An integer is a number that includes 0, positive numbers, and negative numbers. It can never be a fraction, decimal, or percent. Integers are mainly used in our day-to-day lives in mathematical terms. Get to know the definition, operations, and use of integers in the below-mentioned sections. Also, get the example questions with solutions for the convenience of grade 6 math students.

Also, Check: Use of Integers as Directed Numbers

## What is an Integer?

Integers are a set of counting numbers (positive and negative) along with zero. Some of the examples of integers are -4, -3, -2, -1, 0, 1, 2, 3. The integers are represented by Z. The types of integers are positive integers, negative integers, and zero.

### Integer Rules

The rules depend on the operations performed on integers given below:

**Addition Rule:**- If the sign of both integers is the same, then the sum will have the same sign.
- If the sign of one integer is positive, the sign of another integer is negative, then the sign of the result is the sign of the larger number.

**Subtraction Rule:**- Convert the operation to addition by changing the sign of the subtrahend.

**Multiplication Rule:**- Multiply the sign of integers to get the result sign.

**Division Rule:**- Divide the signs of two operands and get the resultant sign.

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### Real Life Examples of Integers

The examples on using integers are along the lines:

- If profit is represented by positive integers, losses are by negative integers.
- The rise in the price of a product is represented by positive integers and fill in price by negative integers.
- If heights above the sea level are represented by positive integers, then depths below sea level by negative integers, and so on.

### Integers as Directed Numbers

If a number represents direction, then the number is called a directed number. The below-given examples explain it in detail.

**Example:**

If +4 represents 4 m towards East, then -5 represents 5 m towards its opposite direction i.e towards west.

If a positive integer shows a particular direction, then the negative integer shows the opposite direction.

### Example Questions on Use of Integers

**Question 1:
**Write an integer to describe a situation

(i) Losing Rs 100

(ii) Owing Rs 1500

(iii) Depositing $500 in a bank

**Solution:
**(i) An integer representing a loss of Rs 100 is -100.

(ii) An integer representing an owing of Rs 1500 is -1500

(iii) An integer representing depositing $500 in a bank is +500

**Question 2:
**Write an appropriate integer for each of the following:

(i) earned Rs 800 interest

(ii) a decrease of 5 members

(iii) an increase of 3 inches

**Solution:
**(i) Earned Rs 800 interest is represented by +800

(ii) Decrease of 5 members is represented by -5

(iii) An increase of 3 inches is represented by +3

### Frequently Asked Question’s on Using Integers

**1. What are the applications of integers?**

Integers are used to signify two contradicting situations. The positive and negative integers have different applications. Integers can compare and measure changes in temperature, credits, debits calculation by the bank.

**2. What are the integer rules?**

The integer rules are the sum of two integers is an integer, a difference of two integers is an integer. Multiplication of two or more integers is an integer. The division of integers may or may not be an integer.

**3. What are the integer properties?**

The main properties of integers are closure property, commutative property, associative property, identity property, and distributive property.

**4. What are the 5 integer operations?**

The operations with integers are addition, subtraction, multiplication, and division.