CBSE Class 7 Mathematics/ Integers – Notes

CBSE Class 7 Mathematics / Integers – Chapter 1/ Notes is about the summary of Chapter 1 Integers. Here you can find out all the important points about Integers, that you study for examination.

CBSE Class 7 Mathematics /Integers – Chapter 1 /Notes
Integers form a bigger collection of numbers which contains whole numbers and negative numbers.
Addition of Integers:
Addition of a positive and negative integer:
When we add one positive and one negative integer, you must subtract and give the sign of the greatest number.
Example:
(-6) + 5 = -1
7 + (-2) = 5
Addition of two negative integers:
When we add two negative integers, add the numbers and put negative sign.
Example:
(-5) + (-4) = -9
Subtraction of integers:
Subtraction is the addition of additive inverse.
Additive inverse of (-7) is 7 and additive inverse of 9 is (-9)
Example:
(-7) – (-4) = (-7) + (4) = -3
5 – (-8) = 5 + (8) = 13
(-5) – (7) = (-5) + (-7) = -12
Properties of addition and subtraction of integers:
Closure under addition:
Integers are closed under addition. In general, for any two integers a and b, a + b is an integer.
Closure under subtraction:
Integers are closed under subtraction. In general, if a and b are two integers then a – b is also an integer.
Commutative Property:
Addition is commutative for integers. In general, for any two integers a and b, a + b = b + a.
Note: Subtraction is not commutative for integers.
Associative Property:
Addition is associative for integers.
In general for any integers a, b and c, a + (b + c) = (a + b) + c
Additive Identity:
For any integer a, a + 0 = a = 0 + a
Note: Zero is the additive identity for integers.
Multiplication of Integers:
Multiplication of a positive and a Negative Integer:
While multiplying a positive integer and a negative integer, we multiply them as whole numbers and put a minus sign (-) before the product.
Example:
4 x (-5) = -20
(-3) x 6 = -18
Multiplication of two Negative Integers:
We multiply the two negative integers as whole numbers and put the positive sign before the product.
Note: The product of two negative integers is a positive integer.
Example:
(-3) x (-3) = 9
(-2) x (-5) = 10
Product of three or more Negative Integers:
If the number of negative integers in a product is even, then the product is a positive integer.
If the number of negative integers in a product is odd, then the product is a negative integer.
Example:
(-1) x (-1) = 1
(-1) x (-1) x (-1) = -1
(-1) x (-1) x (-1) x (-1) = 1
(-1) x (-1) x (-1) x (-1) x (-1) = -1
Properties of Multiplication of Integers:
Closure under Multiplication:
Integers are closed under multiplication.
In general, a x b is an integer, for all integers a and b.
Commutativity of Multiplication:
Multiplication is commutative for integers.
In general, for any two integers a and b, a x b = b x a
Multiplication by zero.
In general, for any integer a, a x 0 = 0 x a = 0
Example: (-3) x 0 = 0
Multiplicative Identity:
In general, for any integer a we have, a x 1 = 1 x a = a
Example: (-2) x 1 = -2
Note: One is the multiplicative identity for integers.
Associativity for Multiplication:
For any three integers a, b and c, (a x b) x c = a x (b x c)
Distributive Property:
For any integers a, b and c, a x (b + c) = a x b + a x c
Division of Integers:
When we divide a negative integer by a positive integer, we divide them as whole numbers and then put a minus sign (-) before the quotient.
Example: (- 50)/ (10) = -5
When we divide a positive integer by a negative integer, we divide them as whole numbers and then put a minus sign (-) before the quotient.
Example: 72/ (-8) = -9
When we divide a negative integer by a negative integer, divide them as whole numbers and then put a positive sign (+).
Example: (-12) / (-6) = 2
Properties of Division of Integers:
Any integer divided by 1 gives the same integer.
Example: (-8) /1 = -8
Any integer divided by zero is not defined, but zero divided by an integer other than zero is equal to zero.