# Integers

We learn various types of numbers in Math. Natural and whole numbers, odd and even numbers, rational and irrational numbers, negative, fractions, and so on are all examples. Zero, natural numbers, and the additive inverse of those numbers make up integers. Except for the fractional element, it can be represented on a number line. The letter Z denotes Integer.

Any number that may be either 0 or a positive or negative number is called an integer. Integers can be either + ve or – ve numbers. Like whole numbers, integers do not include fractions. All arithmetic operations, including addition, subtraction, multiplication, and division, can be performed on integers. Integers include numbers such as 2,4,6,9,-8,-10, and so on.

## Types of Integers

There are three types of integers:

• Positive Numbers: Numeric values with a plus sign (+) in front of them are referred to as positive numbers. In most circumstances, the + sign is omitted and the symbol is simply displayed without it. Positive numbers, including zero, are greater than negative numbers. On the number line, positive numbers always appear on the right-hand side of zero. Examples of positive numbers are: 1,3,5,24,32,100,2678 etc
• Negative Numbers: A minus sign in front of a number represents a negative integer. These figures are shown on the number line to the left of the origin.

Negative numbers include…, – 769, –300, -45, -2, and -1

• Zero: On the number line, zero is a neutral number. It is neither positive nor negative.

## Rules of Integers

Case 1: If the signs are the same then add the numbers and keep the sign

1. If the two numbers are positive then add the numbers and the answer is positive.

Ex: 4+6 =10

1.  If the two numbers are negative then add the numbers and the answer is negative.
Ex: (-4) + (-2)= – 6

Case 2: Subtract the numbers and use the sign of the larger number if the signs are different.

1. If one number is positive and the other negative then subtract the numbers and consider the sign of the bigger number. Ex 6-4 =2
2. Ex 8-12 =- 4
• Subtraction

Case 1: If the first number is positive and the second number is negative then the sign of the second number changes to positive.

Ex 8-(-4)= 8 + 4 =12

Case 2: If the first and the second number both are negative then the sign of the first number will remain the same but the sign of the second number will be positive. The answer will take the sign of a bigger number.

Ex (- 6)- (-10)= – 6 + 10 = 4

Case 3: If one number is negative then the second number is positive then add both the number and the sign of the answer will be negative.

Ex -9 – (7) = – 9 – 7= -16

• Multiplying and Dividing Integers

Case 1 : If both the numbers are positive then multiply or divide the answer is always positive.

Ex (-3) x (-4) = 12

(-10) ÷ (-2) = 5

Case 2: If both numbers have different signs then, multiplying or dividing the answer is always negative.

Ex (5) x (- 7)= – 35

A negative number divided by a positive number equals a negative value

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