ANSWER KEY -
Multiple Choice questions:
1. C. 2002
2. C. 99987
3. C. 27
4. A. Whole numbers
5. A. 5940
6. B. 0
7. C. 420
8. B. 1
9. D. 64
10. C. 70009, 70008, 70007
11. C. 37904
12. A. 123 × 8 + 3 = 987
13. D. 29
14. C. 2500
15. B. 0
Match The Following:
Fill in the blanks:
1. Division by 0 is not defined.
2. A number remains unchanged when added to zero.
3. A number remains unchanged when multiplied to 1.
4. 13 × 100 × 1000 = 1300000
True /False:
1. True
2. False, every whole number except 0 is a natural number.
3. False, the predecessor of 10 is 9.
4. True
Very Short Answer:
1. There are 20 whole numbers between 32 and 53. These are 33, 34, 35, 36, 37, 38, 39,
40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51 and 52.
2. No, all whole numbers are not natural numbers. (0 is a whole number but not a natural number.)
3. 12321
4.
I. The next three consecutive whole numbers of 39359 are: 39360, 39361, 39362
II. The next three consecutive whole numbers of 8632157 are: 8632158, 8632159, 8632160.
5. Petrol filled on Monday = 40 liters.
Petrol filled the next day = 50 liters.
∴ Total petrol filled on the two days = 40 liters + 50 liters = 90 liters.
∴ Cost of petrol per liter = Rs. 44
∴ Cost of 90 liters petrol = Rs. 44 × 90 = Rs. 3960.
6.
I. 8 × 391 × 125 = 391 × (125 × 8)
= 391 × 1000
= 391,000
II. 2 × 1234 × 50 =1234 × (2 × 50)
= 1234 × 100
= 123,400
7. Breakfast consisting of 150 calories.
Lunch consisting of 350 calories.
Dinner consisting of 1000 calories.
The sum of the calories consumed that day is
150 + 350 + 1000 = 1500 calories.
8. 0 is the smallest whole number.
9. Whole number 0 has no predecessor.
10. (a) 6 + 4 = 4 + 6 holds commutative property of addition.
(b) 3 + 2 = whole number holds closure property.
11. (a) 25 + 36 + 15
Way I: 25 + (36 + 15) = 25 + 51 = 76
Way II: (25 + 36) + 15 = 61 + 15 = 76
Way III: (25 + 15) + 36 = 40 + 36 = 76
Here, we have used associative property.
(b) 30 + 18 + 22
Way I: 30 + (18 + 22) = 30 + 40 = 70
Way II: (30 + 18) + 22 = 48 + 22 = 70
Way III: (30 + 22) + 18 = 52 + 18 = 70
Here, we have used associative property.
12. (a) 36 × 102 = 36 × (100 + 2)
= 36 × 100 + 36 × 2
= -36000 + 72 = 36072
(b) 35 × 98 = 35 × (100 – 2) = 35 × 100 – 35 × 2
= 3500 – 70 = 3430
13. The greatest 3-digit number = 999
The smallest 2-digit number = 10
∴ Product = 999 x 10 = 9990
14. The smallest 4-digit number = 1000
∴ The predecessor of 1000 = 1000 – 1 = 999
15. Given statement is
10 x n + 1 = n1
Put n = 5, 10 x 5 + 1 = 51
⇒ 50 + 1 = 51
⇒ 51 = 51. Hence, verified.
Short Answer:
1. (a) 736 × 102 = 736 × (100 + 2)
= 736 × 100 + 736 × 2 [Using distributive property]
= 73600 + 1472 = 75072
(b) 8165 × 169 – 8165 × 69 = 8165 × (169 – 69) [Using distributive property]
= 8165 × 100 = 816500
2. Next two terms are
1010101 × 1010101= 1020304030201
101010101 × 101010101=10203040504030201
3. Next two terms are
15873 × 7 × 3 = 333333
15873 × 7 × 4 = 444444
4. (a) 945 × 4 × 25 = 945 × (4 × 25)
= 945 × 100 = 94500
(b) 40 × 328 × 25 = 328 × (40 × 25)
= 328 × 1000 = 328000
5. (a) 3 + 4
(b) 6 – 2
(c) 2 × 4
6. (a) 3 + 4 = 7 (whole number) closure property
(b) 4 + 5 = 5 + 4 Commutative property
(c) 3 + (5 + 7) = (3 + 5) + 7 Associative property
(d) 6 × (8 + 3) = 6 × 8 + 6 × 3 Distributive property.
7. Total cost of 124 LED sets = ₹(38,540 × 124)
= ₹ [38,540 × (100 + 20 + 4)]
= ₹ [38,540 × 100 + 38,540 × 20 + 38,540 × 4]
= ₹ [38,54,000 + 7,70,800 + 1,54,160]
= ₹ 47,789,6
8. Greatest 3-digit number = 999
Greatest 2-digit number = 99
∴ Product = 999 × 99 = 999 × (100 – 1)
= 999 × 100 – 999 × 1
= 99900 – 999 = 98901
9. 2, 5, 7, 11, 13, 17, 19, 23, 29 and 31 are such numbers which
can be shown only as line.
123 × 9 + 4 = 1111.
Long Answer:
1. Total distance = 320 km
Distance covered by the bus = 180 km
Speed of the bus = 40 km/h
∴Time Taken by the bus = Distance/Speed
=180/40 hours= 9/2 hours
Distance covered by the train = 320 – 180 = 140 km.
Speed of the train = 70 km/h
∴ Time taken by the train
= Distance/Speed =140/70 hours = 2hours
Hence, the total time taken by the passenger
= 9/2 hours + 2 hours
= 4 hours 30 min + 2 hours
= 6 hours 30 min
2. (a) 84 × 9 = 84 × (10 – 1) = 84 × 10 – 84 × 1 = 840 – 84 = 756
(b) 84 × 99 = 84 × (100 – 1) = 84 × 100 – 84 × 1 = 8400 – 84 = 8316
(c) 84 × 999 = 84 × (1000 – 1) = 84 × 1000 – 84 × 1 = 84000 – 84 = 83916
(d) 84 × 9999 = 84 × (10000 – 1) = 84 x 10000 – 84 × 1 = 840000 – 84 = 839916
3.
4. Ramesh buys 10 containers from one shop Cost of 1 container = ₹150
He buys 18 containers of the same capacity from another shop.
Cost of 1 container = ₹150
∴ Total money spent by Ramesh
= ₹ [10 × 150 + 18 × 150]
= ₹150 × (10 + 18)
= ₹150 × 28
= ₹4200
5. Number of large buildings = 25
Number of floors = 15
Number of apartments on each floor = 4
∴ Total number of apartments in large buildings = 25 × 15 × 4
Number of small building = 40
Number of floors = 9
Number of apartments on each floor = 3
∴ Total number of apartments in small buildings = 40 × 9 × 3
Hence, the number of apartments in all = 25 × 15 × 4 + 40 × 9 × 3 = 1500 + 1080 = 2580.
6. Number of chairs = 85
Cost of one chair = ₹ 180
Cost of 85 chairs = ₹ (85 × 180)
Number of tables = 25
Cost of one table = ₹ 140
Cost of 25 tables = ₹ (25 × 140)
Total cost of all chairs and tables = ₹(85 × 180 + 25 × 140)
= ₹ (15300 + 3500) = ₹ 18800
Money given in advance = ₹ 2500
∴ Balance money to be paid to the dealer = ₹ 18800 –₹ 2500 = ₹ 16300
Assertion Reason Answers:
(1) (a) Both A and R are true and R is the correct explanation of A
(2) (a) Both A and R are true and R is the correct explanation of A