Addition and Subtraction of Integers

Addition and subtraction of integers are two operations that we perform on integers to increase or decrease their values. Integers include whole numbers and negative numbers like 4, 5, 0, -9, -18, and so on. Every number shown on a number line that does not have a fractional part is an integer. Let us learn more about adding and subtracting integers.

Adding and subtracting integers means carrying out the operations of addition and subtraction on two or more integers by putting the addition and subtraction operator in between. Integers are those numbers that do not have a decimal or a fractional part. They include positive and negative numbers, along with zero. An integer is a complete entity. Like whole numbers, we can add or subtract integers too.

Before going deeper into the concept, it is very important to learn what is an absolute value of an integer. On a number line, the distance of a number from 0 is called the absolute value of an integer. The addition and subtraction of integers can be best demonstrated on a number line although it takes time to work on the number line. So, it is better to learn all the rules for the addition and subtraction of integers.

The rules for addition and subtraction of integers help us to solve mathematical problems easily. Let us learn about these rules in the following section.

The following table shows the rules for adding integers.

Rules for Subtracting Integers

We know that addition and subtraction are inverse operations. So, a subtraction fact can be written as an addition fact. For example, 2-4 = 2 + (-4) and, 6-3 = 6 + (-3), or, -4-3 = -4 + (-3)

In other words, subtraction of integers is done by changing the sign of the subtrahend. After this step, we can simply apply the rules of the addition of integers. This means if both numbers are of the same sign, then we add the absolute values and attach the common sign. If both the numbers are of different signs, then we find the difference of the absolute numbers and place the sign of the bigger number in the result.

The following table shows the rules of subtraction also to ease out our calculations while dealing with operations on integers.

Addition generally means to increase the value. However, in the case of integers, the addition operation might lead to an increase or decrease in the value of the given number. Let us understand this with the help of an example using the rules given above.

Example: Sally had 3 marbles. She got 4 more from her brother. How many marbles does she have now?

Solution:

Sally had 3 marbles and she got 4 more from her brother. So, she has (3 + 4 = 7) marbles now.

This means the number of marbles increased because we had to add positive numbers.

Adding Integers on a Number Line

We need to remember the following rules for adding integers on a number line.

• While adding a negative number we move towards the left side of the number line.
• While adding a positive number we move towards the right side of the number line.

Now let us consider an example in which we need to add negative and positive numbers using a number line.

Example: The temperature of a city was -4° C. It increased by 5^º C. What is the temperature now?

Solution: The temperature of the city increased by 5°, so it became (-4 + 5 = 1°). Observe the number line given below which shows how we added a negative and a positive number. When we add a positive number on a number line we always move to the right, here we moved 5 steps to the right of -4 and we reached 1. This means -4 + 5 = 1

It should be noted that when we add a negative number, we move towards the left side of the number line. Let us recollect all the rules for adding integers using the following number lines.

Subtraction generally means to decrease the value. However, in the case of integers, a subtraction operation might lead to an increase or decrease in the value of the given number. The following rules need to be remembered while subtracting integers.

• Every subtraction fact can be written as an addition fact.
• Then we need to reverse the sign of the second number which is the subtrahend. For example, -8 - (-2) = -8 + (+ 2) = -6

Subtracting Integers on a Number Line

We need to remember the following rules for subtracting integers on a number line.

• After we change the subtraction fact to an addition fact, the operation changes to addition so we can follow the same rules of addition of integers on a number line.
• We should remember that while adding a negative number we move towards the left side of the number line and while adding a positive number we move towards the right side of the number line.

Let us understand this with the help of an example using a number line.

Example: Subtract -7 - (-4)

Solution:

Observe the number line given below to understand the steps.

• Since every subtraction fact can be written as an addition fact, we change the subtraction sign to an addition sign and reverse the sign of the subtrahend. Here, -7 - (-4) = -7 + 4
• While adding a positive number we move towards the right side of the number line. In this case, we will move to the right and reach -3

• When adding integers, when the signs are the same, add the integers and keep the same sign. For example, 4 + 5 = 9. When the signs are different, subtract the integers and keep the sign of the greater absolute value. For example, 11 + (-2) = 9
• When subtracting integers, change the subtraction sign to an addition sign and switch the sign of the second number to its opposite. For example, 6 - (- 9) = 6 + (+9) = 15.
• If there is no sign with a number, we consider it as a positive number. For example, 2 can be rewritten as +2.
• Every subtraction fact can be rewritten as an addition fact. For example, 9-10 can be rewritten as 9+(-10).
• Always write negative numbers in a bracket in an expression.
• While adding a negative number we move towards the left side of the number line.
• While adding a positive number we move towards the right side of the number line.

☛ Related Topics

• Multiplication and Division of Integers
• Integer Calculator
• Subtracting Integers Calculator
• Multiplying Integers Calculator
• Subtracting Integers Calculator

What are the Rules for Adding a Positive and Negative Integer?

The rule for the addition of a positive and negative integer states that we need to find the difference between the absolute value of the two integers and then the sign of the result will be the same as that of the larger integer of the two. For example, if we need to add 5 + (-9), we will find the difference between 5 and 9 which is 9 - 5 = 4 and we will keep the sign of the greater number. In this case, the greater number is 9 which has a negative sign so our result will also have a negative sign and the answer will be 5 + (-9) = -4.

What is the Rule for Addition and Subtraction of Negative Numbers?

• To add two negative numbers, we take the sum of both the numbers and attach a negative sign with the answer.
• While subtracting two negative numbers, we just need to remember that a subtraction fact can be written as an addition fact and the sign of the subtrahend needs to be reversed. For example, -8 - (-4) can be written as -8 + (+4) and then the rule for the addition of integers can be applied. This will result in -8 + (+4) = -4.

How to Add and Subtract Integers?

Addition and subtraction of integers can be done by following the rules given below.

• While adding two positive numbers we simply add both the numbers and get an answer which is a positive value, just like the addition of whole numbers. For example, (+3 + (+4) = 7
• While adding a positive and a negative number, we take the difference of the absolute values of both the numbers and attach the sign of the greater number with the answer. For example, 6 + (-2) = 4
• While adding two negative numbers, we take the sum of both the numbers and attach a negative sign with the answer. For example, (-5) + (-3) = -8
• For subtracting integers, we can change the subtraction fact to an addition fact, and reverse the sign of the subtrahend. After the expression changes to addition we can apply the rules of addition of integers and solve the expression. For example, 9 - (+3) = 9 + (-3) = 6

How to Add and Subtract Integers with Different Signs?

To add and subtract integers with different signs, we have a certain set of rules.

• While adding a positive and a negative number, we take the difference of the absolute values of both the numbers and attach the sign of the greater number with the answer. For example, 6 + (-7) = (-1)
• While subtracting a positive and a negative number, we change the subtraction fact to an addition fact, and then reverse the sign of the subtrahend. After this, we use the same rule of addition of integers and solve the expression. For example, (-6) -8 = -6 -(+8) = -6 + (-8) = -14

How to Add and Subtract Integers on a Number Line?

To add and subtract integers on a number line, we have a certain set of rules.

• If we need to add a positive number to another positive number, we start with the first number and move to the right of the number line. It should be noted that when we add a negative number, we move towards the left side of the number line.
• If we need to subtract a positive number, we can change the subtraction fact to an addition fact, and reverse the sign of the subtrahend. After the expression changes to addition we can apply the rules of addition given above.

What are the Applications of Integers?

The application of positive and negative numbers in the real world is different. They are generally used to represent two contradicting situations.

• One common real-life application of integers is temperature measurement. The negative and positive numbers and zero in the scale denote different temperature readings.
• Bank credit and debit statements also use integers to represent the negative or positive values of the amount.