problem solving addition of integers

Integer Addition

Learn about integer addition with example problems and interactive exercises..

Solution: This problem is quite simple: just add $3 and $6 and the result is $9.

The problem above can be solved using addition of  integers . Owing $3 can be represented by  – 3 and owing $6 can be represented by  – 6. The problem becomes: – 3 +  – 6 =  – 9

Look at the number line below. If we start at 0, and move 3 to the left, we land on  – 3. If we then move another 6 to the left, we end up at  – 9.

Rule: The sum of two negative integers is a negative integer.

Example 1: Find the sum of each pair of integers. You may draw a number line to help you solve this problem.

Do not confuse the sign of the integer with the operation being performed. Remember that: – 2 +  – 9 =  – 11 is read as  Negative 2 plus negative 9 equals negative 11.

Rule: The sum of two positive integers is a positive integer.

Example 2: Find the sum of each pair of integers. You may draw a number line to help you solve this problem.

Do not confuse the sign of the integer with the operation being performed. Remember that:

+ 29 +  + 16 =  + 45 is read as  Positive 29 plus positive 16 equals positive 45.

So far we have added integers with like signs (either both negative or both positive). What happens when we add integers with unlike signs? How do we add a positive and a negative integer, or a negative and a positive integer?

Procedure: To add a positive and a negative integer (or a negative and a positive integer), follow these steps:

1. Find the  absolute value  of each integer.

2. Subtract the smaller number from the larger number you get in Step 1.

3. The result from Step 2 takes the sign of the integer with the greater absolute value.

We will use the above procedure to add integers with unlike signs in Examples 3 through 7. Refer to the number line to help you visualize the process in each example. We will use money as an alternative method for adding integers.

Example 3: Find the sum of  + 7 and  – 4.

Step 1: | + 7| = 7 and | – 4| = 4

Step 2: 7 – 4 = 3

Step 3: The number 3 will take a positive sign since  + 7 is farther from zero than  – 4.

Solution 1:  + 7 +  – 4 =  + 3

Solution 2: If you start with $7 and you owe $4, then you end up with $3.

Example 4: Find the sum of  – 9 and  + 5.

Step 1: | – 9| = 9 and | + 5| = 5

Step 2: 9 – 5 = 4

Step 3: The number 4 will take a negative sign since  – 9 is farther from 0 than  + 5.

Solution 1:  – 9 +  + 5 =  – 4

Solution 2: If you owe $9 and you are paid $5, then you are still short $4.

Example 5: Find the sum of  + 6 and  – 7.

Step 1: | + 6| = 6 and | – 7| = 7

Step 2: 7 – 6 = 1

Step 3: The number 1 will take a negative sign since  – 7 is farther from 0 than  + 6.

Solution 1:  + 6 +  – 7 =  – 1

Solution 2: If you start with $6 and you owe $7, then you are still short $1.

Example 6: Find the sum of  – 6 and  + 7.

Step 1: | – 6| = 6 and | + 7| = 7

Step 3: The number 1 will take a positive sign since  + 7 is farther from 0 than  – 6.

Solution 1:  – 6 +  + 7 =  + 1

Solution 2: If you owe $6 and you are paid $7, then you end up with $1.

Example 7: Find the sum of  + 9 and  – 9.

Step 1: | + 9| = 9 and | – 9| = 9

Step 2: 9 – 9 = 0

Step 3: The integer 0 has no sign.

Solution 1:  + 9 +  – 9 = 0

Solution 2: If you start with $9 and you owe $9, then you end up with $0.

In Example 7 you will notice that the integers  + 9 and  – 9 are  opposites . Look at the problems below. Do you see a pattern?

– 100 +  + 100 = 0

+ 349 +  – 349 = 0

– 798 +  + 798 = 0

Rule:   The sum of any integer and its opposite is equal to zero.

Summary: Adding two positive integers always yields a positive sum; adding two negative integers always yields a negative sum. To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values. The result takes the sign of the integer with the larger absolute value. The sum of any integer and its opposite is equal to zero.

Directions: Read each question below. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

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A and S Integers

Adding and subtracting integers

Here you will learn strategies on how to add and subtract integers, including using visual models as well as the number line.

Students will first learn about integers in 6th grade math as part of their work with the number system and expand that knowledge to operations with integers in the 7th grade.

Every week, we teach lessons on adding and subtracting integers to students in schools and districts across the US as part of our online one-on-one math tutoring programs. On this page we’ve broken down everything we’ve learnt about teaching this topic effectively.

What are adding and subtracting integers?

Adding and subtracting integers is when you add or subtract two or more positive or negative numbers together.

You can add and subtract integers using visual models or a number line.

Adding Integers \hspace{2cm}

Subtracting Integers \hspace{2cm}

[FREE] Addition and Subtraction Worksheet (Grade 2 to 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!

Common Core State Standards

How does this apply to 6th grade math and 7th grade math?

• Grade 6: Number System (6.NS.C.6) Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
• Grade 7: Number System (7.NS.A.1) Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

How to add and subtract integers?

In order to add and subtract integers using counters:

• Represent the problem with counters identifying zero pairs with addition or adding zero pairs when necessary for subtraction.

The answer is the leftover counters.

In order to add and subtract integers using a number line:

To add, start at the first number and move to the second number; to subtract, start from the second number and move to the first number.

Write your answer.

Adding and subtracting integers examples

Example 1: adding integers with different signs using counters.

Add: -2 + 7 = \, ?

Represent the problem with counters, identifying zero pairs with addition or adding zero pairs when necessary for subtraction.

There are two zero pairs with 5 positive counters left.

2 The answer is the leftover counters.

Answer: -2 + 7 = 5

Example 2: subtracting integers with counters

Subtract: -4-(-5) = \, ?

-4 remove -5. Add 1 zero pair in order to remove -5.

-4-(-5) = 1

Example 3: adding integers with a number line

Add: -8 + (-5) = \, ?

-8 + (-5) is addition. Start at -8 and move in the negative direction (left) 5 places. You land at -13.

-8 + (-5) = -13

Example 4: subtracting integers with a number line

Solve: 7-(+9) = \, ?

From positive 9 move in the negative direction until you get to 7. You move 2 places to the left, which is -2.

7-(+9) = -2

Teaching tips for adding and subtracting integers

• Adding and subtracting integers is a foundational skill for Algebra 1. Using counters and/or a number line helps students formulate conceptual understanding of the concept.
• Using actual hand-held counters help students to manipulate the zero pairs instead of using digital counters.
• Have students try and identify the patterns with adding and subtracting integers so that they can figure out the rules on their own.
• Although practice integer worksheets have their place, have students practice problems through digital games or scavenger hunts around the room to make it engaging.

Easy mistakes to make

Related addition and subtraction lessons

This adding and subtracting integers topic guide is part of our series on adding and subtracting. You may find it helpful to start with the main adding and subtracting topic guide for a summary of what to expect or use the step-by-step guides below for further detail on individual topics. Other topic guides in this series include:

• Addition and subtraction
• Standard algorithm addition
• Adding and subtracting negative numbers
• Adding and subtracting rational numbers
• Add and subtract within 100

Practice adding and subtracting integers

1. Look at the model below to add -7 + 6.

There are 6 zero pairs with one negative counter leftover.

-7 + 6 = -1

2. Subtract: -15-(9) = \, ?

Using the rule, change the sign of the second number, +9 becomes -9.

Then add the two numbers together.

-15 + (-9) = -24

From 9 move left 24 units, you get to -15.

So, -15-(9) = -24

3. Add: 8 + (-19) = \, ?

Using the rule, since the signs of the numbers are different, the difference between 8 and 19 is 11.

19 is the larger number, and it is negative, so the sum will be negative.

8 + (-19) = -11

You can also check your answer using a number line.

Start at 8 and move 19 places in the negative direction. You land at -11.

4. Subtract: -14-(-8) = \, ?

Using the rule for subtracting integers, change the sign of the second number.

-8 will become +8.

Then add the number to the first one, -14 + 8 = -6

You can also use a number line to check your answer.

From -8 move left 6 places until you get to -14.

So, -14-(-8) = -6

5. Add: -13 + (-12) = \, ?

Using the rule, the signs of the numbers are both negative, so add the numbers.

The sum is negative too.

-12 + (-13) = -25

6. On a February day in Chicago, the morning temperature was -3 degrees Fahrenheit. Later that day, the temperature increased by 4 degrees. What is the new temperature in degrees?

-3 increased by 4 degrees is -3 + 4.

The signs of the numbers are different.

The difference between 3 and 4 is 1.

4 is the larger number, so the sum is positive.

Adding and subtracting integers FAQs

Yes, using the number line when adding and subtracting integers will always work. However, it might not always be the fastest way to get the answer.

A zero pair is a number and its opposite. For example, 5 and -5 are a zero pair. The opposite of positive integers is negative integers.

The sum of zero pairs is an additive inverse because the sum is 0.

Addition of integers and subtraction of integers help when simplifying algebraic expressions and also when factoring algebraic expressions.

The positive sign does not necessarily need to be written in front of a number. For example, +5 is the same as 5. The positive sign is understood.

The next lessons are

• Multiplication and division
• Multiplying and dividing integers
• Types of numbers
• Rounding numbers
• Solving one step equations
• Order of operations

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Integer Addition

Adding integers.

Below is a quick summary of the rules for adding integers.

Integer addition is a very straightforward process. Just follow the basic steps provided below and you’ll get the correct answers every time. There are two cases when adding integers. The first scenario is when we add integers having the same sign. These are the steps:

Case 1: Steps/Rules for Adding Integers with the Same Sign

Step 1: Take the absolute value of each number.

Step 2: Add the absolute values of the numbers.

Step 3: Keep the same sign.

For more practice, click the link below:

• Adding Integers Practice Problems with Answers

Examples of Integer Additions with Like Sign

Example 1 : Add the integers below that have the same sign.

• Step 1: Take the absolute values of the numbers.
• Step 2: Add the absolute values.
• Step 3: Keep the same sign which is positive.

Example 2 : Add the integers below that have the same sign.

• Step 1: Find the absolute values of negative 10 and negative 3.
• Step 2: Find the sum of their absolute values.
• Step 3: Keep the same sign which is negative.

Now here’s the little twist. We are now going to add integers that have different signs.

Case 2: Steps/Rules for Adding Integers with Different Signs

Step 2: Subtract the number with a smaller absolute value from the number with bigger or larger absolute value.

Step 3: Copy the sign of the number with the bigger or larger absolute value.

Examples of Integer Additions with Unlike Signs

Example 1 : Add the integers below that have different signs.

• Step 2: Since the absolute value of positive 7 is less than the absolute value of negative 15, subtract 7 from 15.
• Step 3: The absolute value of negative 15 is greater than the absolute value of positive 7. Therefore, the final answer will have a negative sign because we copy the sign the sign of the number that has a bigger absolute value.

Example 2 : Add the integers below that have different signs.

• Step 1: Find the absolute value of each number.
• Step 2: Since the absolute value of negative 18 is less than the absolute value of positive 23, we will subtract 18 from 23.
• Step 3: The final answer will have a positive sign because we will get it from positive 23 which has a larger absolute value than negative 18.

Take a quiz:

• Adding Integers Quiz

You might also like these tutorials:

• Subtracting Integers
• Multiplying Integers
• Dividing Integers

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How to Add and Subtract Integers: Word Problems

Mastering the art of tackling word problems involving the addition and subtraction of integers is a vital skill in the mathematical universe. Integers, which include positive, negative, and zero, are more nuanced than their natural number counterparts. To craft a highly detailed, comprehensive, and sophisticated guide, let's dive into the labyrinth of integers, unraveling the mystery of word problems step-by-step.

A Step-by-step Guide to Solve Integers Addition and Subtraction: Word Problems

Here is a step-by-step guide to solving word problems of integers addition and subtraction:

Step 1: Decipher the Problem

The journey begins with an intensive reading of the word problem. Identify the integers involved, noting their signs (\(+\) or \(-\)), and the operations stated or implied (addition or subtraction). Understand the context and constraints of the problem to guide your strategy.

Step 2: Pinpoint the Unknowns

Next, determine what the problem demands you to find. This could be an unknown quantity or a relationship between different quantities. Assign variables to these unknowns, typically ‘\(x\)’, ‘\(y\)’, or ‘\(z\)’.

Step 3: Translate into Mathematical Language

Now, morph the word problem into an equivalent mathematical expression or equation. Expressions such as “increased by” or “more than” often signify addition, while “decreased by” or “less than” hint towards subtraction. This translation serves as a bridge between the narrative of the problem and the mathematical steps to solve it.

Step 4: Construct the Equation(s)

Based on your translation, construct an equation or a system of equations that encapsulate the conditions outlined in the problem. Be vigilant of the signs of the integers; a positive integer added to a negative integer can be treated as subtraction and vice versa.

Step 5: Resolve the Equation(s)

Once your equation(s) are set, deploy your arithmetic and algebraic skills to solve them. Remember the basic rules of integer arithmetic, such as the fact that subtracting a negative integer is equivalent to adding a positive one.

Step 6: Validate Your Solution

Substitute your solution back into the original equation(s) to verify its correctness. If it stands the test, your solution is accurate. If it fails, reexamine your steps to identify potential missteps or miscalculations.

Step 7: Answer the Query

The final act is responding to the original question asked in the problem. Ensure your answer aligns with the question and is phrased appropriately, incorporating units if necessary.

by: Effortless Math Team about 1 year ago (category: Articles )

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Adding Integers: Definition, Rules for Addition, Examples

What is adding integers, how to add integers, what are the rules for adding integers, solved examples on adding integers, practice problems on adding integers, frequently asked questions on adding integers.

Finding the sum of two or more integers is known as adding integers . These integers may have the same or different signs. 

We can define integers as numbers that can be written without a fractional component. Fractions can be positive, negative, or zero . The set of integers includes positive integers, negative integers, and 0. It is given by $Z = \left\{…,-3,-2,\;-\;1, 0, 1, 2, 3, …\right\}$

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Three Main Cases to Consider When Adding Integers

When adding two integers, we come across the following situations:

• Addition of two positive integers $(a + b)$
• Addition of two negative integers  $\left[(\;-a) + (\;-b)\right]$
• Addition of a negative integer and a positive integer $\left[a +(\;-b)\right]$

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We can add integers with the help of the rules for addition of integers with different signs, which have been discussed below.

Positive integer $+$ Positive integer $=$ Positive integer

Negative integer $+$ Negative integer $=$ Negative integer

When two integers of the different signs are added, we perform subtraction and add the sign of the number with the largest absolute value.

Let’s learn these rules in detail with examples.

When adding two or more integers, certain rules must be followed. 

• The sum of an integer and its additive inverse is equal to 0. 

Example: $2 + (\;–2) = 0$

• The addition of two positive integers will be positive. 

Example: $3 + 5 = 8$

• The addition of two negative integers will be negative. 

Example: $–3 + (\;– 5) =  –8$

When two integers of the different signs are added, only subtraction will be performed and the sign of the result will be the same as the number with the largest absolute value. 

Examples: $–3 + 5 =  2$

      $3 + (\;– 5) =  –2$

• The result of adding integers with 0 is the same number. 

Example: $2 + 0 = 2$.

Integer Addition Rules Chart

The rules for addition with examples of adding integers are summarized in the table below:

Adding Integers with the Same Sign

The addition of two positive integers will have a positive sign. 

Example: $5 + 8 = 13$

The addition of two negative integers will have a negative sign. Here, we find the sum of the absolute values and add the negative sign to the sum.

Example: $–5 + (\;– 8) =  –13,$

Adding Integers with Different Signs

Example: $– 4 + 8 = 4$

$5 + (\;– 7) =  –2$

In other words, to add integers with different signs, subtract the absolute values of two integers with different signs, and then attach the sign of the number with the greater absolute value.

Adding Integers on a Number Line

Zero is placed at the center of the number line. All positive integers lie on the right side of zero, and all negative integers lie on the left side of zero.

To add integers on a number line, apply the following rules:

• Draw a number line, and look for the first addend, i.e., starting point. The starting point for moving along the number line is any of the given integers.
• To add a positive integer, move to the right side (or positive side) of the number line.
• To add a negative integer, move to the left side (or negative side) of the number line.
• The result of the addition is where you land on the number line.

Example 1: $(–3) + 4$ on the number line.

Draw a number line, and look for the starting point. Here, $–3$ is the starting point.

Now, to add a positive integer 4, move 4 units to the right side (or positive side).

We landed on the number 1. 

Thus, $–3 + 4 = 1$.

Example 2: $2 + (\;–5)$ on the number line.

Draw a number line, and look for the starting point. Here, 2 is the starting point.

Now, to add a negative integer $–5$, move 5 units to the left side (or negative side).

We landed on the number –3.

Thus, $2 + (\;–5) = –3$.

Example 3: $5 + 4$ on the number line

Properties of Addition of Integers

When adding two or more integers, the following properties can be used to simplify expressions and speed up the calculations.

Closure Property

The sum of two integers is always an integer.

For integers a and b, the sum $a + b$ is also an integer.

Commutative Property

The sum of two integers is not affected by the order of the integers.

$a + b = b + a$

Associative Property

The sum of three integers is not affected, no matter how we group three or more integers.

$(a + b) + c = a + (b + c)$

Additive Identity

The additive identity for integers is 0. Adding 0 to any integer results in the same integer.

$a + 0 = a$

Additive Inverse

The sum of an integer and its additive inverse is 0. For any integer a, the additive inverse is -a.

Facts about Adding Integers

• The sum does alter when the order of the numbers added is changed.
• Adding zero to a number gives the number itself.
• When we add 1 to a number, we get the next number.

In this article, we have discussed different rules of adding integers, adding integers on number lines, facts based on integer addition, solved examples, and some important FAQs.

• Using the rules for adding integers, find the sum $12 + 13$ .

The sum of two positive integers is always positive. 

Hence, $12 + 13 = 25$

• Using the rules for adding integers, add the integers $7,\; −9$ , and 12.

Given integers are $7, \;−9,$ and 12. 

We have to find $7 + (\;−9) + 12$.

In such a case, first, add both the positive integers 7 and 12. 

$7 + 12 = 19$. 

So, the expression becomes $19 + (\;−9)$.

Subtract 9 from 19 and give the positive sign.

$19 + (\;−9) = 10$. 

• Find which number should be added to 14 to get $−5$ as the result.

“x” should be added to 14 to get $−5$ as the result.

Therefore, 

$14 + x = −5$

$14 + x = -5$

$x = -5 \;-\;14$

$x = -5 + (\;-14)$

Hence, $−19$ should be added to 14 to get $−5$ as the result.

• Using the number line, find $4 + (\;-7)$ .

To find $4 + (\;-7)$, we have to move 7 steps to the left from 4. That will give us the answer $−3$.

• Joe spent $\$35$ on groceries on Monday. He spent $\$13$ more than that on Tuesday. How much did he spend on groceries in total?

Money spent for groceries on Tuesday $= \$35 + \$13 = \$48$

Now, money spent for groceries on both days $= \$35 + \$48 = \$83$

Attend this quiz & Test your knowledge.

$13 + (\;−7) =$ __________.

Which of the following is equal to $−5 + (\;−6)$, find the value of $−15 +(\;− 11)$., $0 + (\;−7) =$ __________., daniel has 10 red pens and 12 blue pens. how many pens does he own.

Is 0 an integer?

Yes. 0 is an integer because an integer is defined as a number without any fractional part, and zero has no fractional part.

What is the rule for adding integers with different signs?

When two integers of the different signs are added, only subtraction will be performed and the sign of the result will be the same as the number with the largest absolute value.

Example: $–5 + 11 = 6$, 

     $7 + (–\; 15) =  –8$.

What is the rule for adding integers on a number line?

• Draw a number line, and look for the first addend, the starting point.
• To add a positive integer move to the right side (or positive side) of the number line.
• To add a negative integer move to the left side (or negative side) of the number line.

What is the sign of the result when two negative integers are added together?

When two negative integers are added together, the sign of the result is always negative.

What is the sign of the result when positive and negative integers are added together?

When two integers of the different signs are added, only subtraction will be performed and the sign of the result will be the same as that of the larger number.

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Integers Worksheets

Welcome to the integers worksheets page at Math-Drills.com where you may have a negative experience, but in the world of integers, that's a good thing! This page includes Integers worksheets for comparing and ordering integers, adding, subtracting, multiplying and dividing integers and order of operations with integers.

If you've ever spent time in Canada in January, you've most likely experienced a negative integer first hand. Banks like you to keep negative balances in your accounts, so they can charge you loads of interest. Deep sea divers spend all sorts of time in negative integer territory. There are many reasons why a knowledge of integers is helpful even if you are not going to pursue an accounting or deep sea diving career. One hugely important reason is that there are many high school mathematics topics that will rely on a strong knowledge of integers and the rules associated with them.

We've included a few hundred integers worksheets on this page to help support your students in their pursuit of knowledge. You may also want to get one of those giant integer number lines to post if you are a teacher, or print off a few of our integer number lines. You can also project them on your whiteboard or make an overhead transparency. For homeschoolers or those with only one or a few students, the paper versions should do. The other thing that we highly recommend are integer chips a.k.a. two-color counters. Read more about them below.

Most Popular Integers Worksheets this Week

Integer Resources

Coordinate graph paper can be very useful when studying integers. Coordinate geometry is a practical application of integers and can give students practice with using integers while learning another related skill. Coordinate graph paper can be found on the Graph Paper page:

Coordinate Graph Paper

Integer number lines can be used for various math activities including operations with integers, counting, comparing, ordering, etc.

• Integer Number Lines Integers Number Lines from -10 to 10 Integers Number Lines from -15 to 15 Integers Number Lines from -20 to 20 Integers Number Lines from -25 to 25 OLD Integer Number Lines

Comparing and Ordering Integers

For students who are just starting with integers, it is very helpful if they can use an integer number line to compare integers and to see how the placement of integers works. They should quickly realize that negative numbers are counter-intuitive because they are probably quite used to larger absolute values meaning larger numbers. The reverse is the case, of course, with negative numbers. Students should be able to recognize easily that a positive number is always greater than a negative number and that between two negative integers, the one with the lesser absolute value is actually the greater number. Have students practice with these integers worksheets and follow up with the close proximity comparing integers worksheets.

• Comparing Integers Worksheets Comparing Positive and Negative Integers (-9 to +9) Comparing Positive and Negative Integers (-15 to +15) Comparing Positive and Negative Integers (-25 to +25) Comparing Positive and Negative Integers (-50 to +50) Comparing Positive and Negative Integers (-99 to +99) Comparing Negative Integers (-15 to -1)

By close proximity, we mean that the integers being compared differ very little in value. Depending on the range, we have allowed various differences between the two integers being compared. In the first set where the range is -9 to 9, the difference between the two numbers is always 1. With the largest range, a difference of up to 5 is allowed. These worksheets will help students further hone their ability to visualize and conceptualize the idea of negative numbers and will serve as a foundation for all the other worksheets on this page.

• Comparing Integers in Close Proximity Comparing Positive and Negative Integers (-9 to +9) in Close Proximity Comparing Positive and Negative Integers (-15 to +15) in Close Proximity Comparing Positive and Negative Integers (-25 to +25) in Close Proximity Comparing Positive and Negative Integers (-50 to +50) in Close Proximity Comparing Positive and Negative Integers (-99 to +99) in Close Proximity
• Ordering Integers Worksheets Ordering Integers on a Number Line Ordering Integers (range -9 to 9) Ordering Integers (range -20 to 20) Ordering Integers (range -50 to 50) Ordering Integers (range -99 to 99) Ordering Integers (range -999 to 999) Ordering Negative Integers (range -9 to -1) Ordering Negative Integers (range -99 to -10) Ordering Negative Integers (range -999 to -100)

Adding and Subtracting Integers

Two-color counters are fantastic manipulatives for teaching and learning about integer addition. Two-color counters are usually plastic chips that come with yellow on one side and red on the other side. They might be available in other colors, so you'll have to substitute your own colors in the following description.

Adding with two-color counters is actually quite easy. You model the first number with a pile of chips flipped to the correct side and you also model the second number with a pile of chips flipped to the correct side; then you mash them all together, take out the zeros (if any) and behold, you have your answer! Need further elaboration? Read on!

The correct side means using red to model negative numbers and yellow to model positive numbers. You would model —5 with five red chips and 7 with seven yellow chips. Mashing them together should be straight forward although, you'll want to caution your students to be less exuberant than usual, so none of the chips get flipped. Taking out the zeros means removing as many pairs of yellow and red chips as you can. You can do this because —1 and 1 when added together equals zero (this is called the zero principle). If you remove the zeros, you don't affect the answer. The benefit of removing the zeros, however, is that you always end up with only one color and as a consequence, the answer to the integer question. If you have no chips left at the end, the answer is zero!

• Adding Integers Worksheets with 75 Questions Per Page (Some Parentheses) Adding Integers from -9 to 9 (75 Questions) ✎ Adding Integers from -12 to 12 (75 Questions) ✎ Adding Integers from -15 to 15 (75 Questions) ✎ Adding Integers from -20 to 20 (75 Questions) ✎ Adding Integers from -25 to 25 (75 Questions) ✎ Adding Integers from -50 to 50 (75 Questions) ✎ Adding Integers from -99 to 99 (75 Questions) ✎
• Adding Integers Worksheets with 75 Questions Per Page (All Parentheses) Adding Integers from (-9) to (+9) All Parentheses (75 Questions) ✎ Adding Integers from (-12) to (+12) All Parentheses (75 Questions) ✎ Adding Integers from (-15) to (+15) All Parentheses (75 Questions) ✎ Adding Integers from (-20) to (+20) All Parentheses (75 Questions) ✎ Adding Integers from (-25) to (+25) All Parentheses (75 Questions) ✎ Adding Integers from (-50) to (+50) All Parentheses (75 Questions) ✎ Adding Integers from (-99) to (+99) All Parentheses (75 Questions) ✎
• Adding Integers Worksheets with 75 Questions Per Page (No Parentheses) Adding Integers from -9 to 9 No Parentheses (75 Questions) ✎ Adding Integers from -12 to 12 No Parentheses (75 Questions) ✎ Adding Integers from -15 to 15 No Parentheses (75 Questions) ✎ Adding Integers from -20 to 20 No Parentheses (75 Questions) ✎ Adding Integers from -25 to 25 No Parentheses (75 Questions) ✎ Adding Integers from -50 to 50 No Parentheses (75 Questions) ✎ Adding Integers from -99 to 99 No Parentheses (75 Questions) ✎
• Adding Integers Worksheets with 50 Questions Per Page (Some Parentheses) Adding Integers from -9 to 9 (50 Questions) ✎ Adding Integers from -12 to 12 (50 Questions) ✎ Adding Integers from -15 to 15 (50 Questions) ✎ Adding Integers from -20 to 20 (50 Questions) ✎ Adding Integers from -25 to 25 (50 Questions) ✎ Adding Integers from -50 to 50 (50 Questions) ✎ Adding Integers from -99 to 99 (50 Questions) ✎
• Adding Integers Worksheets with 50 Questions Per Page (All Parentheses) Adding Integers from (-9) to (+9) All Parentheses (50 Questions) ✎ Adding Integers from (-12) to (+12) All Parentheses (50 Questions) ✎ Adding Integers from (-15) to (+15) All Parentheses (50 Questions) ✎ Adding Integers from (-20) to (+20) All Parentheses (50 Questions) ✎ Adding Integers from (-25) to (+25) All Parentheses (50 Questions) ✎ Adding Integers from (-50) to (+50) All Parentheses (50 Questions) ✎ Adding Integers from (-99) to (+99) All Parentheses (50 Questions) ✎
• Adding Integers Worksheets with 50 Questions Per Page (No Parentheses) Adding Integers from -9 to 9 No Parentheses (50 Questions) ✎ Adding Integers from -12 to 12 No Parentheses (50 Questions) ✎ Adding Integers from -15 to 15 No Parentheses (50 Questions) ✎ Adding Integers from -20 to 20 No Parentheses (50 Questions) ✎ Adding Integers from -25 to 25 No Parentheses (50 Questions) ✎ Adding Integers from -50 to 50 No Parentheses (50 Questions) ✎ Adding Integers from -99 to 99 No Parentheses (50 Questions) ✎
• Adding Integers Worksheets with 25 Large Print Questions Per Page (Some Parentheses) Adding Integers from -9 to 9 (Large Print; 25 Questions) ✎ Adding Integers from -12 to 12 (Large Print; 25 Questions) ✎ Adding Integers from -15 to 15 (Large Print; 25 Questions) ✎ Adding Integers from -20 to 20 (Large Print; 25 Questions) ✎ Adding Integers from -25 to 25 (Large Print; 25 Questions) ✎ Adding Integers from -50 to 50 (Large Print; 25 Questions) ✎ Adding Integers from -99 to 99 (Large Print; 25 Questions) ✎
• Adding Integers Worksheets with 25 Large Print Questions Per Page (All Parentheses) Adding Integers from (-9) to (+9) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-12) to (+12) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-15) to (+15) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-20) to (+20) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-25) to (+25) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-50) to (+50) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-99) to (+99) All Parentheses (Large Print; 25 Questions) ✎
• Adding Integers Worksheets with 25 Large Print Questions Per Page (No Parentheses) Adding Integers from -9 to 9 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -12 to 12 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -15 to 15 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -20 to 20 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -25 to 25 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -50 to 50 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -99 to 99 No Parentheses (Large Print; 25 Questions) ✎
• Vertically Arranged Integer Addition Worksheets 3-Digit Integer Addition (Vertically Arranged) 3-Digit Positive Plus a Negative Integer Addition (Vertically Arranged) 3-Digit Negative Plus a Positive Integer Addition (Vertically Arranged) 3-Digit Negative Plus a Negative Integer Addition (Vertically Arranged)

Subtracting with integer chips is a little different. Integer subtraction can be thought of as removing. To subtract with integer chips, begin by modeling the first number (the minuend) with integer chips. Next, remove the chips that would represent the second number from your pile and you will have your answer. Unfortunately, that isn't all there is to it. This works beautifully if you have enough of the right color chip to remove, but often times you don't. For example, 5 - (-5), would require five yellow chips to start and would also require the removal of five red chips, but there aren't any red chips! Thank goodness, we have the zero principle. Adding or subtracting zero (a red chip and a yellow chip) has no effect on the original number, so we could add as many zeros as we wanted to the pile, and the number would still be the same. All that is needed then is to add as many zeros (pairs of red and yellow chips) as needed until there are enough of the correct color chip to remove. In our example 5 - (-5), you would add 5 zeros, so that you could remove five red chips. You would then be left with 10 yellow chips (or +10) which is the answer to the question.

• Subtracting Integers Worksheets with 75 Questions Per Page (Some Parentheses) Subtracting Integers from -9 to 9 (75 Questions) ✎ Subtracting Integers from -12 to 12 (75 Questions) ✎ Subtracting Integers from -15 to 15 (75 Questions) ✎ Subtracting Integers from -20 to 20 (75 Questions) ✎ Subtracting Integers from -25 to 25 (75 Questions) ✎ Subtracting Integers from -50 to 50 (75 Questions) ✎ Subtracting Integers from -99 to 99 (75 Questions) ✎
• Subtracting Integers Worksheets with 75 Questions Per Page (All Parentheses) Subtracting Integers from (-9) to (+9) All Parentheses (75 Questions) ✎ Subtracting Integers from (-12) to (+12) All Parentheses (75 Questions) ✎ Subtracting Integers from (-15) to (+15) All Parentheses (75 Questions) ✎ Subtracting Integers from (-20) to (+20) All Parentheses (75 Questions) ✎ Subtracting Integers from (-25) to (+25) All Parentheses (75 Questions) ✎ Subtracting Integers from (-50) to (+50) All Parentheses (75 Questions) ✎ Subtracting Integers from (-99) to (+99) All Parentheses (75 Questions) ✎
• Subtracting Integers Worksheets with 75 Questions Per Page (No Parentheses) Subtracting Integers from -9 to 9 No Parentheses (75 Questions) ✎ Subtracting Integers from -12 to 12 No Parentheses (75 Questions) ✎ Subtracting Integers from -15 to 15 No Parentheses (75 Questions) ✎ Subtracting Integers from -20 to 20 No Parentheses (75 Questions) ✎ Subtracting Integers from -25 to 25 No Parentheses (75 Questions) ✎ Subtracting Integers from -50 to 50 No Parentheses (75 Questions) ✎ Subtracting Integers from -99 to 99 No Parentheses (75 Questions) ✎
• Subtracting Integers Worksheets with 50 Questions Per Page (Some Parentheses) Subtracting Integers from -9 to 9 (50 Questions) ✎ Subtracting Integers from -12 to 12 (50 Questions) ✎ Subtracting Integers from -15 to 15 (50 Questions) ✎ Subtracting Integers from -20 to 20 (50 Questions) ✎ Subtracting Integers from -25 to 25 (50 Questions) ✎ Subtracting Integers from -50 to 50 (50 Questions) ✎ Subtracting Integers from -99 to 99 (50 Questions) ✎
• Subtracting Integers Worksheets with 50 Questions Per Page (All Parentheses) Subtracting Integers from (-9) to (+9) All Parentheses (50 Questions) ✎ Subtracting Integers from (-12) to (+12) All Parentheses (50 Questions) ✎ Subtracting Integers from (-15) to (+15) All Parentheses (50 Questions) ✎ Subtracting Integers from (-20) to (+20) All Parentheses (50 Questions) ✎ Subtracting Integers from (-25) to (+25) All Parentheses (50 Questions) ✎ Subtracting Integers from (-50) to (+50) All Parentheses (50 Questions) ✎ Subtracting Integers from (-99) to (+99) All Parentheses (50 Questions) ✎
• Subtracting Integers Worksheets with 50 Questions Per Page (No Parentheses) Subtracting Integers from -9 to 9 No Parentheses (50 Questions) ✎ Subtracting Integers from -12 to 12 No Parentheses (50 Questions) ✎ Subtracting Integers from -15 to 15 No Parentheses (50 Questions) ✎ Subtracting Integers from -20 to 20 No Parentheses (50 Questions) ✎ Subtracting Integers from -25 to 25 No Parentheses (50 Questions) ✎ Subtracting Integers from -50 to 50 No Parentheses (50 Questions) ✎ Subtracting Integers from -99 to 99 No Parentheses (50 Questions) ✎
• Subtracting Integers Worksheets with 25 Large Print Questions Per Page (Some Parentheses) Subtracting Integers from -9 to 9 (Large Print; 25 Questions) ✎ Subtracting Integers from -12 to 12 (Large Print; 25 Questions) ✎ Subtracting Integers from -15 to 15 (Large Print; 25 Questions) ✎ Subtracting Integers from -20 to 20 (Large Print; 25 Questions) ✎ Subtracting Integers from -25 to 25 (Large Print; 25 Questions) ✎ Subtracting Integers from -50 to 50 (Large Print; 25 Questions) ✎ Subtracting Integers from -99 to 99 (Large Print; 25 Questions) ✎
• Subtracting Integers Worksheets with 25 Large Print Questions Per Page (All Parentheses) Subtracting Integers from (-9) to (+9) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-12) to (+12) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-15) to (+15) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-20) to (+20) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-25) to (+25) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-50) to (+50) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-99) to (+99) All Parentheses (Large Print; 25 Questions) ✎
• Subtracting Integers Worksheets with 25 Large Print Questions Per Page (No Parentheses) Subtracting Integers from (-9) to 9 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-12) to 12 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-15) to 15 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-20) to 20 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-25) to 25 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-50) to 50 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-99) to 99 No Parentheses (Large Print; 25 Questions) ✎
• Vertically Arranged Integer Subtraction Worksheets 3-Digit Integer Subtraction (Vertically Arranged) 3-Digit Positive Minus a Positive Integer Subtraction (Vertically Arranged) 3-Digit Positive Minus a Negative Integer Subtraction (Vertically Arranged) 3-Digit Negative Minus a Positive Integer Subtraction (Vertically Arranged) 3-Digit Negative Minus a Negative Integer Subtraction (Vertically Arranged)

The worksheets in this section include addition and subtraction on the same page. Students will have to pay close attention to the signs and apply their knowledge of integer addition and subtraction to each question. The use of counters or number lines could be helpful to some students.

• Adding and Subtracting Integers Worksheets with 75 Questions Per Page (Some Parentheses) Adding & Subtracting Integers from -9 to 9 (75 Questions) ✎ Adding & Subtracting Integers from -10 to 10 (75 Questions) ✎ Adding & Subtracting Integers from -12 to 12 (75 Questions) ✎ Adding & Subtracting Integers from -15 to 15 (75 Questions) ✎ Adding & Subtracting Integers from -20 to 20 (75 Questions) ✎ Adding & Subtracting Integers from -25 to 25 (75 Questions) ✎ Adding & Subtracting Integers from -50 to 50 (75 Questions) ✎ Adding & Subtracting Integers from -99 to 99 (75 Questions) ✎
• Adding and Subtracting Integers Worksheets with 75 Questions Per Page (All Parentheses) Adding & Subtracting Integers from (-5) to (+5) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-9) to (+9) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-12) to (+12) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-15) to (+15) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-20) to (+20) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-25) to (+25) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-50) to (+50) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-99) to (+99) All Parentheses (75 Questions) ✎
• Adding and Subtracting Integers Worksheets with 75 Questions Per Page (No Parentheses) Adding & Subtracting Integers from -9 to 9 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -12 to 12 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -15 to 15 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -20 to 20 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -25 to 25 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -50 to 50 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -99 to 99 No Parentheses (75 Questions) ✎
• Adding and Subtracting Integers Worksheets with 50 Questions Per Page (Some Parentheses) Adding & Subtracting Integers from -9 to 9 (50 Questions) ✎ Adding & Subtracting Integers from -12 to 12 (50 Questions) ✎ Adding & Subtracting Integers from -15 to 15 (50 Questions) ✎ Adding & Subtracting Integers from -20 to 20 (50 Questions) ✎ Adding & Subtracting Integers from -25 to 25 (50 Questions) ✎ Adding & Subtracting Integers from -50 to 50 (50 Questions) ✎ Adding & Subtracting Integers from -99 to 99 (50 Questions) ✎
• Adding and Subtracting Integers Worksheets with 50 Questions Per Page (All Parentheses) Adding & Subtracting Integers from (-9) to (+9) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-12) to (+12) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-15) to (+15) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-20) to (+20) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-25) to (+25) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-50) to (+50) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-99) to (+99) All Parentheses (50 Questions) ✎
• Adding and Subtracting Integers Worksheets with 50 Questions Per Page (No Parentheses) Adding & Subtracting Integers from -9 to 9 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -12 to 12 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -15 to 15 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -20 to 20 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -25 to 25 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -50 to 50 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -99 to 99 No Parentheses (50 Questions) ✎
• Adding and Subtracting Integers Worksheets with 25 Large Print Questions Per Page (Some Parentheses) Adding & Subtracting Integers from -9 to 9 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -12 to 12 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -15 to 15 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -20 to 20 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -25 to 25 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -50 to 50 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -99 to 99 (Large Print; 25 Questions) ✎
• Adding and Subtracting Integers Worksheets with 25 Large Print Questions Per Page (All Parentheses) Adding & Subtracting Integers from (-9) to (+9) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-12) to (+12) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-15) to (+15) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-20) to (+20) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-25) to (+25) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-50) to (+50) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-99) to (+99) All Parentheses (Large Print; 25 Questions) ✎
• Adding and Subtracting Integers Worksheets with 25 Large Print Questions Per Page (No Parentheses) Adding & Subtracting Integers from (-9) to 9 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-12) to 12 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-15) to 15 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-20) to 20 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-25) to 25 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-50) to 50 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-99) to 99 No Parentheses (Large Print; 25 Questions) ✎

These worksheets include groups of questions that all result in positive or negative sums or differences. They can be used to help students see more clearly how certain integer questions end up with positive and negative results. In the case of addition of negative and positive integers, some people suggest looking for the "heavier" value to determine whether the sum will be positive of negative. More technically, it would be the integer with the greater absolute value. For example, in the question (−2) + 5, the absolute value of the positive integer is greater, so the sum will be positive.

In subtraction questions, the focus is on the subtrahend (the value being subtracted). In positive minus positive questions, if the subtrahend is greater than the minuend, the answer will be negative. In negative minus negative questions, if the subtrahend has a greater absolute value, the answer will be positive. Vice-versa for both situations. Alternatively, students can always convert subtraction questions to addition questions by changing the signs (e.g. (−5) − (−7) is the same as (−5) + 7; 3 − 5 is the same as 3 + (−5)).

• Scaffolded Integer Addition and Subtraction Positive Plus Negative Integer Addition (Scaffolded) ✎ Negative Plus Positive Integer Addition (Scaffolded) ✎ Mixed Integer Addition (Scaffolded) ✎ Positive Minus Positive Integer Subtraction (Scaffolded) ✎ Negative Minus Negative Integer Subtraction (Scaffolded) ✎

Multiplying and Dividing Integers

Multiplying integers is very similar to multiplication facts except students need to learn the rules for the negative and positive signs. In short, they are:

In words, multiplying two positives or two negatives together results in a positive product, and multiplying a negative and a positive in either order results in a negative product. So, -8 × 8, 8 × (-8), -8 × (-8) and 8 × 8 all result in an absolute value of 64, but in two cases, the answer is positive (64) and in two cases the answer is negative (-64).

Should you wish to develop some "real-world" examples of integer multiplication, it might be a stretch due to the abstract nature of negative numbers. Sure, you could come up with some scenario about owing a debt and removing the debt in previous months, but this may only result in confusion. For now students can learn the rules of multiplying integers and worry about the analogies later!

• Multiplying Integers with 100 Questions Per Page Multiplying Mixed Integers from -9 to 9 (100 Questions) ✎ Multiplying Positive by Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying Negative by Positive Integers from -9 to 9 (100 Questions) ✎ Multiplying Negative by Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying Mixed Integers from -12 to 12 (100 Questions) ✎ Multiplying Positive by Negative Integers from -12 to 12 (100 Questions) ✎ Multiplying Negative by Positive Integers from -12 to 12 (100 Questions) ✎ Multiplying Negative by Negative Integers from -12 to 12 (100 Questions) ✎ Multiplying Mixed Integers from -20 to 20 (100 Questions) ✎ Multiplying Mixed Integers from -50 to 50 (100 Questions) ✎
• Multiplying Integers with 50 Questions Per Page Multiplying Mixed Integers from -9 to 9 (50 Questions) ✎ Multiplying Positive by Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying Negative by Positive Integers from -9 to 9 (50 Questions) ✎ Multiplying Negative by Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying Mixed Integers from -12 to 12 (50 Questions) ✎ Multiplying Positive by Negative Integers from -12 to 12 (50 Questions) ✎ Multiplying Negative by Positive Integers from -12 to 12 (50 Questions) ✎ Multiplying Negative by Negative Integers from -12 to 12 (50 Questions) ✎
• Multiplying Integers with 25 Large Print Questions Per Page Multiplying Mixed Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Positive by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Negative by Positive Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Negative by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Mixed Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying Positive by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying Negative by Positive Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying Negative by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎

Luckily (for your students), the rules of dividing integers are the same as the rules for multiplying:

Dividing a positive by a positive integer or a negative by a negative integer will result in a positive integer. Dividing a negative by a positive integer or a positive by a negative integer will result in a negative integer. A good grasp of division facts and a knowledge of the rules for multiplying and dividing integers will go a long way in helping your students master integer division. Use the worksheets in this section to guide students along.

• Dividing Integers with 100 Questions Per Page Dividing Mixed Integers from -9 to 9 (100 Questions) ✎ Dividing Positive by Negative Integers from -9 to 9 (100 Questions) ✎ Dividing Negative by Positive Integers from -9 to 9 (100 Questions) ✎ Dividing Negative by Negative Integers from -9 to 9 (100 Questions) ✎ Dividing Mixed Integers from -12 to 12 (100 Questions) ✎ Dividing Positive by Negative Integers from -12 to 12 (100 Questions) ✎ Dividing Negative by Positive Integers from -12 to 12 (100 Questions) ✎ Dividing Negative by Negative Integers from -12 to 12 (100 Questions) ✎
• Dividing Integers with 50 Questions Per Page Dividing Mixed Integers from -9 to 9 (50 Questions) ✎ Dividing Positive by Negative Integers from -9 to 9 (50 Questions) ✎ Dividing Negative by Positive Integers from -9 to 9 (50 Questions) ✎ Dividing Negative by Negative Integers from -9 to 9 (50 Questions) ✎ Dividing Mixed Integers from -12 to 12 (50 Questions) ✎ Dividing Positive by Negative Integers from -12 to 12 (50 Questions) ✎ Dividing Negative by Positive Integers from -12 to 12 (50 Questions) ✎ Dividing Negative by Negative Integers from -12 to 12 (50 Questions) ✎
• Dividing Integers with 25 Large Print Questions Per Page Dividing Mixed Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Positive by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Negative by Positive Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Negative by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Mixed Integers from -12 to 12 (25 Questions; Large Print) ✎ Dividing Positive by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎ Dividing Negative by Positive Integers from -12 to 12 (25 Questions; Large Print) ✎ Dividing Negative by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎

This section includes worksheets with both multiplying and dividing integers on the same page. As long as students know their facts and the integer rules for multiplying and dividing, their sole worry will be to pay attention to the operation signs.

• Multiplying and Dividing Integers with 100 Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (100 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (100 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (100 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (100 Questions) ✎
• Multiplying and Dividing Integers with 75 Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (75 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (75 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (75 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (75 Questions) ✎
• Multiplying and Dividing Integers with 50 Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (50 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (50 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (50 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (50 Questions) ✎
• Multiplying and Dividing Integers with 25 Large Print Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (25 Questions; Large Print) ✎

All Operations with Integers

In this section, the integers math worksheets include all of the operations. Students will need to pay attention to the operations and the signs and use mental math or another strategy to arrive at the correct answers. It should go without saying that students need to know their basic addition, subtraction, multiplication and division facts and rules regarding operations with integers before they should complete any of these worksheets independently. Of course, the worksheets can be used as a source of questions for lessons, tests or other learning activities.

• All Operations with Integers with 50 Questions Per Page (Some Parentheses) All operations with integers from -9 to 9 (50 Questions) ✎ All operations with integers from -12 to 12 (50 Questions) ✎ All operations with integers from -15 to 15 (50 Questions) ✎ All operations with integers from -20 to 20 (50 Questions) ✎ All operations with integers from -25 to 25 (50 Questions) ✎ All operations with integers from -50 to 50 (50 Questions) ✎ All operations with integers from -99 to 99 (50 Questions) ✎
• All Operations with Integers with 50 Questions Per Page (All Parentheses) All operations with integers from (-9) to (+9) All Parentheses (50 Questions) ✎ All operations with integers from (-12) to (+12) All Parentheses (50 Questions) ✎ All operations with integers from (-15) to (+15) All Parentheses (50 Questions) ✎ All operations with integers from (-20) to (+20) All Parentheses (50 Questions) ✎ All operations with integers from (-25) to (+25) All Parentheses (50 Questions) ✎ All operations with integers from (-50) to (+50) All Parentheses (50 Questions) ✎ All operations with integers from (-99) to (+99) All Parentheses (50 Questions) ✎
• All Operations with Integers with 50 Questions Per Page (No Parentheses) All operations with integers from -9 to 9 No Parentheses (50 Questions) ✎ All operations with integers from -12 to 12 No Parentheses (50 Questions) ✎ All operations with integers from -15 to 15 No Parentheses (50 Questions) ✎ All operations with integers from -20 to 20 No Parentheses (50 Questions) ✎ All operations with integers from -25 to 25 No Parentheses (50 Questions) ✎ All operations with integers from -50 to 50 No Parentheses (50 Questions) ✎ All operations with integers from -99 to 99 No Parentheses (50 Questions) ✎

Order of operations with integers can be found on the Order of Operations page:

Order of Operations with Integers

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Adding Integers

Adding integers is the process of finding the sum of two or more integers. It may result in an increase or a decrease in value, depending on whether the integers are positive or negative or a mixture. The addition of integers is an arithmetic operation performed on integers with the same sign or with different signs to find the sum. Let us learn more about adding integers in this article.

Rules for Addition of Integers

There are certain rules to be followed to add two or more integers. Integers are complete numbers that do not have fractional parts. It includes positive integers, zero, and negative integers.

How to Add Integers?

The rules for adding integers are given below:

• The sum of an integer and its additive inverse is 0. For example, 4 + (-4) = 0
• Adding two positive integers always results in a positive value. For example, 6 + 6 = 12
• Adding two negative integers always results in a negative number. For example, (-6) + (-6) = -12
• Adding integers with 0 results in the same number. For example, 6 + 0 = 6, and -8 + 0 = -8
• Adding a positive number with a negative number is done by finding the difference between the absolute value of both numbers. Then, the sign with the greater number gets attached to the sum. For example, +7 - 3 = +4

The rules for the addition of integers can be understood with the help of the table given below.

Adding Integers with the Same Sign

When we add two integers with the same sign, we add their absolute values and attach the common sign with the sum. For example, 2 + 3 = 5, (-2) + (-3) = - (2 + 3) = -5. The absolute value of a number is the positive value of the given number. For instance, the absolute value of 6 is 6, the absolute value of -6 is 6, and so on. Some examples of adding integers with the same sign are given below:

• (-1) + (-9) = - (1 + 9) = -10
• (-2) + (-17) = - (2 + 17) = -19

Use Cuemath's online adding integers calculator to verify these answers.

Adding Integers with Different Signs

Adding two integers with different signs is done by subtracting the absolute values, and then attaching the sign of the number with the greater absolute value. For example, if we want to add -2 and 3, first we find the absolute values of both. The absolute value of -2 is 2, and of 3 is 3. Now, find the difference between these absolute values which is 3 - 2 = 1. Since 3 > 2, and 3 has a positive sign, the sign of the resultant number will be positive. Therefore, - 2 + 3 = 1.

Adding Integers on a Number Line

The addition of integers on a number line is based on the given principles:

• Adding a positive number is done by moving towards the right side (or the positive side) of the number line.
• Adding a negative integer is done by moving towards the left side (or the negative side) of the number line.
• Any one of the given integers is taken as the base point from where we start moving on the number line.

Now, let us learn how to add integers on a number line.

• Step 1: The first step is to choose a scale on the number line. For example, whether we want to plot numbers in multiples of 1, 5, 10, 50, and so on depends on the given integers. For example, if we have to add 10 and -30, we can take a scale of 10 on the number line to ease our work.
• Step 2: If we have to add -2 and 7, we can take a scale of counting numbers starting from 1.
• Step 3: The next step is to locate any one of the integers on the number line, preferably a number with a greater absolute value. For example, if we need to add 2 and 19, it is better if we locate 19 on the line first and then take 2 jumps towards the right, rather than locating 2 and then take 19 jumps.
• Step 4: The final step is to add the second integer to the number located in the previous step by taking jumps either to the left or to the right depending on whether the number is positive or negative.

Let us take an example to understand more about adding integers on a number line.

Example: Use the number line and add the following integers: 5 + (-10)

Solution: Since we need to add a negative number (-10), we will move towards the left on the number line. Starting from 5, we will take 10 steps towards the left which will bring us to -5.

☛ Related Topics

• Integer Formulas
• Addition and Subtraction of Integers
• Multiplication and Division of Integers

Addition of Integers Examples

Example 1: Add the following integers by using the rules of integers in addition.

4 + (-6) + 13

Solution: There are three integers given. So, first let us add both the positive integers 4 and 13, which gives us 17. Now, we are left with the following expression 17 + (-6). Here, we have to apply the rule of addition of a negative and a positive integer. We get, 17 + (-6) = 11. Therefore, 11 is the result of the given integers.

Example 2: Using the rules of integers in addition, find which number should be subtracted from 13 to get -10 as the answer.

Solution: Let x be the number that needs to be subtracted from 13 to get -10. So, we can form an equation in terms of x.

13 - x = -10

- x = - 10 - 13

Therefore, 23 needs to be subtracted from 13 to get -10.

Example 3: Add the following integers: -2 and -9.

Solution: While adding integers with the same sign, we add their absolute values and attach the common sign of the addends with the answer.

-2 + (-9) = - (2 + 9) = -11

Therefore, the sum of -2 and -9 is -11.

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Practice Questions on Adding Integers

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FAQs on Adding Integers

What is addition of integers.

Addition of integers means when we find the sum of integers. Since integers include positive numbers, negative numbers and zero, adding these may result in an increase or a decrease in value. This depends on whether the integers are positive or negative. For example, 5 + 6 = 11, and 5 + (-6) = -1, and -5 + 0 = -5

What are the Rules for Addition of Integers?

The rules for the addition of integers are listed below:

• The sum of an integer and its additive inverse is 0. For example, 6 + (-6) = 0
• Adding two negative integers always results in a negative number. For example, -6 + (-6) = -12
• Adding a positive number with a negative number is done by finding the difference between the absolute value of both numbers. Then, the sign with the greater number gets attached to the sum. For example, +6 - 2 = +4
• Adding integers with 0 results in the same number. For example, 6 + 0 = 6, or -6 + 0 = -6

What is the Rule for Adding Integers with Different Signs?

For adding integers with different signs, we follow the steps given below. Let us add 5 and (-8)

• Step 1: Find the absolute values of the given integers. This means it will be 5 and 8.
• Step 2: Find the difference between the absolute values found in step 1. The difference of 5 and 8 is 3.
• Step 3: Attach the sign of the number with the greater absolute value. Since 8 has a negative sign, the answer will also have a negative sign. This means 5 + (-8) = -3

What is the Rule for Adding Integers with the Same Sign?

To add integers with the same sign, we add the absolute values of the numbers and then attach the common sign with the final answer. For example, (-9) + (-3) = -12.

How is Subtracting Integers Related to Adding Integers?

Subtracting integers is related to adding integers because when we add two integers with different signs, we find their absolute values and then find their difference, This means we make use of subtraction while we add integers with different signs. Apart from this, addition and subtraction are inverse operations. This means every addition expression can be expressed in subtraction and vice-versa. Subtracting integers is related to adding integers because both can be expressed in each other's form. For example, we can write 2 + (-9) as 2 - 9. Similarly, we can write - 3 - 5 as -3 + (-5).

What are the Steps for Adding Integers?

The steps for adding integers are given below:

• Find the absolute values of the given numbers.
• If both the numbers are of the same sign, then add the values. Attach the common sign with the answer.
• If they have different signs, then subtract them and find the difference between the absolute values. Then, the sign of the integer with the greater absolute value will attach to the final answer.

What is an Example of Adding Integers?

Some examples of the addition of integers are listed below:

• (-9) + (-4) = -13
• -6 + 4 = -2
• 12 + (-8) = 4

What is the Identity Element for Addition of Integers?

The identity element for addition of integers is zero (0). This is because when 0 is added to any integer, it results in the number itself. For example, 0 + 56 = 56, or, 0 + (-7) = -7

What are the Rules for Integers in Addition?

• We first need to find the absolute value of the given integers.
• If both the numbers are of the same sign, then we add the values and attach the common sign with the answer.
• If they have different signs, then we subtract them and find the difference between the absolute values. Then, the sign of the integer with the greater absolute value will attach to the final answer.
• Adding integers with 0 results in the same number.

How to Add Positive and Negative Numbers?

In order to add positive and negative numbers, we need to use the following steps. Let us understand this with an example and add 7 + (-2)

• First, we need to find the absolute value of the given numbers. In this case, the absolute value of 7 is 7 and the absolute value of -2 is 2.
• Then, we find the difference between the absolute values. Here, it will be 7 - 2 = 5.
• Then, the sign of the integer with the greater absolute value will attach to the final answer. In this case, since 7 > 2, and 7 has a positive sign, the sign of the resultant number will be positive. Therefore, 7 + (-2) = 5.

How to Add Two Negative Numbers?

In order to add two negative numbers, we apply the rule which says that if the given numbers are of the same sign, then we add the values and attach the common sign with the answer. For example, let us add -7 + (-8). So, we will add the absolute values which is 7 + 8 = 15. Then, we will attach the common sign which is (-). Therefore, -7 + (-8) = -15.

Adding Integers and Subtracting Integers

In these lessons, we will look at adding integers and subtracting integers using the number line and using rules.

Related Topics: Integer Worksheets Integer Games More Lessons on Integers

Using the Number Line

When we add , we move right on the number line.

When we subtract , we move left on the number line

Adding Integers

To evaluate –3 + 2 , we start at –3 and move 2 places to the right

The answer is –1

Subtracting integers

To evaluate –3 – 2 , we start at –3 and move 2 places to the left

The answer is –5

How to add integers and subtract integers using the number line?

How to think about adding and subtracting integers on a number line?

Using Rules to Add Integers

Using the number line to add or subtract integers may be quite tedious. A quicker method would be to use the following rules:

The sum of two or more positive integers is a positive integer. The sum of two or more negative integers is a negative integer.

(+7) + (+ 4) = + 11 (– 8) + (– 9) = – 17

To find the sum of a positive and a negative integer: Subtract the two numbers (ignore the signs) and then keep the sign of the larger integer.

(– 9) + (+ 7) = – 2 (– 3) + (+ 5) = + 2

The sum of an integer and its opposite is equal to zero

(– 9) + (+ 9) = 0 (– 3) + (+ 3) = 0

How to use the rules to add integers?

Using Rules to Subtract Integers

To subtract integers, we can rewrite the subtraction problem as an addition problem. Instead of subtracting, we add the opposite.

Subtracting a positive is the same as adding a negative. 3 − (4) = 3 + (−4)

Subtracting a negative is the same as adding a positive. 3 − (− 4) = 3 + 4

We then follow the rules for adding integers.

Basic rules for subtracting integers and provides examples Each subtraction problem is rewritten as an addition problem.

Subtracting Integers using Rules

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• Addition Subtraction Integers

Addition And Subtraction Of Integers

In addition and subtraction of integers, we will learn how to add and subtract integers with the same sign and different signs. We can also make use of the num ber line to add and subtract signed integers. There are certain rules for integers that have to be followed to perform operations on them.

Adding two positive integers results in positive integers, whereas adding two negative integers will result in the sum with a negative sign. But, the addition of two different signed integers will result in subtraction only and the sign of the result will be the same as the larger number has. See a few examples below:

• 2 + (-2) = 0
• -2 + (-2) = -4
• -2 – (-2) = 0

Addition and subtraction

Addition and subtraction are two primary arithmetic operations in Maths. Besides these two operations, multiplication and division are also two primary operations that we learn in basic Maths. 

The addition represents the values added to the existing value. For example, a basket has two balls, and if we add more than 2 balls to it, there will be four balls in total. Similarly, if there are four balls in a basket and if we take out two balls out of it, then the basket is left with only two balls, which shows subtraction.

Addition and subtraction are not only used for integers but also rational numbers and irrational numbers. Therefore, both the operations are applicable for all real numbers and complex numbers. Also, the addition and subtraction algebraic expressions are done based on the same rules while performing algebraic operations.  

Learn more about addition and subtraction here.

Also, read:

Rules to Add and Subtract

Integers are a special group of numbers that are positive, negative and zero, which are not fractions. Rules for addition and subtraction are the same for all.

Negative Sign and Positive Sign

The integers which we add or subtract could be positive or negative.  Hence, it is necessary to know the rules for positive and negative symbols.

Positive sign/symbol: (+)

Negative sign/symbol: (-)

Addition of Integers

The three main possibilities in the addition of integers are:

• Addition between two positive numbers
• Addition between two negative numbers
• Addition between a positive number and a negative number

Whenever a positive number and a negative number are added, the sign of the greater number will decide the operation and sign of the result. In the above example 10 + (-15) = -5 and (-10) + 15 =5; here, without sign 15 is greater than 10 hence, numbers will be subtracted and the answer will give the sign of the greater number.

We know that the multiplication of a negative sign and a positive sign will result in a negative sign, therefore if we write 10 + (-5), it means the ‘+’ sign here is multiplied by ‘-’ inside the bracket. Therefore, the result becomes 10 – 5 = 5.

Alternatively, to find the sum of a positive and a negative integer, take the absolute value (“ absolute value ” means to remove any negative sign of a number, and make the number positive) of each integer and then subtract these values. Take the above example, 10 + (-15); absolute value of 10 is 10 and -15 is 15.

⇒ 10 – 15 = -5

Thus, we can conclude the above table as follow:

Note: The sum of an integer and its opposite is always zero. (For example, -5 + 5= 0)

Subtraction of Integers

Like in addition, the subtraction of integers also has three possibilities. They are:

• Subtraction between two positive numbers
• Subtraction between two negative numbers
• Subtraction between a positive number and a negative number

For ease of calculation, we need to renovate subtraction problems the addition problems. There are two steps to perform this and are given below.

• Convert the subtraction sign into an addition sign.
• After converting the sign, take the inverse of the number which comes after the sign.

Once the transformation is done, follow the rules of addition given above.

For example, finding the value of (-5) – (7)

Step 1: Change the subtraction sign into an addition sign

⇒ (-5) + (7)

Step 2: Take the inverse of the number which comes after the sign

⇒ – 5 + (-7)                                  (opposite of 7 is -7)

⇒ – 5 + (-7) = -12      [Add and put the sign of greater number]

Properties Of Addition Of Integers

The addition properties for whole numbers are valid for integers.

Closure Property:  The sum of any 2 integers results in an integer.

For instance, 12 + 3 = 15 and 15 is an integer.

In the same way, 17 + (- 20) = – 3 and -3 is an integer.

Commutative property: Even if the order of addition is changed, the total of any 2 integers is the same.

For instance, – 19 + 15 = 15 + (- 19) = – 4

Associative property: The grouping of the integers does not matter when the total of 3 or more integers is computed.

For example, – 13 + (- 15 + 16) = (- 13 + (- 15)) + 16 = – 12

Additive identity: When the sum of zero with any integer is taken, the resultant answer is an integer. The additive identity is the integer zero.

For instance, 0 + 15 = 15

Additive inverse: For each integer, when an integer is added to that integer results in 0. The two converse integers are termed additive inverse of one another.

For instance, 9 + (- 9) = 0.

Properties Of Subtraction Of Integers

Closure property: The difference between any two given integers results in an integer.

For instance, 13 – 17 = – 4 and – 4 is an integer. In the same way, – 5 – 8 = – 13 and – 13 is an integer.

Commutative property: The difference between any two given integers changes when the order is reversed.

For example, 6 – 3 = 3 but 3 – 6 = – 3.

So, 6 – 3 ≠ 3 – 6

Associative property: In the method of subtraction, there is a change in the result if the grouping of 3 or more integers changes.

For example, (80 – 30) – 60 = – 10 however [80 – (30 – 60)] = 110.

So, (80 – 30) – 60 ≠ [80 – (30 – 60)].

Multiplication of Integers

In addition and subtraction, the sign of the resulting integer depends on the sign of the largest value. For example, -7+4 = -3 but in the case of multiplication of integers, two signs are multiplied together. 

• When two positive integers are multiplied then the result is positive.
• When two negative integers are multiplied then also the result is positive.
• But when one positive and one negative integer is multiplied, then the result is negative.
• When there is no symbol, then the integer is positive.

Solved Examples

Example 1: Evaluate the following:

• (-1) – ( -2)
• (-5 )+ 9 = 4  [Subtract and put the sign of greater number]

(-1) – ( -2) = 1

Example 2: Add -10 and -19.

Solution: -10 and -19 are both negative numbers. So if we add them, we get the sum in negative, such as;

(-10)+(-19) = -10-19 = -29

Example 3: Subtract -19 from -10.

Solution: (-10) – (-19)

Here, the two minus symbols will become plus. So,

-10 + 19 = 19 -10 = 9

Example 4: Evaluate 9 – 10 +(-5) + 6

Solution: First open the brackets.

9 – 10 -5 + 6

Add the positive and negative integers separately.

= 9 + 6 – 10 -5

= 15 – 15

Integers Addition and Subtraction Worksheet

Practice Problems

• Add -5 and -10.
• Subtract 20 from 10.
• Find the sum of 12 and 13.
• Find the difference between 40 and 30.

Frequently Asked Questions – FAQs

What is the rule to add integers, what is the rule for the subtraction of integers, are the rules of addition and subtraction the same as rules for the multiplication of integers, give examples of the addition of integers., when two negative integers are added together, then what is the sign of resulted value.

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