On this page, you will find Integers Class 7 Notes Maths Chapter 1 Pdf free download. CBSE NCERT Class 7 Maths Notes Chapter 1 Integers will seemingly help them to revise the important concepts in less time.
CBSE Class 7 Maths Chapter 1 Notes Integers
Integers Class 7 Notes Conceptual Facts
1. Number line
For a positive integer on number line, we move towards right of zero and for a negative integer, we move towards the left of the zero.
2. Integers are closed under addition, subtraction and multiplication.
For example:
- a + b = integer
- a – b = integer
- a x b = integer
3. Addition and multiplication are cumulative for integers.
For example:
- a + b = b + a
- a x b = b x a
4. Addition and multiplication are associative for integers.
For example:
- (a + b) + c = a + (b + c)
- (a x b) x c = a x (b x c)
5. Zero (0) is an additive identity for integers.
For example: a + 0 = 0 + a = a
6. One (1) is a multiplicative identity for integers.
For example: a x 1 = 1 x a = a
7. Algebra of integers,
- a x (-b) = -ab
- (-a) xb = -ab
- (-a) x (-b) = ab
- a xb = ab
8. Product of even number of negative integers is positive whereas the product of odd number of negative integers is negative. For example:
- (-a) x (-b) x (-c) x (-d) (-e) -a x b x c x d x e …. even number times
- (-a) x (-b) x (-c) x (-d) (-e) = -(a x b x c x d x e) odd number times
9. Division on integers:
(i) \(\frac{(-a)}{(b)}=-\left(\frac{a}{b}\right)\)
(ii) \(\frac{(-a)}{(-b)}=\left(\frac{a}{b}\right)\)
(iii) \(\frac{(a)}{(-b)}=-\left(\frac{a}{b}\right)\)
(iv) \(\left(\frac{+a}{+b}\right)=\left(\frac{a}{b}\right)\)