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Exercise-2.1

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1. Write the next three natural numbers after 10999.

Solution:

The next three natural number after 10999 are:

10999+1, 10999+2, 10999+3

i.e. 11000, 11001, 11002

2. Write the three whole numbers occurring just before 10001.

Solution:

The next three natural number after 10999 are:

 10999+1, 10999+2, 10999+3

 i.e. 11000, 11001, 11002

3. Which is the smallest whole number?

Solution: 0 is the smallest whole number.

4. How many whole numbers are there between 32 and 53?

Solution:

there are (53 - 32) - 1 = 21 - 1 = 20

whole numbers between 32 and 53 are 20.

5. Write the successor of :

(a) 2440701 (b) 100199 (c) 1099999 (d) 2345670

(a) 2440701

Solution: 2440701 + 1 = 2440702

(b) 100199

Solution: 100199 + 1 = 100200

(C) 1099999

Solution: 1099999 + 1 = 1100000

(d) 2345670

Solution: 2345670 + 1 = 2345671

6. Write the predecessor of :

(a) 94 (b) 10000 (c) 208090 (d) 7654321

(a) 94

Solution: 94 - 1= 93

(b) 10000

Solution: 10000 – 1= 9999

(c) 208090

Solution: 208090 – 1= 208089

(d) 7654321

Solution: 7654321 – 1= 7654320

7. In each of the following pairs of numbers, state which whole number is on the left of the other number on the number line. Also write them with the appropriate sign (>, <) between them.
(a) 530, 503

(b) 370, 307

(c) 98765, 56789

(d) 9830415, 10023001

(a) 530, 503

Solution: Here, 503 lies on the left of the 530 on number line

Therefore, 530 > 503 or 503<530

(b) 370,307

Solution: Here, 307 lies on the left of the 370 on number line

Therefore, 307<370 or 370>307

(c) 98765, 56789

Solution: Here, 56789 lies on the left of the 98765 on number line

Therefore, 56789 < 98765 or98765 > 56789

(d) 9830415, 10023001

Solution: Here, Here, 10023001 lie on the left of the 9830415on number line

Therefore, 9830415<0023001 or 9830415>10023001

8. Which of the following statements are true (T) and which are false (F) ?
(a) Zero is the smallest natural number.

(b) 400 is the predecessor of 399.

(c) Zero is the smallest whole number.

(d) 600 is the successor of 599.

(e) All natural numbers are whole numbers.

(f ) All whole numbers are natural numbers.

(g) The predecessor of a two digit number is never a single digit number.

(h) 1 is the smallest whole number.

(i) The natural number 1 has no predecessor.

(j) The whole number 1 has no predecessor.

(k) The whole number 13 lies between 11 and 12.

(l) The whole number 0 has no predecessor.

(m) The successor of a two digit number is always a two digit number. 

Answer :

(a) Fallse 

(b) False

(c) True

(d) True

(e) True

(f) False

(g) False

(h) False

(i) True

(j) False

(k) False

(l) True

(m) False 

 

Exercise-2.2

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Q1. Find the sum by suitable rearrangement:

(a) 837 + 208 + 363

Solution: 837 + 208 + 363 

= (837 + 208) + 363

= 1045 + 363

= 1408

Or Second Method 

= 837 + 363 + 208

= (837 + 363) + 208

= 1200 + 208

= 1408

(b) 1962 + 453 + 1538 + 647

Solution:  1962 + 453 + 1538 + 6477

= (1962 + 453) + (1538 + 647)

= 2415 + 2185

= 4600

Or Second Method 

= 1962 + 453 + 1538 + 6477

= (1538 + 1962) + (453 + 647)

= 3500 + 1100

= 4600

Q2. 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

Solution: 

(a) 2 x 1768 x 50                           

Solution:

2 x 50 x 1768

= (2 x 50) x 1768

= 100 x 1768

= 176800

(b) 4 x 166 x 25

Solution: 

4 x 25 x 166

= (4 x 25) x 166

= 100 x 166

= 16600

(c) 8 x 291 x 125

Solution:

8 x 125 x 291

= 1000 x 291`

= 291000

(d) 125 x 40 x 8 x 25

Solution:

125 x 8 x 40 x 25

= (125 x 8) x (40 x 25)

= 1000 x 1000

= 1000000

(e) 285 × 5 × 60

Solution:

  285 × 5 × 60

= 285 × (5 × 60)

= 285 × 300

= 85500

(f) 125 × 40 × 8 × 25

Solution: 

  125 × 40 × 8 × 25

= (125 × 8) × (40 × 25)

= 1000 × 1000

= 1000000 

Q3. Find the value of the following:

(a) 297 × 17 + 297 × 3

Solution:

  297 x (17 + 3)

= 297 x 20

= 5940

(b) 54279 × 92 + 8 × 54279

Solution:

  54279 x (92 + 8)
= 54279 x 100

= 5427900

(c) 81265 × 169 – 81265 × 69

Solution: 

  81265 × 169 – 81265 × 69

= 81265 (169 – 69)

= 81265 (100)

= 8126500

(d) 3845 × 5 × 782 + 769 × 25 × 218

Solution: 

  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

Q4. Find the product using suitable properties.

(a) 738 × 103

(b) 854 × 102

(c) 258 × 1008

(d) 1005 × 168

Solution: 

(a) 738 × 103

= 738 (100 + 3) 

= 738 × 100 + 738 × 3

= 73800 + 2214

= 76014

Solution: 

(b) 854 × 102

= 854(100 + 2) 

= 854 × 100 + 854 × 2

= 85400 + 1708

=  87108  

Solution:  

(c) 258 × 1008

= 258(1000 + 8) 

= 258 × 1000 + 258 × 8 

= 258000 + 2064

= 260064

Solution:

(d) 1005 × 168

= (1000 + 5) x 168

= 1000 x 168 + 5 x 168

= 168000 + 840

= 168840

5. A taxidriver 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?

Solution:  Taxi driver filled his car petrol tank on Monday = 40 L

 He filled the petrol tank on Tuesday = 50 L

 The petrol costs per liter = 44 Rs

 He spend in all on petrol = (40 + 50) x 44

                           = 90 x 44

                           = 3960 Rs

6. 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 Rs 15 per liter, how much money is due to the vendor per day?

Solution:  A vendor supplies milk to a hotel in the morning = 32 liters

=> A vendor supplies milk to a hotel in the evening = 68 liters

=> The cost of milk per liter = Rs 15

7. Match the following:

Solution: 

(i) ----------- (c) 

(ii) ---------- (a) 

(iii) ---------- (b) 

 

Exercise-2.3

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Q1. Which of the following will not represent zero:
(a) 1 + 0 (b) 0 × 0 (c) ⁰/₂     (d) ^{10 -10}/₂ 

Solution:

(a) 1 + 0  = 1

So, it is not represent zero

(b) 0 × 0 = 0

it is represent zero

(c)  0/2 = 0

it is represent zero

Q2. If the product of two whole numbers is zero, can we say that one or both of them will be zero? Justify through examples.

Solution: 

Yes, we know that the product of any whole numbers with zero is always zero.

Q3. If the product of two whole numbers is 1, can we say that one or both of them will be 1? Justify through examples.

Solution: 

If only one number be 1 then the product cannot be 1.

Examples:

Here we see that one of two is 1 then product will be always second number. 

If both numbers are 1, then the product is 1

Q4. Find using distributive property :
(a) 728 × 101    (b) 5437 × 1001    (c) 824 × 25    (d) 4275 × 125 (e) 504 × 35

Solution: 

(a) 728 × 101

= 728(100 + 1) 

= 728 × 100 + 728 × 1

= 72800 + 728 

= 73528

Solution: 

(b) 5437 × 1001

= 5437(1000 + 1) 

= 5437 × 1000 + 5437 × 1 

= 5437000 + 5437 

= 5442437

Solution: 

(c) 824 × 25

= 824(20 + 5) 

= 824 × 20 + 824 × 5

= 16480 + 4120

= 20600

Solution: 

(d) 4275 × 125

= 4275(100 + 20 + 5)

= 4275 × 100 + 4275 × 20 + 4275 × 5

= 427500 + 85500 + 21375

= 534375

Solution: 

(e) 504 × 35 

= (500 + 4) × 35

= 500 × 35 + 4 × 35

= 17500 + 140

= 17640

Q5. Study the pattern :
1 × 8 + 1 = 9       1234 × 8 + 4 = 9876
12 × 8 + 2 = 98     12345 × 8 + 5 = 98765
123 × 8 + 3 = 987
Write the next two steps. Can you say how the pattern works?
(Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).