PPT: We Distribute, Yet Things Multiply | Mathematics Class 8- New NCERT (Ganita Prakash) PDF Download

 Page 1


WE DISTRIBUTE, YET 
THINGS MULTIPLY
Page 2


WE DISTRIBUTE, YET 
THINGS MULTIPLY
Distributive Property
The distributive property relates multiplication and addition in a special way:
a ( b + c ) = a b + a c
When we multiply a number by a sum, we can multiply each part separately 
and then add the results.
For example: 23 × (27 + 1) = (23 × 27) + (23 × 1) = 23 × 27 + 23
Page 3


WE DISTRIBUTE, YET 
THINGS MULTIPLY
Distributive Property
The distributive property relates multiplication and addition in a special way:
a ( b + c ) = a b + a c
When we multiply a number by a sum, we can multiply each part separately 
and then add the results.
For example: 23 × (27 + 1) = (23 × 27) + (23 × 1) = 23 × 27 + 23
Increments in Products
If one number is increased by 1
a(b + 1) = ab + a
³ The product increases by a.
1.
2. If both numbers are increased by 1
(a + 1)(b + 1) = ab + a + b + 1
³ The product increases by a + b + 1.For 
example: If a = 23, and, b = 27, we get
Page 4


WE DISTRIBUTE, YET 
THINGS MULTIPLY
Distributive Property
The distributive property relates multiplication and addition in a special way:
a ( b + c ) = a b + a c
When we multiply a number by a sum, we can multiply each part separately 
and then add the results.
For example: 23 × (27 + 1) = (23 × 27) + (23 × 1) = 23 × 27 + 23
Increments in Products
If one number is increased by 1
a(b + 1) = ab + a
³ The product increases by a.
1.
2. If both numbers are increased by 1
(a + 1)(b + 1) = ab + a + b + 1
³ The product increases by a + b + 1.For 
example: If a = 23, and, b = 27, we get
In General,
3.  If one number increases by 1 and the other decreases 
by 1
³ Here, the product may increase or decrease, depending 
on the values of a and b.
For example: If a = 23, and, b = 27, we get
In General,
Page 5


WE DISTRIBUTE, YET 
THINGS MULTIPLY
Distributive Property
The distributive property relates multiplication and addition in a special way:
a ( b + c ) = a b + a c
When we multiply a number by a sum, we can multiply each part separately 
and then add the results.
For example: 23 × (27 + 1) = (23 × 27) + (23 × 1) = 23 × 27 + 23
Increments in Products
If one number is increased by 1
a(b + 1) = ab + a
³ The product increases by a.
1.
2. If both numbers are increased by 1
(a + 1)(b + 1) = ab + a + b + 1
³ The product increases by a + b + 1.For 
example: If a = 23, and, b = 27, we get
In General,
3.  If one number increases by 1 and the other decreases 
by 1
³ Here, the product may increase or decrease, depending 
on the values of a and b.
For example: If a = 23, and, b = 27, we get
In General,
What Happens When Both Numbers Change?
When both numbers in a product increase by 1:
( a + 1 ) ( b + 1 ) = a b + a + b + 1
The product increases by the sum of the original numbers plus 1!
Example: (23 + 1)(27 + 1) = 23 × 27 + (27 + 23 + 1)