USING SUITABLE PROPERTIES FIND THE PRODUCT

Find the value of the following :

Problem 1 :

297 × 17 + 297 × 3

Solution :

= 297 × 17 + 297 × 3

Here 297 is in common, taking out 297.

= 297 x (17 + 3)

Simplifying 17 and 3, we will get 20

= 297 x 20

= 5940

Problem 2 :

54279 × 92 + 8 × 54279

Solution :

= 54279 × 92 + 8 × 54279

Here we observe that 54279 is in common. Taking that out.

= 54279 x (92 + 8)

= 54279 x 100

= 5427900 

Problem 3 :

81265 × 169 – 81265 × 69

Solution :

= 81265 × 169 – 81265 × 69

Here 81265 is in common, taking that out

= 81265 x (169 - 69)

= 81265 x 100

= 5126500

Problem 4 :

 3845 × 5 × 782 + 769 × 25 × 218

Solution :

= 3845 × 5 × 782 + 769 × 25 × 218

Decomposing 3845, we get 769 x 5

= 769 x 5 x 5 x 782 + 769 x 25 x 218

= 769 x 25 x 782 + 769 x 25 x 218

= 769 x 25 x (782 + 218)

= 19225 x 1000

= 19225000

Problem 5 :

Find the product using suitable properties :

738 × 103

Solution :

= 738 x 103

= 738 x (100 + 3)

By distributing, we get

= 738 x 100 + 738 x 3

= 73800 + 2214

= 76014

Problem 6 :

 854 × 102

Solution :

= 854 x 102

= 854 x (100 + 2)

= 854 x 100 + 854 x 2

= 85400 + 1708

= 87108

Problem 7 :

258 × 1008

Solution :

= 258 × 1008

Decomposing 1008, we get 

= 258 × (1000 + 8)

= 258 x 1000 + 258 x 8

= 258000 + 2064

= 260064

Problem 8 :

1005 × 168

Solution :

= 1005 x 168

Decomposing 1005, we get 1000 + 5

= (1000 + 5) x 168

= 1000 x 168 + 5 x 168

= 168000 + 840

= 168840

Problem 9 :

728 × 101

Solution :

= 728 x 101

= 728 x (100 + 1)

Distributing 728, we get

= 728 x 100 + 728 x 1

= 72800 + 728

= 73528

Problem 10 :

5437 × 1001

Solution :

= 5437 x 1001

= 5437 x (1000 + 1)

Distributing 5437, we get

= 5437 x 1000 + 5437 x 1

= 5437000 + 5437

= 5442437

Problem 11 :

824 × 25

Solution :

824 × 25

Here 824 can be broken into 800 + 20 + 4

= (800 + 20 + 4) x 25

Distributing 25, we get

= 800(25) + 20(25) + 4(25)

= 20000 + 500 + 100

= 20600

Problem 12 :

4275 × 125

Solution :

= (4000 + 200 + 70 + 5) x 125

= 4000(125) + 200(125) + 70(125) + 5(125)

= 500000 + 25000 + 8750 + 625

= 525000 + 9375

= 534375

Problem 13 :

Raju purchased 35 cricket balls for $350 each 35 foot balls for $650 each. Find how much did he pay in all ?

Solution :

Number of cricket balls purchased = 35

Number of foot balls purchased = 35

Cost of each cricket ball = $350

Cost of each foot ball = $650

Total cost = 35 (350) + 35 (650)

= 35(350 + 650)

= 35 (1000)

= 35000

Problem 14 :

Giya distributed some chocolates to 26 students of her class. Each student got 7 chocolates and finally 14 chocolates left with her. How many chocolates did she bring to the class ?

Solution :

Number of students = 26

Number of chocolates get by each student = 7

Total number of chocolates distributed = 26 (7)

= (30 - 4) x  7

= 210 - 28

= 182

Number of chocolates left = 14

Total number of chocolates = 182 + 14

= 196