# 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:

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.