An integer is a number that includes 0, positive numbers and negative numbers. It can never be a fraction, decimal or per cent. 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.
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.
Use 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.
Also, Read
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.