FIND THE PRODUCT USING DISTRIBUTIVE PROPERTY

Find the product using distributive property :

Problem 1 :

728 x 101

Solution :

728 = 700 + 28

101 = 100 + 1

728 x 101 = (700 + 28)(100 + 1)

= 700(100) + 700(1) + 28(100) + 28(1)

= 70000 + 700 + 2800 + 28

Arranging based on the number of digits, we get

= 70000 + 2800 + 700 + 28

= (72800 + 700) + 28

= 73500 + 28

= 73528

Problem 2 :

854 x 102

Solution :

854 = 800 + 54

102 = 100 + 2

854 x 102 = (800 + 54)(100 + 2)

= 800(100) + 800(2) + 54(100) + 54(2)

= 80000 + 1600 + 5400 + 108

Arranging based on the number of digits, we get

= 80000 + (1600 + 5400) + 108

= 80000 + 7000 + 108

= 87000 + 108

= 87108

Problem 3 :

258 x 1008

Solution :

258 = 200 + 58

1008 = 1000 + 8

258 x 1008 = (200 + 58)(1000 + 8)

= 200(1000) + 200(8) + 58(1000) + 58(8)

= 200000 + 1600 + 58000 + 464

Arranging based on the number of digits, we get

= 200000 + 58000 + 1600 + 464

= 258000 + 1600 + 464

= 259600 + 464

= 260064

Problem 4 :

1005 x 168

Solution :

1005 = 1000 + 5

168 = 100 + 68

1005 x 168 = (1000 + 5)(100 + 68)

= 1000(100) + 1000(68) + 5(100) + 5(68)

= 100000 + 68000 + 500 + 340

Arranging based on the number of digits, we get

= 100000 + 68000 + 500 + 340

= 168000 + 840

= 168840

Problem 5 :

The cost of a chair is ₹7635 and the cost of a table is ₹12365. Find the total cost of 12 chairs and 12 tables.

Solution :

Cost of a chair = ₹7635

Cost of table = ₹12365

Cost of 12 chairs = 12 (7635)

Cost of 12 tables = 12(12365)

Total cost = 12(7635) + 12(12365)

= 12(7635 + 12365)

= 12 (20000)

= 240000

So, the total cost of 12 chairs and tables is ₹240000.

Simplify by suitable rearrangement:

Problem 6 :

 643 + 346 + 357

Solution :

= 643 + 346 + 357

Arranging in correct order.

= (643 + 357) + 346

= 1000 + 346

= 1346

Problem 7 :

5 × 241 × 20

Solution :

= 5 x 241 x 20

= 5 x 20 x 241

= 100 x 241

= 100 x (200 + 41)

= 100 x 200 + 100 x 41

= 20000 + 4100

= 24100

Problem 8 :

 Simplify the following using the distributive property:

234 × 256 – 234 × 56

Solution :

234 × 256 – 234 × 56

= 234 x (256 - 56)

= 234 x 200

200 can be broken into 2 x 100

= 234 x 2 x 100

= 468 x 100

= 46800

Problem 9 :

Simplify 126 × 45 + 126 × 55 by using suitable property.

Solution :

= 126 × 45 + 126 × 55

= 126 x (45 + 55)

= 126 x 100

= 12600

Problem 10 :

Simplify using distributive property

23 x 99

Solution :

= 23 x 99

= 23 x (100 - 1)

= 23 (100) - 23(1)

= 2300 - 23

= 2277

Problem 11 :

2698 × (100+9) = 2698 × 100 + 2698 × 9

is true by _________property.

Solution :

The required property is distributive property.

Problem 12 :

Use the same property to solve the expression:

51887 × 88 + 51887 × 12

Solution :

= 51887 × 88 + 51887 × 12

= 51887 x (88 + 12)

= 51887 x 100

= 5188700

Problem 13 :

A vendor supplies 32 liters of milk to a hotel in the morning and 68 liters of milk in the evening. If the milk costs $15 per liter, how much is due to the vendor per day ?

Solution :

Quantity of milk in the morning = 32 liter

Quantity of milk delivered in the evening = 68 liters

Total quantity milk delivered = 32 + 68

= 100 liter

Cost of each liter of milk = $15

Total cost = 15 x 100

= $1500

Problem 14 :

A taxi driver filled his car petrol tank with 40 liters of petrol on Monday. The next day, he filled the tank with 50 liters of petrol cost $44 per liter, how much did he spend in all ?

Solution :

Quantity of petrol on Monday = 40 liters

On Tuesday he filled = 50 liters

Total quantity of petrol = 40 + 50

= 90 liters

Cost of 1 liter of petrol = $44

Total cost = 90 x 44

= $3960