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**Joy of Mathematics Class 6 Solutions Chapter 2 Number System**

Welcome to NCTB Solution. Here with this post we are going to help 6th class students for the Solutions of Joy of Mathematics Class 6 Book, Chapter 2 Number System. Here students can easily find step by step solutions of all the problems for Number System. Exercise wise proper solutions for every problems. All the problem are solved with easily understandable methods so that all the students can understand easily. Students will get chapter 2 solutions. Here students will find exercise wise solutions for chapter 2 Exercise 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7 and 2.9

**Number System Exercise 2.1 Solution : **

**Question no – (1) **

**Solution :**

**(a)** 56,004 = Fifty six thousand four.

Fifty six thousand four.

**(b)** 8,05,065 = Eight lakh five thousand sixty five.

Eight hundred five thousand sixty five.

**(c)** 56,23,008 = Fifty six lakh twenty three thousand eight.

Five million six hundred twenty three thousand eight.

**(d)** 5,60,002 = Five lakh sixty thousand two.

Five hundred sixty thousand two.

**(e)** 32,10,10,010 = Thirty two crore ten lakh ten thousand ten.

Three hundred twenty one million ten thousand ten.

**Question no – (2) **

**Solution :**

**(a)** 70000000 + 6000000 + 300000 + 400 + 80 + 9

= 76030489.

**∴** Seven crore sixty lakh thirty thousand four hundred eighty nine.

**(b)** 6,4005,061 = Six crore forty lakh five thousand sixty one.

**(c)** 90,07,06052 = Ninety crore seven lakh six thousand fifty two.

**(d)** 20,40,08,999 = Twenty crore forty lakh eight thousand nine hundred ninety nine.

**Question no – (3) **

**Solution :**

**(a)** 1,00202,550

**(b)** 1,005,010,005

**Question no – (4)**

**Solution :**

Required numbers are, 306, 603, 360, 630.

**Question no – (5)**

**Solution :**

Numbers are, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494.

**Question no – (6)**

**Solution :**

1^{st} term = 105

Difference = 5

**∴** It occurs 40 times.

**Question no – (7)**

**Solution :**

The required numbers are,

666, 665, 660, 600, 650, 605, 606, 656, 555, 556, 550, 566, 500, 560, 506, 505, 565

**Question no – (8)**

**Solution :**

The required numbers are,

111, 113, 115, 155, 133, 153, 151, 135, 131, 333, 335, 331, 355, 311, 351, 315, 353, 313, 555, 551, 553, 511, 513, 533, 531, 535.

**Question no – (9)**

**Solution :**

Largest number is = 95432

Smallest number is = 23459

**Question no – (10)**

**Solution :**

Smallest = 203579

Largest = 975320

**Question no – (11)**

**Solution :**

**(a)** Place value of 4 is 4000000

**(b)** Place value of 4 is 40000000

**(c)** Place value 0f 4 is 400

**(d)** Place value of 4 is 400000000

**Question no – (12) **

**Solution :**

**(a)** Sum = (200000 + 2) = 200002

**(b)** Sum = (20000 + 2) = 20002

**(c)** Sum = (20000 + 2) = 20002

**(d)** Sum = (2000 + 2) = 2002

**Question no – 13**

**Solution :**

Product = (600000 × 600)

= 360000000

**Question no – 14**

**Solution :**

Largest number is = 98765432

Smallest number is = 10234567

**Number System Exercise 2.2 Solution : **

**Question no – (1)**

**Solution :**

**(a)** Successor is (2000569 + 1)

= 2000570

**(b)** Successor is = (5648392 + 1)

= 5648393

**(c)** Successor is = (743659520 + 1)

= 743659521

**(d)** Successor is = (569354525 + 1)

= 569354526

**Question no – (2)**

**Solution :**

**(a)** Predecessor is = (9000009 – 1)

= 9000008

**(b)** Predecessor is = (593946539 – 1)

= 593946538

**(c)** Predecessor is = (727272727 – 1)

= 727272726

**(d)** Predecessor is = (305645321 – 1)

= 305645320

**Question no – (3)**

**Solution :**

**(a)** All natural numbers between 100 and 120 are,

101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119.

**(b)** Between 10 and 15 numbers are 11, 12, 13, 14.

**(c)** Between 405 and 409 are 406, 407, 408.

**(d)** Numbers are 501, 502, ….., 600

**Question no – (4)**

**Solution :**

**(a)** Three consecutive numbers are 199, 200, 201.

**(b)** Consecutive numbers are 347, 346, 345, 344.

**Question no – (5)**

**Solution :**

= (632 – 621) = (12 × 100) Rs.

= 1200 Rs.

**Question no – (6)**

**Solution :**

**(a)** 12562 < 13265

**(b)** 312643 > 126656

**(c)** 734999 > 87100

**(d)** 129999 < 210000

**Question no – (7)**

**Solution :**

In descending order, 8, 7, 5, 4, 0.

**Question no – (8)**

**Solution :**

In Ascending order,

6397, 53800, 112535, 361745, 699451

**Question no – (9)**

**Solution :**

**(a)** The numbers are total is 9.

(40 – 30) – 1

= 10 – 1

= 9

**(b)** Numbers are = 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40

Total = 11

**Question no – (10) **

**Solution :**

**(a)** Given statement is – **True**

**(b)** Given statement is – **False**

**(c)** Given statement is – **True**

**(d)** Given statement is – **False**

**(e)** Given statement is – **True**

**Number System Exercise 2.3 Solution : **

**Question no – (1) **

**Solution :**

**(a)** 45 + 37 = 37 + 45

**(b)** 6 + 0 = 0 + 6 = 6

**(c)** 55 + 25 = 25 + 55

**(d)** (1 + 2) + 7 = 1 + (2 + 7)

**(e)** (31 + 36) + 13 = 31 + (36 + 13)

**(f)** (9 + 10) + 11 = 9 + (10 + 11)

**Question no – (2) **

**Solution :**

**(a) 425 + 375**

= 800

And, 375 + 425

= 800

**∴** Both are equal.

**(b) 111 + 333**

= 444

and, 333 + 111

= 444

**(c) 99 + 101**

= 200

and, 101 + 99

= 200

**(d) 73 + 137**

= 210

and, 137 + 73

= 210

**(e) 25 + 27**

= 52

and,27 + 25

= 52

**(f) 69 + 131**

= 200

and, 131 + 69

= 200

**Question no – (3)**

**Solution :**

**(a) 38, 347, 62**

= 347 + (62 + 38)

= 347 + 100

= 447

**(b) 75 + (107.9 + 121)**

= (75 + 1200)

= 1275

**(c) (129 + 421) + (37 + 113)**

= 550 + 150

= 700

**(d) (17 + 23) + (227 + 413)**

= 100 + 640

= 740

**Question no – (4)**

**Solution :**

**(a) 45 + 37 = x + 45**

=> x = 37

**(b) x + 35 = 35 + 49**

=> x = 49

**(c) 37 + 0 = 45 + x = 45**

=> x = 45 – 45

= 0

**(d) (41 + 19) + 140 = x + (19 + 140)**

=> 60 + 140 = x + 159

=> x = 200 – 159

= 41

**Question no – (5)**

**Solution :**

**(a)** Commutative property

**(b)** Commutative property

**(c)** Additive Identity

**(d)** Associative property

**(e)** Commutative property

**(f)** Associative property.

**Question no – (6) **

**Solution :**

**(a)** Given statement is – **False**

**(b)** Given statement is – **True**

**(c)** Given statement is – **False**

**(d)** Given statement is – **True**

**(e)** Given statement is – **False**

**(f)** Given statement is – **False**

**Number System Exercise 2.4 Solution : **

**Question no – (1) **

**Solution :**

**(a) **341

– 255

———————–

86

**(b) **5764

– 3223

———————–

2541

**(c) **7896

– 3959

———————–

3937

**(d) **719

– 162

———————–

557

**(e)** 8432

– 4558

———————–

3874

**Question no – (2)**

**Solution :**

Difference = (100000 – 99999)

= 1

**Question no – (3)**

**Solution :**

Difference = (1000000 – 99999)

= 900001

**Question no – (4)**

**Solution :**

Money left

= (32500 – 9999) Rs

= 22499 Rs

**Question no – (5)**

**Solution :**

Money left = 2500 – (1000 + 560 + 800)

= 2500 – 2360

= 140

**Question no. – 6**

**Solution :**

Number of females will be,

= (6,83,562 – 4,32169)

= 251393

**Question no – (7)**

**Solution :**

= (975689 + 4563 – 8976)

= 971276

**Question no – (8)**

**Solution :**

Watch movie channels

= 6900 – (1200 + 3157)

= 6900 – 4357

= 2543

**Question no – (9)**

**Solution :**

Other number will be,

= (9395 – 1999)

= 7396

**Question no – (10)**

**Solution :**

Number will be,

= (48367 – 1349)

= 47018

**Question no – (11)**

**Solution :**

No. is = (45967 – 29461)

= 16506

**Question no – (12) **

**Solution :**

**(a)** The statement is – **False**

**(b)** The statement is – **True**

**(c)** The statement is – **True**

**(d)** The statement is – **False**

**(e)** The statement is – **False**

**(f)** The statement is – **True**

**Number System Exercise 2.5 Solution : **

**Question no – (1)**

**Solution :**

**(a) 49 by 1003**

= (50 – 1) × 1003

= (1003 × 50) – (1003 × 1)

= 50150 – 1003

= 49147

**(b) 49 × 998**

= 49 × (1000 – 2)

= (49 × 1000) – (49 × 2)

= 49000 – 98

= 48902

**(c) 87 by 101**

= 87 × (100 + 1)

= (87 × 100) + (87 × 1)

= 8700 + 87

= 8787

**(d) 87 × 99**

= 87 × (100 – 1)

= (87 × 100) – (87 × 1)

= 8700 – 87

= 8613

**Question no – (2)**

**Solution :**

**(a) (4 × 357 × 25)**

= (4 × 25) × 357

= 100 × 357

= 35700

**(b) (8 × 1635 × 125)**

= (8 × 125) × 1635

= 1000 × 1635

= 1635000

**(c) 625 × 312 × 80**

= (625 × 80) × 312

= 50,000 × 312

= 15600000

**(d) 25 × 6 × 5 × 8**

= (25 × 8) × (6 × 5)

= 200 × 30

= 6000

**Question no – (3) **

**Solution :**

**(a) 273 × 8 + 2 × 273**

= 273 (8 + 2)

= 273 × 10

= 2730

**(b) 112 × 97 + 3 × 112**

= 112 (97 + 3)

= 112 × 100

= 11200

**(c) 9876 × 6789 – 9876 × 5789**

= 9876 (6789 – 5789)

= 9876 × 1000

= 9876000

**(d) 4897 × 999 + 4897**

= 4897 (999 + 1)

= 4897 × 1000

= 4897000

**Question no – (4)**

**Solution :**

**(a)** (9999 × 100)

= 999900

**(b) (9999 × 999)**

= 9999 × (1000 – 1)

= (9999 × 1000) – (9999 × 1)

= 9999000 – 9999

= 9989001

**Question no – (5)**

**Solution :**

**(a)** 4355 × 365 = 365 × 4355

**(b)** 10 × 100 × 100 = 100000

**(c)** 49 × 63 + 63 × 51 = 63 × (49 + 51)

**(d)** 835 × 98 + 2 × 835 = 835 × (98 + 2)

**(e)** 891 × 99 + 891 = 891 (99 + 1)

**(f)** 222 + 333 + 444 = 111 × (2 + 3 + 4)

**(g)** 4 × 8444 = 16 × (200 + 111)

**(h)** 45 × 500 × 301 × 0 = 0

**Question no – (6)**

**Solution :**

Total cost = (32615 × 99) Rs/-

= 32615 × (100 – 1) Rs

= 32615 × 100 – 32615

= 3261500 – 32615

= 3228885 Rs/-

**Question no – (7)**

**Solution :**

Total Amount = 197 × 125

= (200 – 3) × 125

= (125 × 200) – (125 × 3)

= 25000 – 375

= 24625 Rs

**Question no – (8)**

**Solution :**

Total Amount paid,

= (20 × 18 + 20 × 17) Rs

= (360 + 340)

= 700 Rs

**Question no – (9)**

**Solution :**

Product of two whole no is zero. Because one of the no is zero so,

a × 0 = 0 always.

**Question no – (10)**

**Solution :**

The no.’s are (1 × 1) = 1

**Number System Exercise 2.6 Solution : **

**Question no – (1) **

**Solution :**

**(a) 2436 ÷ 7**

**∴ **Now, (7 × 348)

= 2436

**(b) 97629 ÷ 23 **

Now, (23 × 423)

= 9729

**(c) 52029 ÷ 123**

**∴** (423 × 123)

= 520

**(d) 40180 ÷ 164 **

Now, (245 × 164)

= 40180

**(e) 34750 ÷ 139 **

Now, (139 × 250)

= 34750

**(f) 7303 ÷ 109 **

Now, (109 × 69)

= 7303

**Question no – (2)**

**Solution :**

No, it is not true for any distinct whole numbers.

**Question no – (3)**

**Solution :**

**(a) 425 ÷ 1**

= 425

**(b) 0 ÷ 425**

= 0

**(c) 315 + 850 ÷ 85**

= 315 + 10

= 325

**(d) 601 – 600 ÷ 600**

= 601 – 1

= 600

**(e) 312 ÷ 312 – 213 ÷ 213**

= 1 – 1

= 0

**(f) 1200 – 200 × (150 ÷ 75)**

= 1200 – 200 × 2

= 1200 – 400

= 800

**Question no – [4]**

**Solution :**

Students in each row,

= (1680 ÷ 35)

= 48 students

**Question no – [5]**

**Solution :**

Bags required,

= (840 ÷ 20)

= 42 bags.

**Question no – (6)**

**Solution :**

**∴** The required number is 20

(1000 – 20)

= 980

**Question no – (7)**

**Solution :**

Now, (35 – 20) = 15

**∴** The required number is 15.

**Question no – (8)**

**Solution :**

Now, (75 – 25) = 50

**∴** The least number is

= (10000 + 50)

= 10050

**Question no – (9)**

**Solution :**

**∴** Required Number will be,

= (99999 – 25)

= 99975

**Question no – (10)**

**Solution :**

Divided = 35 × 30 + 12

= 1050 + 12

= 1062

**∴** Number is 1062

**Question no – (11)**

**Solution :**

Senior citizens = 975176 ÷ 15

= 65011.73

= 65011

**Question no – (12)**

**Solution :**

**(a)** This statement is – **False**

**(b)** This statement is – **False**

**(c)** This statement is – **False**

**(d)** This statement is – **True**

**(e)** This statement is – **False**

**(f)** This statement is – **True**

**(g)** This statement is – **False**

**Number System Exercise 2.7 Solution : **

**Question no – (1)**

**Solution :**

Total friends = 20

Items price = 50 Rs (Let)

**∴** Total expenditure,

= (50 × 20) Rs

= 1000 Rs

**Question no – (2)**

**Solution :**

**(a) 4990 + 605**

= 5000 + 600

= 5600

**(b) 9945 – 390**

= 9950 – 400

= 9550

**(c) 449 × 29**

= 450 × 30

= 13500

**Question no – (3) **

**Solution :**

Total population = 5000

Daily, wheat = 300gm × 7 = 2100gm

Rice = 100g × 7 = 700gm

Sugar = 50g × 7 = 350gm

Pulses = 50g × 7 = 350gm

**∴ Wheat total**

= (2.1 × 5000)

= 10500kg

= 105 quintal

**Rice total, **

= (0.7 × 5000)

= 3500

= 35 quintal

**Sugar,**

= (0.350 × 5000)

= 17500

= 18 quintal

**Pulses,**

= 18 quintal

**Number System Exercise 2.8 Solution : **

**Question no – (1) **

**Solution :**

The next two terms are

= 123456 × 8 + 6

= 987654

and, 1234567 × 8 + 7

= 9876543

**Question no – (2)**

**Solution :**

The next two terms are,

1 + 3 + 5 + 7 + 9 + 11

= 36

= 6 × 6

1 + 3 + 5 + 7 + 9 + 11 + 13

= 49

= 7 × 7

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15

= 64

= 8 × 8

**Next Chapter Solution : **

👉 Chapter 3 👈

above chapter 2 good ans