Positive and negative addition and subtraction rules

When two signs are written next to each other, the rules for adding and subtracting numbers are:

• two signs that are different become a negative sign
• two signs that are the same become a positive sign

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 of Integers

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

Important tips on Adding and Subtracting Integers

• 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

FAQs on Addition and Subtraction of Integers

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.

What is the rule for addition and subtraction?

What happens when you subtract a positive from a negative?