Addition and Subtraction of Integers (Rules and Examples)

Positive integers are produced when two positive numbers are added as opposed to two negative integers, which results in a sum with a negative sign. However, adding two different signed integers will only yield subtraction, with the sign of the result matching that of the larger number. Integers can be increased or decreased in value using the operations of addition and subtraction. Whole numbers and negative numbers are both integers. An integer is any number displayed on a number line without a fractional component. The absolute value of an integer on a number line is the distance between a number and 0.

What Are Addition And Subtraction?

The two main arithmetic operations in mathematics are addition and subtraction. In addition to these two operations, multiplication and division are the other two fundamental operations we learn in elementary math. The value added to the original value is represented by the addition. In addition to integers, rational and irrational numbers can also be added to and subtracted from. Both operations are therefore applicable to all real and complex numbers. Additionally, the same rules that apply to performing algebraic operations apply to adding and subtracting algebraic expressions.

Rules For Addition And Subtraction

Positive, negative, and zero-valued numbers that are not fractions are referred to as integers. There are universal rules for addition and subtraction. The integers that we add or subtract may be positive or negative. Thus, understanding the principles for positive and negative symbols is essential.

Rules For Addition

• A positive integer is obtained when two positive integers are added. For instance, 10 + 6 =16.

• When a positive number and a negative number are added, the operation and the output are determined by the sign of the larger number. For instance, 15 + (-20) = - 5.

• A sum of integers with a negative sign is obtained when two negative numbers are added. For instance, (- 10) + (- 6) = - 16.

• An integer when added to the inverse of itself, results in zero. For instance, 6 + (- 6) = 0.

Rules For Subtraction

Calculations are made easier by rewriting subtraction questions as additional questions. To accomplish this, change the subtraction sign to an addition sign. Take the inverse of the number that follows the sign after you have converted the sign. If the signs of the two numbers match, the absolute values are added, and the common sign is attached. If the signs of the two numbers differ, we calculate the difference between the absolute values and assign the larger number's sign to the output.

As an illustration, (- 2) - 4 = - 6

2 - 6 = - 4

Properties Of Addition Of Integers

• Closure property - Any two integers added together to yield an integer. For instance, 6 and 4 are integers which when added result in an integer, that is, 10.

• Commutative property - Any two integers added together have the same sum regardless of the sequence in which they are added. For instance, 2 + 3 = 3 + 2 = 5.

• Associative property - When the sum of three or more numbers is calculated, the order in which the integers are grouped is irrelevant. For example, (2 + 3) + 5 = 2 + (3 + 5) = 10.

• Additive identity - When you add zero to any number, the outcome is always an integer. The number zero is the additive identity. For instance, 0 + 6 = 6.

• Additive inverse - When an integer is added to an integer, the result is always 0. The two opposite numbers are known as their additive inverses. For instance, 6 + (- 6) = 0.

Properties Of Subtraction Of Integers

• Closure property - Any two integers are given, and the difference between them yields an integer. For instance, 6 and 4 are integers which when subtracted result in an integer, that is, 2.

• Commutative property - When the order is reversed, the difference between any two provided integers changes. For instance, 6 - 4 = 2 but 4 - 6 = - 2.

• Associative property - If there is a change in the grouping of three or more integers, the outcome of the subtraction technique will change. For instance, 8 - (3 - 6) = 11 but (8 - 3) - 6 = -1.

How To Add Integers On A Number Line?

• We travel to the left side of the number line while adding a negative number.

• We move to the right side of the number line while adding a positive number.

How To Subtract Integers On A Number Line?

• The operation switches to addition after the subtraction fact is changed to an addition fact, allowing us to add numbers on a number line according to the same principles.

• It's important to keep in mind that when adding a negative number, we move to the left side of the number line, and when adding a positive number, we move to the right side.

Points To Remember

• When adding integers, maintain the same sign when the signs are the same.

• Add the integers when the signs are different, but keep the sign of the absolute value with the higher number.

• When subtracting integers, transform the subtraction sign to an addition sign and the second number's sign to the opposite.

• If a number has no accompanying sign, we consider it to be positive.

• Any fact that involves subtraction can be converted into an addition fact.

• In an expression, negative integers are always included in brackets.

• We go to the left side of the number line as we add a negative number.

• We go to the right side of the number line as we add a positive number.