Class 6 | Mathematics | Chapter 2|
Whole Numbers | Exercise 2.2
Question 1 : Find the sum by suitable rearrangement:
(a) 837 + 208 + 363
(b) 1962 + 453 + 1538 + 647
Answer: (a) 837 + 208 + 363
=(837+ 363 ) + 208
=1200 + 208
= 1408
(b) 1962 + 453 + 1538 + 647
= (1962 + 1538) + (453 + 647)
3500 + 1100
= 4600
Question 2: Find the product by suitable arrangement:
(a) 2 x 1768 x 50
(b) 4 x 166 x 25
(c) 8 x 291 x 125
(d) 625 x 279 x 16
(e) 285 x 5 x 60
(f) 125 x 40 x 8 x 25
Answer: (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
(c) 8 x 291 x 125
= (8 x 125) x 291
= 1000 x 291
=291000
(d) 625 x 279 x 16
=(625 x 16) x 279
=10000 x 279
= 2790000
(e) 285 x 5 x 60
=285 x (5 x 60)
=285 x 300
=85500
(f) 125 x 40 x 8 x 25
= (125 x 8) x (40 x 25)
= 1000 x 1000
= 1000000
Question 3:Find the value of the following:
(a) 297 x 17 + 297 x 3
(b) 54279 x 92 + 8 x 54279
(c) 81265 x 169 – 81265 x 69
(d) 3845 x 5 x 782 + 769 x 25 x 218
Answer: (a) 297 x 17 + 297 x 3
= 297 x (17 + 3)
= 297 x 20
= 5940
(b) 54279 x 92 + 8 x 542379
= 54279 x (92 + 8)
= 54279 x 100
=5427900
(c) 81265 x 169 – 81265 x 69
= 81265 x (169 – 69)
= 81265 x 100
= 8126500
(d) 3845 x 5 x 782 + 769 x 25 x 218
= 3845 x 5 x 782 + 769 x 5 x 5 x 218
= 3845 x 5 x 782 + 3845 x 5 x 218
= 3845 x 5 x (782 + 218)
= 3845 x 5 x 1000
= 19225000
Question 4: Find the product using suitable properties:
(a) 738 x 103
(b) 854 x 102
(c) 258 x 1008
(d) 1005 x 168
Answer:
(a) 738 x 103
738 × (100+3)
= 738 x 100 + 738 x 3
= 73800 + 2214
= 76014
(b) 854 x 102 = 738 x (100 + 3)
= 854 x (100 + 2)
= 854 x 100 + 854 x 2
= 85400 + 1708
= 87108
(c) 258 x 1008
= 258 x (1000 + 8)
258 x 1000 + 258 x 8
= 258000 + 2064
= 260064
(d) 1005 x 168
= (1000 + 5) x 168
=1000 x 168 + 5 x 168
= 168000 + 840
= 168840
Question 5: A taxi-driver, filled his car petrol tank with 40 litres of petrol on Monday. The next day, he filled the tank with 50 litres of petrol. If the petrol costs ₹ 44 per litre, how much did he spend in all on petrol?
Answer: Petrol filled on Monday = 40 litres
Petrol filled on next day = 50 litres
Total petrol filled = 90 litres
Now, Cost of 1 litre petrol = ₹ 44
Cost of 90 litres petrol = 44 x 90
= 44 x (100 – 10)
= 44 x 100 – 44 x 10
= 4400 – 440
= ₹ 3960
Therefore, he spent ₹ 3960 on petrol.
Question 6: A vendor supplies 32 litres of milk to a hotel in a morning and 68 litres of milk in the evening. If the milk costs ₹15 per litre, how much money is due to the vendor per day?
Answer: Supply of milk in morning = 32 litres
Supply of milk in evening = 68 litres
Total supply = 32 + 68 = 100 litres
Now Cost of 1 litre milk = ₹15
Cost of 100 litres milk = 15 x 100 = ₹1500
Therefore, ₹1500 is due to the vendor per day.
Question 7: Match the following:
(i) 425 x 136 = 425 x (6 + 30 + 100) (a)Commutativity under multiplication
(ii) 2 x 48 x 50 = 2 x 50 x 49 (b) Commutativity under addition
(iii) 80 + 2005 + 20 = 80 + 20 + 2005 (c) Distributivity multiplication under addition
Answer: (i) 425 x 136 = 425 x (6 + 30 + 100) (c) Distributivity of multiplication over addition
(ii) 2 x 49 x 50 = 2 x 50 x 49 (a) Commutativity under multiplication
(iii) 80 + 2005 + 20 = 80 + 20 + 2005 (b) Commutativity under addition