USING PROPERTIES OF MULTIPLICATION AND DIVISION

Simplify, if possible :

Problem 1 :

6 × 0

Solution :

Any number multiplied by 0 gives the result 0.

6 × 0 = 0

Problem 2 :

6 ÷ 0

Solution :

When we divide any non-zero number by zero, the quotient is undefined.

So, dividing any non-zero number by zero is meaningless.

6 ÷ 0 = undefined

Problem 3 :

0 × 6

Solution :

If 0 is multiplied to any real number.

The product of any real number and zero is zero

= 0 × 6

= 0

Problem 4 :

0 ÷ 11

Solution :

When zero is divided by any non-zero number, the quotient is zero.

0 ÷ 11 = 0

Problem 5 :

11 × 0

Solution :

Every number multiplied by 0 gives the result 0.

11 × 0 = 0

Problem 6 :

0 × 11

Solution :

If 0 is multiplied to any real number.

The product of any real number and zero is zero

= 0 × 11

= 0

Problem 7 :

0 × 1

Solution :

If 0 is multiplied to any real number.

The product of any real number and zero is zero

= 0 × 1

= 0

Problem 8 :

0 × 0

Solution :

If 0 is multiplied to any real number.

The product of any real number and zero is zero

= 0 × 0

= 0

Problem 9 :

0 ÷ 1

Solution :

When zero is divided by any non-zero number, the quotient is zero.

0 ÷ 1 = 0

Problem 10 :

0 × 37

Solution :

If 0 is multiplied to any real number.

The product of any real number and zero is zero

= 0 × 37

= 0

Problem 11 :

87 × 0

Solution :

Every number multiplied by 0 gives the result 0.

87 × 0 = 0

Problem 12 :

87 ÷ 0

Solution :

When we divide any non-zero number by zero, the quotient is undefined.

So, dividing any non-zero number by zero is meaningless.

87 ÷ 0 = undefined

Multiplication Using Shortcut

Simplify the following, taking short cuts where possible :

Problem 1 :

5 × 41 × 2

Solution :

5 × 41 × 2

Here while multiplying 5 and 2 first, we will get 10, then multiplying it by 41 we will get 410.

So, steps should be,

= 5 × 41 × 2

= (5 × 2) × 41

= 10 × 41

= 410

Problem 2 :

25 × 91 × 4

Solution :

25 × 91 × 4

Here while multiplying 25 and 4 first, we will get 100, then multiplying it by 91 we will get 9100.

So, steps should be,

= 25 × 91 × 4

= (25 × 4) × 91

= 100 × 91

= 9100

Problem 3 :

20 × 113 × 5

Solution :

20 × 113 × 5

Here while multiplying 20 and 5 first, we will get 100, then multiplying it by 113 we will get 11300.

So, steps should be,

= 20 × 113 × 5

= (20 × 5) × 113

= 100 × 113

= 11300

Problem 4 :

50 × 200 × 19

Solution :

50 × 200 × 19

Here while multiplying 50 and 19 first, we will get 950, then multiplying it by 200 we will get 190000.

So, steps should be,

= 50 × 200 × 19

= (50 × 19) × 200

= 950 × 200

= 190000

Problem 5 :

57 × 125 × 8

Solution :

57 × 125 × 8

Here while multiplying 57 and 8 first, we will get 456, then multiplying it by 125 we will get 57000.

So, steps should be,

= 57 × 125 × 8

= (57 × 8) × 125

= 456 × 125

= 57000

Problem 6 :

789 × 250 × 40

Solution :

789 × 250 × 40

Here while multiplying 250 and 40 first, we will get 10000, then multiplying it by 789 we will get 7890000.

So, steps should be,

789 × 250 × 40

= (250 × 40) × 789

= 10000 × 789

= 7890000

Problem 7 :

4 × 8 × 125 × 250

Solution :

4 × 8 × 125 × 250

Here while multiplying 4 and 8 first, we will get 32, second multiplying 125 and 250 we will get 31250, then multiplying 32 and 31250, we will get 1000000.

So, steps should be,

4 × 8 × 125 × 250

= (4 × 8) × (125 × 250)

= 32 × 31250

= 1000000

Problem 8 :

8 × 2 × 96 × 125 × 50

Solution :

8 × 2 × 96 × 125 × 50

Here while multiplying 2 and 8 first, we will get 16, second multiplying 50 and 96 we will get 4800, then multiplying 125, we will get 9600000.

So, steps should be,

= (2 × 8) × (50 × 96) × 125

= 16 × 4800 × 125

= 9600000

Problem 9 :

5 × 57 × 8 × 125 × 200

Solution :

5 × 57 × 8 × 125 × 200

Here while multiplying 5 and 8 first, we will get 40, second multiplying 57 and 125 we will get 7125, then multiplying 200, we will get 57000000.

So, steps should be,

5 × 57 × 8 × 125 × 200

= (5 × 8) × (57 × 125) × 200

= 40 × 7125 × 200

= 57000000