Integers

In quantitative aptitude, what is an integer?  An integer is a collection of positive and negative numbers including zero. It is a number with no decimal and fractional parts.  Further integer numbers are divided into three main categories given below:

Positive Integers: Integer numbers greater than zero are termed as positive integers. Example: 23,45,76, and many more up to infinity.

Negative Integers: An integer number smaller than zero is termed a negative integer. Example -23, -45, -76, and many more up to negative infinity.

Zero: Zero is neither a positive integer nor a negative integer.

Integers are represented by the symbol Z and are defined as follows:

Z = { -2, 0, 56, }

Rules of Integers

Integer numbers follow certain rules for the solution of several operations.

• The sum of two integers is an integer
• The sum of two negative integers is also an integer
• The product of two negatives and two positive numbers is also an integer
• Multiplication of numbers and its reciprocal results in one

Integers Operation

There are usually four basic operations for solving problems similar to integers to have four basic arithmetic operations.

• Addition of Integers
• Subtraction of Integers
• Multiplication of Integers
• Division of Integers

Addition of Integers

Addition rules:

• If both the operands are positive then the addition will result in a positive number
• If both the operands are negative then the addition will result in a negative number
• If a positive number is greater than another negative number then the addition will result in a positive integer
• If a negative number is greater than the positive number then the addition will result in a negative integer

Problems on Addition of Integers

Example 1: Add 2+7

Solution: 2+7 = 9

Example 2: Add -2 + (-7)

Solution: – 2 – 7 = -9

Example 3: Add 2 + (-7)

Solution: 2 – 7 = -5

Example 4: Add – 2 + 7 

Solution: – 2 + 7 = 5

Subtraction of Integers

The subtraction of two integer numbers follows some specific rules given as follows:

• If both the operands are positive then the difference of both the numbers will be the same as the basic difference between two numbers
• If both the operands are negative then convert the operation into an addition problem by changing the sign of the subtrahend
• If a positive number is greater than another negative number then the subtraction will result in a positive integer
• If a negative number is greater than the positive number then the subtraction will result in a negative integer

Problems on Subtraction of Integers

Example 1: Subtract 2-7

Solution: 2 – 7 = -5

Example 2: Subtract -2 – (-7)

Solution: – 2 – (-7) = -5

Example 3: Subtract 2 – (-7)

Solution: 2 – (-7) = -9

Example 4: Subtract – 2 – 7 

Solution: – 2 – 7 = -9

Multiplication of Integers 

The product of two integer numbers follows some specific rules given as follows:

• Two positive integers result in a positive product.
• Two negative integers result in a positive product.
• Positive and negative integers will result in a negative product.

Problems on Multiplication of Integers

Example 1: Multiply 2 x 7

Solution: 2 x 7 = 14

Example 2: Multiply -2 x (-7)

Solution: – 2 x (-7) = 14

Example 3: Multiply 2 x (-7)

Solution: 2 x (-7) = -14

Example 4: Multiply – 2 – 7 

Solution: – 2 x 7 = -14

Division of Integers

The division of two integer numbers follows some specific rules given as follows:

• Division of two positive operands results in a positive integer
• Division of two negative integers results in a positive integer
• Division of positive and negative integers will result in a negative integer

Problems on Division of Integers

Example 1: Divide 14/2

Solution:  14/2 = 7

Example 2: Divide 14/2

Solution: -14/-2 = 7

Example 3: Divide 14/2

Solution: 14/-2 = -7

Example 4: Divide 14/2

Solution: -14/2 = -7

Conclusion

In quantitative aptitude, integers include positive, negative numbers, and zero. Integers neither include a decimal nor a fractional part.  -4, -9, 0, 98, 45 are all examples of integers. It is generally represented by the symbol Z, Z = {-4, -9, 0, 98, 45}. It helps in computing the efficiency in positive or negative numbers in almost all fields. It helps in representing many real-life world situations such as temperature being represented in both positive and negative integers, locations below and above sea level, and many more. All basic arithmetic operations properties are too applicable to all the integer’s arithmetic operations.