Class Vii: Integers
Class Vii: Integers
Class Vii: Integers
CHAPTER 1
INTEGERS
Natural numbers together with the number
zero are called whole number.
Integers are set of numbers comprising of
negative and whole numbers.
DECREASE INCREASE
BASEMENT CAR PARKING LEVELS FLOORS ABOVE GROUND LEVEL
WITHDRAWAL DEPOSIT
DOWN UP
We will learn 4 operations of
Integers-
ADDITION AND SUBTRACTION OF INTEGERS
Whenever two signs are together, we always bring it one sign.
(+) (+) = (+)
(+) (-) = (-)
(-) (+) = (-)
(-) (-) = (+)
1. When we add two positive integers, we get a positive integer.
e.g. 2, 5 2+5=8
2. When we add two negative integers, we get a negative integer.
e.g. -2,-5 -2 + (-5) = - 2 - 5 = (-7)
3. When we add a positive integer and a negative integer, we actually
subtract them and put the sign of the bigger number. e.g.
i. -3, 5 -3 + 5 = 2
ii. -8, 3 -8 + 3 = (-5)
iii. 6, -10 6 + (-10) = 6 -10 = (-4)
Subtraction of integers can be
verified similarly.
R2 -5 -2 7
C1=5 -5 + 0 =0
C2 = -1 -2 +3 = 0
R3 0 3 -3
C3 = -4 + 7 -3 =0
D1 = 5 -2 -3 = 0
D2 =-4 -2 + 0 =(-6)
Since,sum of each is not the
same , so it is not a
magic square.
Q8 Verify a-(-b) = a + b
(i) a =21, b = 18
LHS = a –(-b) RHS = a+ b
= 21- (-18) = 21+ 18
= 21+18 = 39
= 39
As LHS = RHS
Hence verified
Q9 use the sign >,< or =
34+(-24) –(15)_____36+(-52)-(-36)
-7 is an Integer. 3 is an Integer.
(a + b) is an Integer. (a – b) is an Integer.
MULTIPLICATION DIVISION
a x b= a ÷ b=
-2 x (-5) = 10 6÷ 4 = 1.5
b+a= b–a=
-5 + (-2) = - 5 - 2 = (-7) -5 - (-2) = - 5 + 2 = -3
a+b=b+a a-b≠b-a
MULTIPLICATION DIVISION
axb= a÷b=
-2 x (-5) = 10 6÷3=2
bxa= b÷a=
-5 x (-2) = 10 3 ÷ 6 = 0.5
axb=bxa a÷b≠b÷a
ASSOCIATIVE PROPERTY
ADDITION SUBTRACTION
a + (b + c) = a - (b - c) =
-2 + [-5 + (-3)] = - 2 + [-5- 3] -2 - [5 - (-3)] = - 2 - [5 + 3]
= -2 +(-8) = -2 - 8 = (-10) = - 2 - 8 = (-10)
(a + b) + c = (a - b) - c =
[-2 + (-5)] + (-3) = [-2 - 5] – 3 [-2 - 5] - (-3) = -7 + 3
= -7 - 3 = (-10) = (- 4)
a + (b + c) = (a + b) + c a - (b - c) ≠ (a - b) - c
MULTIPLICATION DIVISION
(a × b) × c = (a ÷ b) ÷ c =
[-2 x (-5)] x (-3) = 10 x (-3) = (-30) [12 ÷ (-6)] ÷ (-2) = [-2] ÷ (-2) = 1
a × (b × c) = a ÷ (b ÷ c) =
-2 x [(-5) x (-3)] = -2 x 15 = (-30) 12 ÷ [(-6) ÷ (-2)] = 12 ÷ 3 = 4
(a × b) × c = a × ( b × c ) (a ÷ b) ÷ c ≠ a ÷ (b ÷ c)
DISTRIBUTIVE PROPERTY
DISTRIBUTIVE PROPERTY OF MULTIPICATION OVER
ADDITION
a × ( b + c) =
-2 x [-5 + (-3)] = - 2 x [-5 - 3] = -2 x (-8) = 16
(a × b) + (a × c) =
[-2 x (-5)] + [-2 x (-3)] = 10 + 6 = 16
a × (b + c) = (a × b) + (a × c)
DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER
SUBTRACTION
a x ( b - c) =
2 x [-5 - (-3)] = 2 x (-5 + 3) = 2 x (-2) = (- 4)
(a × b) - (a × c) =
[2 x (-5)] – [2 x (-3)] = -10 – (-6) = - 10 + 6 = (- 4)
a × (b - c) = (a × b) - (a × c)
Additive & Multiplicative Identity