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 rearrangement:
(a) 2 × 1768 × 50 (b) 4 × 166 × 25
(c) 8 × 291 × 125 (d) 625 × 279 × 16
(e) 285 × 5 × 60 (f) 125 × 40 × 8 × 25
Answer:
(a) 2 × 1768 × 50 = 2 × 50 × 1768
= 100 × 1768 = 176800
(b) 4 × 166 × 25 = 4 × 25 × 166
= 100 × 166 = 16600
(c) 8 × 291 × 125 = 8 × 125 × 291
= 1000 × 291 = 291000
(d) 625 × 279 × 16 = 625 × 16 × 279
= 10000 × 279 = 2790000
(e) 285 × 5 × 60 = 285 × 300 = 85500
(f) 125 × 40 × 8 × 25 = 125 × 8 × 40 × 25
= 1000 × 1000 = 1000000
Question 3:
Find the value of the following:
(a) 297 × 17 + 297 × 3 (b) 54279 × 92 + 8 × 54279
(c) 81265 × 169 − 81265 × 69 (d) 3845 × 5 × 782 + 769 × 25 × 218
Answer:
(a) 297 × 17 + 297 × 3 = 297 × (17 + 3)
= 297 × 20 = 5940
(b) 54279 × 92 + 8 × 54279 = 54279 × 92 + 54279 × 8
= 54279 × (92 + 8)
= 54279 × 100 = 5427900
(c) 81265 × 169 − 81265 × 69 = 81265 × (169 − 69)
= 81265 × 100 = 8126500
(d) 3845 × 5 × 782 + 769 × 25 × 218
= 3845 × 5 × 782 + 769 × 5 × 5 × 218
= 3845 × 5 × 782 + 3845 × 5 × 218
= 3845 × 5 × (782 + 218)
= 19225 × 1000 = 19225000
Question 4:
Find the product using suitable properties.
(a) 738 × 103 (b) 854 × 102
(c) 258 × 1008 (d) 1005 × 168
Answer:
(a) 738 × 103 = 738 × (100 + 3)
= 738 × 100 + 738 × 3 (Distributive property)
= 73800 + 2214
= 76014
(b) 854 × 102 = 854 × (100 + 2)
= 854 × 100 + 854 × 2 (Distributive property)
= 85400 + 1708 = 87108
(c) 258 × 1008 = 258 × (1000 + 8)
= 258 × 1000 + 258 × 8 (Distributive property)
= 258000 + 2064 = 260064
(d) 1005 × 168 = (1000 + 5) × 168
= 1000 × 168 + 5 × 168 (Distributive property)
= 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 Rs 44 per litre, how much did he spend in all on petrol?
Answer:
Quantity of petrol filled on Monday = 40 l
Quantity of petrol filled on Tuesday = 50 l
Total quantity filled = (40 + 50) l
Cost of petrol (per l) = Rs 44
Total money spent = 44 × (40 + 50)
= 44 × 90 = Rs 3960
Question 6:
A vendor supplies 32 litres of milk to a hotel in the morning and 68 litres of milk in the evening. If the milk costs Rs 15 per litre, how much money is due to the vendor per day?
Answer:
Quantity of milk supplied in the morning = 32 l
Quantity of milk supplied in the evening = 68 l
Total of milk per litre = (32 + 68) l
Cost of milk per litre = Rs 15
Total cost per day = 15 × (32 + 68)
= 15 × 100 = Rs 1500
Question 7:
Match the following:
(i) 425 × 136 = 425 × (6 + 30 + 100)
(a) Commutativity under multiplication
(ii) 2 × 49 × 50 = 2 × 50 × 49
(b) Commutativity under addition
(iii) 80 + 2005 + 20 = 80 + 20 + 2005
(c) Distributivity of multiplication over addition
Answer:
(i) 425 × 136 = 425 × (6 + 30 + 100) [Distributivity of multiplication over addition]
Hence, (c)
(ii) 2 × 49 × 50 = 2 × 50 × 49 [Commutativity under multiplication]
Hence, (a)
(iii) 80 + 2005 + 20 = 80 + 20 + 2005 [Commutativity under addition]
Hence, (b)