)

Subtracting A Positive Number

Subtracting positive numbers is just simple subtraction.

We can take away balloons (we are subtracting positive value)

the basket gets pulled downwards (negative)

Example: 6 − 3 = 3

"Positive 6 minus Positive 3 equals Positive 3"

We could write it as (+6) − (+3) = (+3)

Adding A Negative Number

Now let's see what adding and subtracting negative numbers looks like:

We can add weights (we are adding negative values)

Example: 6 + (−3) = 3

"Positive 6 plus Negative 3 equals Positive 3"

We could write it as (+6) + (−3) = (+3)

The last two examples showed us that taking away balloons (subtracting a positive) or adding weights (adding a negative) both make the basket go down.

So these have the same result :

• (+6) − (+3) = (+3)
• (+6) + (−3) = (+3)

In other words subtracting a positive is the same as adding a negative .

Subtracting A Negative Number

Lastly, we can take away weights (we are subtracting negative values)

Example: What is 6 − (−3) ?

6−(−3) = 6 + 3 = 9

Yes indeed! Subtracting a Negative is the same as adding!

Two Negatives make a Positive

What Did We Find?

Adding a positive number is simple addition ..., positive and negative together ..., example: what is 6 − (+3) .

6−(+3) = 6 − 3 = 3

Example: What is 5 + (−7) ?

5+(−7) = 5 − 7 = −2

Subtracting a negative ...

Example: what is 14 − (−4) .

14−(−4) = 14 + 4 = 18

It can all be put into two rules :

They are "like signs" when they are like each other (in other words: the same).

So, all you have to remember is:

Two like signs become a positive sign

Two unlike signs become a negative sign

Example: What is 5+(−2) ?

+(−) are unlike signs (they are not the same), so they become a negative sign .

5+(−2) = 5 − 2 = 3

Example: What is 25−(−4) ?

−(−) are like signs, so they become a positive sign .

25−(−4) = 25+4 = 29

Starting Negative

What if we start with a negative number?

Using The Number Line can help:

Example: What is −3+(+2) ?

+(+) are like signs, so they become a positive sign .

−3+(+2) = −3 + 2

−3+(+2) = −3 + 2 = −1

Example: What is −3+(−2) ?

+(−) are unlike signs, so they become a negative sign .

−3+(−2) = −3 − 2

−3+(−2) = −3 − 2 = −5

Now Play With It!

A Common Sense Explanation

And there is a "common sense" explanation:

If I say "Eat!" I am encouraging you to eat (positive)

If I say "Do not eat!" I am saying the opposite (negative).

Now if I say "Do NOT not eat!", I am saying I don't want you to starve, so I am back to saying "Eat!" (positive).

So, two negatives make a positive, and if that satisfies you, then you are done!

Another Common Sense Explanation

A friend is + , an enemy is −

A Bank Example

Example: last year the bank subtracted $10 from your account by mistake, and they want to fix it..

So the bank must take away a negative $10 .

Let's say your current balance is $80, so you will then have:

$80−(−$10) = $80 + $10 = $90

So you get $10 more in your account.

A Long Example You Might Like

Ally's points.

Ally can be naughty or nice. So Ally's parents have said

"If you are nice we will add 3 points (+3). If you are naughty, we take away 3 points (−3). When you reach 30 Points you get a toy."

So when we subtract a negative, we gain points (i.e. the same as adding points).

See: both " 15 − (+3) " and " 15 + (−3) " result in 12.

It doesn't matter if you subtract positive points or add negative points, you still end up losing points.

Try These Exercises ...

Now try This Worksheet , and see how you go.

And also try these questions:

Negative Numbers

A negative number is a number whose value is always less than zero and it has a minus (-) sign before it. On a number line, negative numbers are represented on the left side of zero. For example, -6 and -15 are negative numbers. Let us learn more about negative numbers in this lesson.

What are Negative Numbers?

Negative numbers are numbers that have a minus sign as a prefix. They can be integers, decimals, or fractions. For example, -4, -15, -4/5, -0.5 are termed as negative numbers. Observe the figure given below which shows how negative numbers are placed on a number line .

Negative Integers

Negative integers are numbers that have a value less than zero. They do not include fractions or decimals. For example, -7, -10 are negative integers.

Rules for Negative Numbers

When the basic operations of addition, subtraction , multiplication, and division are performed on negative numbers, they follow a certain set of rules.

• The sum of two negative numbers is a negative number. For example, -5 + (-1) = -6
• The sum of a positive number and a negative number is the difference between two numbers. The sign of the bigger absolute value is placed before the result. For example, -9 + 3 = -6
• The product of a negative number and a positive number is a negative number. For example, -9 × 2 = -18
• The product of two negative numbers is a positive number. For example, -6 × -3 =18
• While dividing negative numbers, if the signs are the same, the result is positive. For example, -56 ÷ -7 = 8
• While dividing negative numbers, if the signs are different, the result is negative. For example, -32 ÷ 4 = -8

Adding and Subtracting Negative Numbers

For adding and subtracting negative numbers, we need to remember the following rules.

Addition of Negative Numbers

Case 1: When a negative number is added to a negative number, we add the numbers and use the negative sign in the answer. For example, -7 + (- 4) = -7 - 4 = -11. In other words, the sum of two negative numbers always results in a negative number.

This can be understood with the help of a number line. The number line rule says, " To add a negative number we move to the left on the number line ". Therefore, observe the following number line, and apply the rule on -7 + (- 4). We can see that when we start from -7 and move 4 numbers to the left, it brings us to -11.

Case 2: When a positive number is added to a negative number, we find their difference and use the sign of the larger absolute value in the answer. For example, -9 + (5) ⇒ - 4. Since we are using the sign of the greater absolute value, the answer is -4.

This can be understood better with the help of a number line. The number line rule says, " To add a positive number we move to the right on the number line ". Observe the following number line and apply the rule on -9 + (+5). We start from -9 and move 5 numbers to the right that brings us to -4.

Subtraction of Negative Numbers

The subtraction of negative numbers is similar to addition. We just need to remember a rule which says:

Rule of Subtraction: Change the operation from subtraction to addition, and change the sign of the second number that follows.

Case 1: When we need to subtract a positive number from a positive number, we follow the subtraction rule given above. For example, 5 - (+6) becomes 5 + (-6) = 5 - 6 = -1.

Now, if we apply the rule of the number line on 5 + (-6), to add a negative number, we move to the left. Therefore, we start with 5 and move 6 numbers to the left, which brings us to -1.

Case 2: When we need to subtract a positive number from a negative number, we will follow the same rule of subtraction which says:

For example, -3 - (+1), will become -3 + (-1). This can be simplified as -3 -1 = -4.

Now, if we apply the rule of the number line on -3 + (-1), to add a negative number we move to the left. Therefore, we start with -3 and move 1 number to the left, which brings us to -4.

Case 3: When we need to subtract a negative number from a negative number, we will follow the rule of subtraction:

For example, -9 - (-12) ⇒ -9 + 12 = 3. Here, 12 becomes positive. We use the sign of the bigger absolute value that is 12 and the answer is 3.

Multiplication and Division of Negative Numbers

There are two basic rules related to the multiplication and division of negative numbers.

Multiplying Positive and Negative Numbers

• Rule 1: When the signs of the numbers are different, the result is negative. (-) × (+) = (-). In other words, when we multiply a negative number with a positive number, the product is always negative. For example, -3 × 6 = -18.
• Rule 2: When the signs of the numbers are the same, the result is positive. (-) × (-) = (+); (+) × (+) = (+). In other words, when we multiply two negative or two positive numbers, the product is always positive. For example, -3 × - 6 = 18.

Dividing Positive and Negative Numbers

• Rule 1: When we divide a negative number by a positive number, the result is always negative. (-) ÷ (+) = (-). For example, (-36) ÷ (4) = -9
• Rule 2: When we divide a negative number by a negative number, the result is always positive. (-) ÷ (-) = (+) For example, (-24) ÷ (-4) = 6

Negative Integers With Exponents

There are two basic rules related to negative integers with exponents:

• If a negative integer has an even number in the exponent, then the final product will always be a positive integer. For example, -4 6 = -4 × -4 × -4 × -4 × -4 × -4 = 4096
• If a negative integer has an odd number in the exponent, then the final product will always be a negative integer. For example, -9 3 = -9 × -9 × -9 = -729

☛ Related Topics

• Positive Rational Numbers
• Natural Numbers
• Whole Numbers
• Real Numbers
• Rational Numbers
• Irrational Numbers
• Counting Numbers

Negative Numbers Examples

Example 1: Add the given negative numbers.

a.) -45 and -78

b.) -90 and -67

a.) Since both -45 and -78 are negative numbers, we will add the negative integers and place a negative sign before the sum.

45 + 78 = 123

Now, we will place a minus sign before the sum. Thus, the answer is -123.

b.) To add -90 and -67, we will add the negative numbers and place a negative sign before the sum.

90 + 67 = 157

Now, we will place a minus sign before the sum. Thus, the answer is -157.

Example 2: Subtract the given negative integers: Subtract -5 from -8

When we need to subtract a negative number from a negative number, we will follow the rule of subtraction, ' Change the operation from subtraction to addition, and change the sign of the second number that follows.'

In this case, -8 - (-5) ⇒ -8 + 5 = -3.

Example 3: Simplify the negative integers:

a.) (-3) × (-2)

b.) -24 ÷ -3

a.) To multiply (-3) × (-2), we will multiply the given negative numbers and the sign of the product will be positive. Therefore, in this case, the product of (-3) × (-2) = 6

b.) In order to divide the negative numbers, (-24) ÷ (-3), we will divide them and the sign of the answer will be positive. In this case, (-24) ÷ (-3) = 8

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Practice Questions on Negative Numbers

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FAQs on Negative Numbers

What are negative numbers in math.

A negative number is a number whose value is always less than zero and it has a minus (-) sign before it. On a number line , negative numbers are shown to the left of zero. For example, - 2, - 3, - 4, - 5 are called negative numbers.

What are the Rules for Negative Numbers?

When the basic operations of addition , subtraction, multiplication , and division are performed on negative numbers, they follow a certain set of rules.

• The sum of two negative numbers is a negative number. For example, -3 + (-1) = -4
• The sum of a positive number and a negative number is the difference between the two numbers. The sign of the bigger absolute value is placed before the result. For example, -6 + 3 = -3
• The product of a negative number and a positive number is always a negative number. For example, -5 × 2 = -10
• The product of two negative numbers is a positive number. For example, -5 × -3 =15
• While dividing negative numbers, if the signs are the same, the result is positive. For example, (-28) ÷ (-7) = 4
• While dividing negative numbers, if the signs are different, the result is negative. For example, (-21) ÷ (3) = -7

What is the Sum of Two Negative Numbers?

The sum of two negative numbers is always a negative number. For example, (-7) + (-2) = -9

What are Negative Numbers used for?

There are situations in real life where we use numbers that are less than zero. Negative numbers are used to measure temperature. For example, the lowest possible temperature is absolute zero which is expressed as -273.15°C on the Celsius scale, and -459.67°F on the Fahrenheit scale. Negative numbers are also used to measure the geographical locations that are below the sea level and which are expressed in negative integers like -100 ft Mean Sea Level.

How to Multiply Negative Numbers?

There are two basic rules related to the multiplication of negative numbers.

• Rule 1: When the signs of the numbers are different, the result is negative. In other words, when we multiply a negative number with a positive number, the product is always negative. For example, -2 × 6 = -12.
• Rule 2: When the signs of the numbers are the same, the result is positive. In other words, when we multiply two negative or two positive numbers, the product is always positive. For example, -4 × - 6 = 24.

How to Divide Negative Numbers?

The rules that are applied for the multiplication of numbers are also used in the division of negative numbers.

• Rule 1: When the signs of the numbers are different, the result is negative. In other words, when we divide a negative number with a positive number, the answer is always negative. For example, -12 ÷ 3 = -4.
• Rule 2: When the signs of the numbers are the same, the result is positive. In other words, when we divide two negative numbers or two positive numbers, the answer is always positive. For example, -14 ÷ - 2 = 7.

What is the Difference Between Negative Integers and Positive Integers?

The main difference between negative integers and positive integers is that negative integers have a value less than zero and positive integers have a value greater than zero. It should be noted that zero is neither a positive integer nor a negative integer.

How do you Add Two Negative Integers?

Adding two negative integers together is easy because we just add the given numbers and then place a negative sign in front of the sum. For example, (-2) + (-5) = -7

What are the Rules For Subtracting Negative Numbers?

There is a basic rule for subtracting negative numbers. "Change the operation from subtraction to addition, and change the sign of the second number that follows". For example, let us subtract -2 - (-5). In this case, we change the operation from subtraction to addition and change the sign of (-5) to (+5). This makes it -2 + (+5) = -2 + 5 = 3.

How to Subtract Negative Numbers?

When we subtract negative numbers, we just need to remember a rule which says: Change the operation from subtraction to addition, and change the sign of the second number that follows. Now, let us apply this rule, for example, subtract 5 from -8. This means -8 - (5). After applying the rule, -8 - (5) becomes -8 + (-5) = -13.

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• Negative Numbers Worksheet Ks2

Negative numbers worksheet – KS2 resources and advice for teaching negative numbers

Two sets of PDF worksheets

Use our negative numbers worksheets and the advice below to tackle this particular area of mathematics with your KS2 pupils…

Negative numbers worksheet

What are negative numbers, where are negative numbers taught in the primary curriculum , initial things to think about, introducing negative numbers using a number line, common early misconceptions, examples of negative number sats questions.

Our negative numbers worksheet will give your KS2 pupils plenty of negative number practice. Pupils will practise:

• Counting backwards through zero including negative numbers
• Solving number and practical problems that involve negative numbers
• Interpreting negative numbers in context
• Counting forwards and backwards with positive and negative whole numbers including through zero

Download this negative numbers worksheet from the top of this page.

This download also contains three sets of negative number worksheets from White Rose Maths, covering counting backwards and forwards in negative numbers to problem-solving with negative numbers.

Negative numbers are a type of numerical value that represent quantities less than zero. They are essentially the opposite or inverse of positive numbers. 

Teaching negative numbers is crucial as it enables understanding of real-world situations like temperatures below zero and financial transactions. It also develops mathematical skills for operations, algebraic reasoning, and problem-solving. 

The primary national curriculum introduces the concept of negative numbers in Year 4 where the children learn to count backwards through zero and into negative numbers.   

Statutory national curriculum objectives

• Count backwards through zero including negative numbers (Year 4)
• Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers including through zero (Year 5)
• Use negative numbers in context, and count intervals across zero (Year 6)  
• Solving number and practical problems that involve negative numbers (Year 6)  

Non-statutory guidelines (Year 6) 

• Using the number line, pupils use, add and subtract positive and negative integers for measures such as temperature. 
• Pupils draw and label a pair of axes in all four quadrants with equal scaling. This extends their knowledge of one quadrant to all four quadrants, including the use of negative numbers. 

Introducing children to numbers below zero opens up a new world to them. The idea that numbers can be less than zero introduces a totally new way of thinking about maths.   

One of the challenging things to get children to remember is that when we use negative numbers, the larger the digit the smaller the number.

Naturally, because they’ve had seven or eight years of experience of learning about numbers gaining value as the digits get bigger, children often initially see larger digits as being a bigger number even when the negative context is introduced. 

“The idea that numbers can be less than zero introduces a totally new way of thinking about maths”

This is where using ‘zero’ and a number line is very helpful. Teaching children on a number line and recognising that when numbers get further away from the zero (on the negative side) the smaller the number is, should be one of the first things to think about when we address the Year 4 objective to ‘count back through zero including negative numbers’. 

Another new concept for the children is recognising the negative symbol (-) to represent negative numbers and not just when used for subtraction.

This is where mathematical language is especially important, as the children should begin to use the word ‘negative’ when using the – symbol in this context. It is therefore important that you continue to model that language in class (-5 is ‘negative 5’ for example).   

Using a number line when teaching negative numbers is a helpful visual tool that aids in understanding and conceptualizing the concept. It helps with: 

• Visual representation : A number line provides a clear visual representation of numerical order, including positive and negative numbers. It allows students to see the relationship between numbers. 
• Sequential order : It helps students understand that numbers are arranged in a specific order. They can see that as they move from left to right, the numbers increase, and as they move from right to left, the numbers decrease. 
• Relating numbers : The number line helps students understand the relationship between different numbers. They can easily see that numbers to the right of zero (positive numbers) are greater than zero, while numbers to the left of zero (negative numbers) are less than zero. 
• Adding and subtracting : The number line is useful for teaching addition and subtraction of negative numbers. Students can physically move along the number line to understand the effect of adding or subtracting a specific value. 
• Real-world examples : By using a number line, teachers can provide real-world examples that students can relate to, such as temperatures, bank balances, and elevations. This helps students connect the abstract concept of negative numbers to practical scenarios. 

Adding a negative number makes the value smaller 

Children may struggle to understand the concept of adding negative numbers. Some pupils may mistakenly believe that any calculation involving a negative number always results in a smaller value.

However, it’s crucial to clarify that it depends which way round we do it.

For example, if we start with a negative number and add a positive number, the answer is larger than the original negative value: -4 + 3 = -1. (Negative one is larger than negative four.)  But, if we start with a positive number, and add a negative number, the answer is smaller than the original positive value: 4 + -3 = 1. (One is smaller than four.) 

Activity example

To begin with, start on the ‘right’ side of the number line (on the positive side) and carry out a number of calculations where you start with a positive number and add a negative number. Don’t cross through zero yet as this can be done once the children are more confident.

The children will spot a pattern that each time a negative number is added to a positive number, the answer gets smaller. They will assume that when adding a positive number and negative number together you will always get a smaller answer.

You can then ‘test’ this by starting on the ‘left’ side of zero (the negative side) and take a negative number and add a positive number to it. They will quickly notice that this way round the answer actually gets bigger. 

Once the children are confident in recognising negative numbers and using number lines to cross through zero, etc, they can move on to adding and subtracting negative numbers with whole numbers.

Again, this is where it is important to think about the number line and explain how when negative numbers have a whole number added to them, the answer moves closer to (and through if required) the zero.

Do not underestimate how important the number line element of negative numbers is! Spend plenty of time getting the children confident this way first. 

“Do not underestimate how important the number line element of negative numbers is”

Negative numbers don’t exist in real life  

Pupils may find it difficult to relate negative numbers to real-life situations. They might think that negative quantities or temperatures, for example, are impossible or have no practical significance.

It can be helpful to provide examples such as temperatures below zero , or the concept of debt, to demonstrate real-life applications of negative numbers. Contextualising negative numbers is important to add more meaning and use to learning. 

Activity example 

To address these misconceptions, we should be using concrete examples, visual representations and real-world applications to help students develop a solid understanding of negative numbers.

By providing multiple opportunities for hands-on practice and meaningful discussions, we can help students overcome these misconceptions and build a strong foundation in mathematics. 

You can do this via simple examples such as showing your class: 

• Temperature charts (of different places during winter, for example) and comparing real-life negative numbers.   
• How money can actually go below zero when talking about ‘debt’.
• Examples of thermometers reading less than zero. 

Real-world applications are what really allow children to move forward with their understanding of negative numbers and shows them how ‘real’ these numbers are.

It allows us to bring negative numbers into real life rather than just seeing them as patterns on a number line, or figures we add or subtract.    

“Real-world applications are what really allow children to move forward with their understanding of negative numbers”

These eight questions have all been taken from previous papers. 

James Grocott is a Year 4 teacher, maths lead, and deputy head in Suffolk.  

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Negative numbers

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

10 March 2023

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Very clear and easy to use. Sensible start point and progression builds up through questions.

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Not used yet will come back and review once used but thanks for posting

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