Integers Lesson 8

HELLO STUDENTS!

LET US CONTINUE WITH THE REST OF THE PROPERTIES OF MULTIPLICATION.

The students will be able to:

1. Understand that the order of integers does not change the result and apply the same by multiplying two and three integers.
2. Verify distribution of integers under multiplication.

THE PROPERTIES OF MULTIPLICATION:Remember that the first two properties were discussed yesterday.3. Commutativity of Multiplication 4. Associativity of Multiplication5. Distributive Property

Commutativity and Associativity of Multiplication are similar to each other. It suggests that integers can be multiplied in any order. For example, 2 x (-5) = -10 Also, (-5) x 2 = -10 [ COMMUTATIVITY OF MULTIPLICATION ]

Check if LHS = RHS: Example 1: (-16) x 3 = 3 x (-16)
In general, for any two integers a and b;a x b = b x a
The same we may apply to three different integers. 

For example[(-3) x (2) ] x (-5) =(-6) x (-5)=30 Or, (-3) x [ (2) x (-5) ]=(-3) x (-10)=30 

Do it Yourself: Check if LHS = RHS for, 12 x [ (-4) x 3 ] = [ 12 x (-4)] x 3
In general, for any three integers a, b and c;(a x b) x c = a x (b x c)

https://www.youtube.com/watch?v=SkstIM8w4HM&feature=youtu.be Pause at 2:47Now you will be able to solve the Ex 1.3 Q5 (b) and (c)

(c) is done for you.

15 x (-25) x (-4) x (-10) [we will find the easiest arrangement to multiply first. Here, multiplying 25 x 4 x 10 = 1000] 

So, 15 x [ (-25) x (-4) x (-10)]

15 x (-1000)

-15000

Distributive property of Multiplication over Addition

In general, a, b and c are integers wherea x ( b + c) = a x b + a x c. Here, the integer 'a' is distributed to the integers inside the brackets.

Let us verify this with some examples,

(-5) x [(-2) + 5]

=(-5) x 3

= -15

Using the property, (-5) x [(-2) + 5]

[(-5) x (-2)] + [(-5) x 5]

=10 + (-25)

= -15

Do it yourself: 10 x [(-6) +(-1)]

Observe the examples done for you in the textbook page no. 17

https://www.youtube.com/watchv=SkstIM8w4HM&feature=youtu.be  Play from where you paused (at 2:47)

Again pause at 7:27.
Now solve Ex 1.3 Q2 (You may play the video again to recall.)

Also, solve Q5 parts a, d, e, f, g, h
[Two are done for you] 
(a) 26 × (- 48) + (- 48) × (-36)     (You take -48 from these parts)
= −48 × [(26 + (−36)] (distributive property)
= −48 × (−10) 
= 480 
(d) (- 41) × 102 
= (- 41) × (100 + 2) 
= (-41 × 100) + (-41 × 2) (distributive property) 
= -4100 + (-82)
= - 4182

This is all for today.
BYE
TAKE CARE.