INTEGERS_06CBSE
Dear Children,
So far, we have discussed only two types of numbers, namely, natural numbers and whole numbers. In this chapter we shall extend our number system from whole numbers to integers. We shall discuss the representation of integers on the number line, operations on integers and their properties.
What are integers in INTEGERS_06
When a smaller whole number is subtracted from bigger whole number we get a whole number, but when we subtract a bigger whole number from smaller one, how we represent it in INTEGERS_06
Than we get a new representation, which is called negative representation. Thus we have two different type of numbers , numbers like 1,2,3,4….. are called positive numbers and -1,-2,-3,-4…. are called negative numbers and zero is not positive and not even negative, the collection of this type of numbers are called INTEGERS.
Example – we know the freezing point of water is 00C, we shall represent a temperature of
- 200C above the freezing point of water as +200C or 200 C
- 200C below the freezing point of water as -200C
Operation on integers:
- Addition– we have learnt how to add two different whole numbers on the number line. We shall extend the same method for addition of integers in integers_06 by using number line for example-
Adding -4 to a number means moving 4 steps to the left of the number in number line.
Adding +4 to a number means moving 4 steps to the right of the number in number line.
Some rules can be followed for the addition of integers.
Rule1-If two positive integers or two negative integers are added, we add their values regardless of their sign and give the sum their common sign.
Rule 2– To add a positive and a negative integer, we find the difference between their numerical values regardless of their signs and give the sign of the integer with the greater value to it.
- Subtraction- we have learnt how to subtract two whole numbers. We defined subtraction as an inverse process of addition. We extend the same idea to subtraction of integers. Suppose we want to subtract (-3) from5, clearly we want a number which when added to (-3) gives 5 , on number line , find out how many steps should we move from -3 to reach 5 , we see it is 8. Thus
5-(-3) =8
So we can frame a rule – To subtract one integer from another, we take the additive inverse of the integer to be subtracted and add it to the other integer.
a – b = a + (-b)
- Multiplication -two find the product of two integers we can follow the following rules.
Rule1-to find the product of two integers with unlike sign, we find the product of their values regardless of their signs and give a minus sign to the product.
Rule2– to find the product of two integers with the same sign, we find the product of their values regardless of their signs and give a plus sign to the product.
- Division- we know thedivision of whole numbers is an inverse process of multiplication. We extend the same idea to integers. We have the following rules for division of integers.
Rule1- for dividing one integer by another, the two having unlike signs we divided their values regardless of their signs and give minus sign to the quotient.
Rule1- for dividing one integer by another, the two having like signs we divided their values regardless of their signs and give plus sign to the quotient.
INTEGERS_06_Important website:
https://ncert.nic.in/textbook.php
Practice worksheet-
INTEGERS_06_Video link-
Practice link of MCQ-