whole numbers -post 3

April 19, 2020

Good morning boys, 
today we are going to learn 3 properties of multiplication.

1. Closure property 

Whole numbers are close under addition and under multiplication 
EXAMPLE:
6 - 2 = 4 (Whole Number )
7 - 8 = -1(Not a whole No)
3 - 9 = -6 (Not a whole number)
8 ÷ 4 = 2 (A whole Number )
5 ÷ 7 = 5÷ 7 (Not a whole number )

EXAMPLE: 
4 + 5 = 9     [Whole numbers]
13 + 4 = 17 [Whole numbers]

4 x 3 = 12    [whole number]
12 x 4 = 48  [whole numbers]

[NOTE: Are whole numbers closed under addition and subtraction?

ANSWER: NO]

2. Commutative property of add + multiplication

Whole numbers in any order, answer is the same in addition and multiplication
EXAMPLE:
 1. 4 + 5 = 5 + 4
        9    =    9
 2. 4 x 5 = 5 x 4
        20  =   20

3. Associative Property 
To multiply any 3 whole numbers, we can multiply any 2 numbers and then multiply the product with the third number.
EXAMPLE:
While the product of 3 numbers a, b and c
(a x b) x c = a x (b x c) = a + b + c 

Observe the following:

1. (2 + 3) + 4 = 2 + (3 + 4)
       5 + 4      =     2 + 7
          9         =        9 

 2. (4 x 5) x 6 = 4 x (5 x 6)
        20 x 6    =    4 x 30 
          120      =       120

Notice how we have grouped the numbers for our convenience of adding and multiplying. we group the number to make it easy to add or multiply

Let us now do Ex. 2.2 
Q1. Find the sum by suitable rearrangement.

a. 837 + 208 + 363
  =(837 + 363) + 208
  = 1200 + 208
  = 1408

b. 1962 + 453 + 1538 + 647
  =(1952 + 1538) + (453 + 647)
  = 3490 + 1100
  = 4590

Q2. Find the product bu suitable rearrangement 
a. 2 x 1768 x 50
   = (2 x 50) x 1768  
   = 100 x 1768
   = 176800

b. 4 x 166 x 25
   = 4 x 25 x 166
   = 100 x 166
   = 16600

You may do the rest (c, d, e, f) in your copy

Please attempt these extra sum in your copy:

1. Find the product by suitable rearrangement:
a. 311, 528, 289
b. 723, 834, 66, 277
c. 78, 203, 435, 7197, 422

2. Answer the following:
a. 125 x 40 x 8 x 25
b. 625, 239, 16
c. 4 x 528 x 25

Check your answers below:
1. a. 1128
b. 1900
c. 8335

2. a. 52800
b. 2390000
c. 1000000

Thankyou
Have a nice day